diff --git "a/89FQT4oBgHgl3EQfIjX8/content/tmp_files/load_file.txt" "b/89FQT4oBgHgl3EQfIjX8/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/89FQT4oBgHgl3EQfIjX8/content/tmp_files/load_file.txt" @@ -0,0 +1,8273 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf,len=8272 +page_content='Dense Nuclear Matter Equation of State from Heavy-Ion Collisions Agnieszka Sorensen Institute for Nuclear Theory, University of Washington, Seattle, WA 98195, USA Kshitij Agarwal Physikalisches Institut, Eberhard Karls Universit¨at T¨ubingen, D-72076 T¨ubingen, Germany Kyle W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Brown Facility for Rare Isotope Beams, Michigan State University, East Lansing, MI 48824, USA and Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA Zbigniew Chajecki Department of Physics, Western Michigan University, Kalamazoo, MI, 49008, USA Pawe�l Danielewicz, William G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Lynch, Scott Pratt, and ManYee Betty Tsang Department of Physics and Astronomy and Facility for Rare Isotope Beams Michigan State University, East Lansing, MI 48824 USA Christian Drischler Department of Physics and Astronomy and Institute of Nuclear and Particle Physics, Ohio University, Athens, OH 45701, USA Stefano Gandolfi and Ingo Tews Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Jeremy W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Holt and Che-Ming Ko Department of Physics and Astronomy and Cyclotron Institute, Texas A&M University, College Station, TX 77843, USA Matthias Kaminski Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA Rohit Kumar Facility for Rare Isotope Beams, Michigan State University, East Lansing, MI 48824, USA Bao-An Li and William Newton Texas A& M University-Commerce, Commerce, TX 75429, USA Alan B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' McIntosh Cyclotron Institute, Texas A&M University, College Station, Texas 77843, USA Oleh Savchuk Facility for Rare Isotope Beams, Michigan State University, East Lansing, MI 48824, USA and Bogolyubov Institute for Theoretical Physics, 03680 Kyiv, Ukraine Maria Stefaniak GSI Helmholtz Centre for Heavy-ion Research, Planckstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 1, 64291 Darmstadt, Germany arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='13253v1 [nucl-th] 30 Jan 2023 2 Ramona Vogt Nuclear and Chemical Sciences Division,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Lawrence Livermore National Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Livermore,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' CA 94551,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' USA and Department of Physics and Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' University of California,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} 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Wolfgang Trautmann GSI Helmholtz Centre for Heavy-ion Research, Planckstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 1, 64291 Darmstadt, Germany Jacquelyn Noronha-Hostler University of Illinois at Urbana-Champaign, Urbana, IL 61801 Christopher Plumberg Natural Science Division, Pepperdine University, Malibu, CA 90263, USA Hans-Rudolf Schmidt Physikalisches Institut, Eberhard Karls Universit¨at T¨ubingen, D-72076 T¨ubingen, Germany and GSI Helmholtz Centre for Heavy-ion Research, Planckstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 1, 64291 Darmstadt, Germany Peter Senger Facility for Antiproton and Ion Research, Planckstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 1, Darmstadt, Germany Richard Seto University of California-Riverside, Riverside, California 92521, USA Chun Shen Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201, USA and RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA Jan Steinheimer Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 1, D-60438 Frankfurt am Main, Germany Joachim Stroth Institut f¨ur Kernphysik, Goethe-Universit¨at, 60438 Frankfurt, Germany and GSI Helmholtz Centre for Heavy-ion Research, Planckstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 64291 Darmstadt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Germany Kai-Jia Sun Institute of Modern Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Fudan University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 200438,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='Shanghai,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='China Giuseppe Verde INFN Sezione di Catania,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 64 Via Santa Sofia,' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' USA (Dated: February 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 2023) 4 Executive Summary The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' motivated by its crucial role in our understanding of the properties of nuclear matter found on Earth,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' in neutron stars,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' and in neutron-star mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Profound questions challenging our understanding of strong interactions remain unanswered: It is still unknown whether the transition between a hadronic gas and a quark-gluon plasma, which at zero baryon density is known to be consistent with a crossover transition predicted by Lattice QCD, becomes of first order in the finite-density region of the QCD phase diagram accessible in terrestrial experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The isospin-dependence of the EOS, crucial to our understanding of both the structure of neutron-rich nuclei and the properties of neutron stars, is poorly known above nuclear saturation density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Moreover, recent observations of very heavy compact stars indicate that the EOS in neutron-rich mat- ter becomes very stiff at densities of the order of a few times saturation density, leading to values of the speed of sound exceeding 1/ √ 3 of the speed of light (breaking the conformal limit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Not only is the mechanism behind this striking behavior not known, but it is also unknown whether a similar stiffening occurs in symmetric or nearly-symmetric nuclear mat- ter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Resolving these and other questions about the properties of dense nuclear matter is possible by taking advantage of the unique opportunities for studying the nuclear matter EOS in heavy-ion collision experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Among controlled terrestrial experiments, collisions of heavy nuclei at interme- diate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and tem- perature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In the next decade, numerous efforts worldwide will be devoted to uncovering the dense nuclear matter EOS through heavy-ion collisions, including studies at FRIB where the isospin-dependence of the EOS can be probed in energetic collisions of rare isotopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Modern detectors and refined analysis techniques will yield measurements that will elucidate the dependence of the EOS on density, temperature, and isospin asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Hadronic transport simulations are currently the only means of interpreting observables measured in heavy-ion collision experiments at intermediate beam energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This means that capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB, depends on the continued development of state-of-the-art hadronic transport simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Support for the hadronic transport community, and in particular for viable career pathways for early career researchers, is imperative to maintain the health of and diversify the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' hadronic transport community, and to fully realize the potential of U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' efforts leading the exploration of the dense nuclear matter EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 5 CONTENTS I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Introduction 7 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Constraining the nuclear matter EOS using heavy-ion collisions 8 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Connections to fundamental questions in nuclear physics 9 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Upcoming opportunities 11 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Needs 12 II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The equation of state from 0 to 5n0 13 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Transport model simulations of heavy-ion collisions 13 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Transport theory 14 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Selected constraints on the EOS obtained from heavy-ion collisions 17 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Challenges and opportunities 19 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Microscopic calculations of the EOS 25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Status 25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Challenges and opportunities 27 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Neutron star theory 28 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Status 28 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Challenges and opportunities 31 III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Heavy-ion collision experiments 33 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Experiments to extract the EOS of symmetric nuclear matter 35 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Measurements sensitive to the EOS 35 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Experiments probing densities between 1–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5n0 36 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Experiments probing densities above 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5n0 38 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Challenges and opportunities 39 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Experiments to extract the symmetry energy 42 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Experiments that probe low densities 42 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Measurements to extract symmetry energy up to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5n0 42 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Selected constraints on the symmetry energy around 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5n0 44 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Challenges and opportunities 46 IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The equation of state from combined constraints 50 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Constraints 51 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' EOS obtained by combining various constraint sets 53 V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Connections to other areas of nuclear physics 54 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Applications of hadronic transport 54 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Detector design 55 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Space exploration, radiation therapy, and nuclear data 55 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Hydrodynamics 57 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Status 57 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Range of applicability 58 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Challenges and opportunities 60 VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Exploratory directions 60 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Dense nuclear matter EOS meeting extreme gravity and dark matter in supermassive neutron stars 60 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Nuclear EOS with reduced spatial dimensions 61 6 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Interplay between nucleonic and partonic degrees of freedom: SRC effects on nuclear EOS, heavy-ion reactions, and neutron stars 62 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' High-density symmetry energy above 2n0 63 E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Density-dependence of neutron-proton effective mass splitting in neutron-rich matter 66 Acknowledgments 68 References 68 7 I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' INTRODUCTION The equation of state (EOS) is a fundamental property of nuclear matter, describing its emergent macroscopic properties originating from the underlying strong interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Around the saturation density of nuclear matter, the EOS controls the structure of nuclei through the binding energy and the incompressibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The EOS also determines, among other things, the neutron-skin thickness in neutron-rich nuclei as well as the properties of nuclear matter at extreme densities and/or tem- peratures, corresponding to conditions produced in experiments colliding heavy nuclei or observed in neutron stars and neutron star mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Far beyond describing the properties of matter com- posed of only protons and neutrons, the EOS can also reflect the appearance of new degrees of freedom, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', strange particles in the cores of neutron stars or quarks and gluons in ultrarelativistic heavy-ion collisions, or the emergence of new states of matter, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', chirally-restored matter, meson condensates, or quarkyonic matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In heavy-ion collision experiments, the EOS is studied by detecting particles emerging from the collision zone and measuring observables sensitive to the properties of nuclear matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Crucially, any interpretation of these observables, including quantitative constraints on the EOS, requires comparisons of experimentally measured observables to results obtained in dynamic simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This white paper highlights the essential role of hadronic transport simulations of heavy-ion collisions in advancing our understanding of the EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' It also elucidates the many connections between inferences of the EOS from heavy-ion collision data and other efforts aiming to describe and understand the properties of nuclear matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Schematic depiction of the ranges of density and temperature probed in experiments and astronom- ical observations sensitive to the EOS of nuclear matter (counterclockwise from bottom left): neutron star crust physics, including nuclear pasta structures;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' properties of nuclei;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' structure of neutron stars;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' dynamics of neutron star mergers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' and outcomes of heavy-ion collisions which can probe both symmetric and asymmetric matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Figures adapted from [1–5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 100 HIC (sym) temperature [MeV] 10 HIC (asym) S ROOKHAVEN NS mergers .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='NS crust nuclear properties 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1 Z neutron stars (NS) 0 1 2 3 4 5 density np/no8 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Constraining the nuclear matter EOS using heavy-ion collisions FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Constraints on the zeroth (Sv) and first (L) coefficient of the symmetry energy ex- pansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Experimental constraints are derived from heavy-ion collisions (HIC) [6], neutron-skin thicknesses of Sn isotopes [7], giant dipole res- onances (GDR) [8], the dipole polarizability of 208Pb [9, 10], nuclear masses [11], and isovector skins (IAS+∆R) [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Also shown are constraints from χEFT (GP-B) [13], microscopic neutron- matter calculations (H, G) [14, 15], and from the unitary gas limit (UG) [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Figure from [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The last decade has brought tremendous progress in extracting the EOS as a function of baryon den- sity nB, temperature T, and the isospin asymme- try δ (or, equivalently, the proton fraction) from a variety of experimental and astronomical data as well as theoretical calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Many-body theory, based on sophisticated approaches with input from nucleon scattering or nuclear structure data, can now state the EOS below and near the saturation density n0 with meaningful uncertainties (see Sec- tion II B, “Microscopic calculations of the EOS”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' New classes of experiments have extracted the thick- ness of neutron skins in nuclei, shedding light on the isospin-dependence of the EOS (or, equivalently, the symmetry energy) near or below n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' High-energy heavy-ion collisions have constrained the EOS of the quark-gluon plasma at high temperatures and small baryon densities, while ongoing experimental efforts worldwide focus on the EOS of nearly-symmetric dense baryonic matter, probed in collisions at in- termediate energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Meanwhile, collisions at lower energies have led to experimental constraints on the symmetry energy at sub- and suprasaturation den- sities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Most remarkably, a revolution in the qual- ity and breadth of astronomical observations, high- lighted by the first simultaneous detection of grav- itational waves and electromagnetic signals from a neutron-star merger, ushered in a new era of multi- messenger astronomy (see Section II C, “Neutron star theory”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Together with the newly available ex- perimental capabilities at the Facility for Rare Iso- tope Beams (FRIB), there are unprecedented oppor- tunities to probe the isospin-dependence of the EOS through astronomical and terrestrial measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Among the experimental efforts discussed above, heavy-ion collisions probe the widest range of baryon densities and, moreover, represent the only means to address the EOS away from n0 in controlled terrestrial experiments, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Indeed, heavy-ion reactions at beam energies from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame probe the EOS of hadronic matter at baryon densities from a few tenths to about 5 times n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Controlling the properties of matter produced in these experiments is possible by varying the beam energy, collision geometry, and isotopic composition of the target and projectile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Insights and constraints obtained from transport model analyses of these experiments are relevant both for our understanding of nuclear matter as found on Earth and for our understanding of neutron stars from crust to core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Within ongoing efforts,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' the STAR experiment’s Beam Energy Scan (BES) fixed-target (FXT) program at the Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Laboratory (BNL),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' which collided gold nuclei at intermediate beam energies and which completed data taking in 2022,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' leads the US effort to constrain the EOS of nearly-symmetric nuclear matter at high 100 Constraints on S-L HIC 80 △R X AS 60 GP-B G 40 H Masses pb 20 Skin UG Analytic UG GDR 0 26 28 30 32 34 Symmetry Energy S [MeV9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 Prior Astro + HIC Pressure P (MeV fm–3) 100 101 102 Number density n (nsat) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Pressure in neutron star matter as a function of density from a Bayesian analysis combining nuclear theory and data from multi- messenger neutron-star observations and heavy- ion collisions [17]: the dark blue and light blue region corresponds to the 68% and 95% credible interval, respectively, while the gray dashed line shows the 95% bound obtained in χEFT calcu- lations and used as a prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Figure from [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' baryon densities up to around 5n0, corresponding to densities present in the deep interiors of neu- tron stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Among comparable efforts in Europe, the HADES experiment at GSI, Germany, probes matter at densities up to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Preliminary results from these contemporary efforts, as well as measure- ments from other heavy-ion collision experiments in the past, have led to competitive constraints on the EOS of symmetric nuclear matter, with future measurements expected to shed more light on its high-density behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Detailed constraints on the isospin-dependence of the EOS can be obtained by varying the isospin content of the target and pro- jectile nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Here, the ability to use radioactive isotopes, as in, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', intermediate-energy heavy-ion collision experiments at RIKEN and FRIB, is cru- cial to resolve the subtle effects arising from changes in the isospin asymmetry of the colliding systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Above all, obtaining constraints on the EOS from heavy-ion measurements would not have been possible if not for advances in theory, and in particular for the collaborative effort to test the robustness and quantify the uncertainties of hadronic transport sim- ulations (see Section II A, “Transport model simulations of heavy-ion collisions”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' At the same time, much remains to be learned, as tight constraints on both the symmetric and asymmetric EOS at higher densities have so far remained elusive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This is predominantly due to model uncer- tainties, which themselves are rooted in the inherent complexity of nucleus-nucleus collisions and the challenging task of describing all processes contributing to the final state observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Connections to fundamental questions in nuclear physics The wealth of data from efforts conducted in recent years not only helps to get a better grasp on the nuclear matter EOS, but also has brought forward fascinating questions challenging our understanding of strong interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Following the successful BES-I campaign at RHIC, questions remain about the structure of the QCD phase diagram at finite baryon densities, where the sign problem prevents obtaining predic- tions with lattice QCD calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Surprisingly, the expected disappearance of the quark-gluon plasma signatures has not been observed in BES-I, with some observables suggesting that the QCD first-order phase transition may be located within the region probed by BES-II experiments, including the region probed by the currently analyzed BES FXT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' If this is the case, then constraining the EOS at lower densities and describing the approach to the transition from the hadronic side, which would manifest as a softening of the EOS, will be crucial for a robust inter- pretation BES-II measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Importantly, due to the largely out-of-equilibrium evolution of collision systems probing that region of the QCD phase diagram, hadronic transport simulations will play a dominant role in describing the dynamics of the collisions, and therefore in constraining the EOS of nearly-symmetric dense nuclear matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Understanding the physics of neutron-rich matter across a range of densities is necessary not only to explain the properties of rare neutron-rich isotopes and the structure of neutron stars, but also to constrain microscopic interactions in isospin-asymmetric nuclear matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' At low densities, this 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1 − 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content="6 '=0 y'y d / 1 v d (AuAu) Protons (10-30%) HADES =0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='25-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='45) 0 (AuAu) Protons (b FOPI (AuAu) Z=1 (b=2-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5fm) FOPI (AuAu) Z=1 Plastic Ball (AuAu) Z=1 (b=2-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5fm) INDRA (AuAu) Protons (12-25%) E895 (AuAu) Protons E877 � (AuAu) h E877 (AuAu) Protons (10-40%) Star FXT (AuAu) Protons (10-25%) Star FXT (AuAu) Protons (10-40%) Star BES (PbPb) Protons (12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5-33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5%) NA49 (PbPb) Protons (15-35%) NA61/SHINE 1 − 10 1 10 2 10 (GeV) N 2m NN s 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='05 − 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1 2 v out-of-plane in-plane (AuAu) Protons (10-30%) HADES (AuAu) Protons (15-29%) FOPI (AuAu) Z=1 (20-30%) FOPI (AuAu) Z=1 (b=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5fm) INDRA (AuAu) Protons EOS (AuAu) Protons (12-25%) E895 (AuAu) Protons E877 � (AuAu) h E877 (AuAu) Protons (10-40%) Star FXT (AuAu) Protons (0-30%) Star FXT (AuAu) Protons (10-40%) Star BES (10-20%) � (AuAu) h Star BES (0-60%) � (AuAu) h Star (0-60%) � (AuAu) h PHOBOS (PbPb) Protons (12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5-33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5%) NA49 (10-30%) � (PbPb) h WA98 � (PbAu) h CERES FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Compilation of the world data on the slope of the directed flow at mid-rapidity (dv1/dy|y′=0, top) and the elliptic flow (v2, bottom) as functions of the reduced center-of-mass energy √sNN − 2mN for protons, Z = 1 nuclei, and inclusive charged particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Figure from [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' challenge is addressed by experimental and theoretical analyses of nuclear structure ob- servables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' An important objective of nuclear many-body theorists is to accurately calcu- late these observables and reliably deduce the EOS using microscopic interactions de- rived within the framework of chiral effective field theory (χEFT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Probing the symmetry energy over a range of densities wider than found in nuclei is possible through heavy-ion collisions and neutron star studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Often, knowledge of the isospin-asymmetric EOS is encoded in terms of constraints on the Tay- lor expansion coefficients of the symmetry energy around n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Numerous analyses yield consistent constraints on the first few expan- sion coefficients (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 2), although they rely on an assumption that the expan- sion remains accurate away from n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The re- cent advent of Bayesian inference techniques allows one to pursue a different approach, within which the isospin-asymmetric EOS is described in terms of the dependence of the pressure on baryon density (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Moreover, Bayesian analyses can shed more light on densities at which measurements constrain the symmetry energy and quan- tify the uncertainties of the extracted EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' As a result, combining diverse measurements and using advanced analysis techniques can lead to significantly tighter constraints, es- pecially on the high-density behavior of the symmetry energy (or, equivalently, on the higher-order symmetry energy expansion co- efficients), which is so far poorly known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Constraints on the EOS of neutron-rich matter at high densities have been dramat- ically affected by discoveries of heavy neutron stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Combined with the properties of all known compact stars, these observations indicate that while the EOS of neutron-rich matter is relatively soft around (1–2)n0, the pressure steeply rises with density for nB >∼ 2n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In fact, multiple analyses show that describing the known population of neutron stars is only possible for EOSs in which the speed of sound in neutron-star matter breaks the conformal limit at high densities, that is exceeds 1/ √ 3 of the speed of light c for nB >∼ 2n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This striking behavior remains to be understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In par- ticular, it is currently not known whether the speed of sound exceeds c/ √ 3 above certain densities at all isospin fractions of nuclear matter or, alternatively, only in neutron-rich matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Importantly, robust constraints on the symmetric matter EOS at nB >∼ 2n0, obtained from heavy-ion collisions at intermediate to high beam energies, would also put constraints on the isospin-dependent part of the EOS through comparisons with the EOS inferred from neutron star studies, thus uncovering the magnitude of isospin-related effects at high baryon density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 11 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Upcoming opportunities The next decade will be an era of high-luminosity heavy-ion collision experiments at high baryon density with modern detector and analysis procedures, as well as detailed studies of the symmetry energy with collisions of proton- and neutron-rich isotopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Many of the discoveries of the BES program in ultra-relativistic heavy-ion collisions at RHIC, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', the discovery of the triangular flow and elliptic flow fluctuations, illustrate that modern analyses of heavy-ion collisions bring new quality to the understanding of the underlying processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Because of this, revisiting the intermediate to high beam energies, previously explored at the AGS at BNL as well as at SIS18 at GSI and now explored by the STAR FXT program and the HADES experiment, is imperative to enable putting tighter constraints on the EOS of dense nuclear matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Moreover, the future CBM experiment at the Facility for Antiproton and Ion Research (FAIR), Germany, will be able to measure interaction rates exceeding those currently used by several orders of magnitude, allowing for exploration of multiple high-statistics observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Furthermore, the explored beam energy range is where lower-order flow observables, reflecting the collective motion of the colliding system due to the underlying hadronic EOS, are particularly 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0150 200 250 300 350 400 450 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content="6 Incompressibility (MeV) dv1/dy'|y '=0 In-medium Xsection modification factor free protons free neutrons Au+Au, Ebeam/A=1." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='23 GeV b=6-9 fm HADES data: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='46+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='03 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='6 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='00 Incompressibility (MeV) v2 In-medium Xsection modification factor free protons free neutrons Au+Au, Ebeam/A=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='23 GeV b=6-9 fm, |ycm|<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='05, pt>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='3 GeV/c HADES data: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='06+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='01 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='01 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Predicted slope of the directed flow at mid- rapidity (dv1/dy|y′=0, top) and elliptic flow (v2, bot- tom) as functions of the incompressibility and the in- medium nucleon-nucleon scattering cross section mod- ification factor, generated in simulations of Au+Au reactions using the isospin-dependent BUU (IBUU) transport model [19, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Figure from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' prominent (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Therefore, the cor- responding precision measurements carry with them the opportunity to bring a richer perspec- tive and a better understanding of the physics underlying the complex dynamics of nuclear matter at extreme conditions (see Section III A, “Experiments to extract the EOS of symmetric nuclear matter”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This advancement can only occur provided a simultaneous development of hadronic transport simulations, as only a de- tailed understanding of various factors affect- ing the dynamics of heavy-ion collisions can lead to meaningful descriptions of the exper- imental data, and, consequently, more robust constraints on the EOS of nearly-symmetric nuclear matter (see Section II A, “Transport model simulations of heavy-ion collisions”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' As an example of the sensitivity of observables to various details of the underlying physics, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 5 shows the dependence of the slope of the di- rected flow (top panel) and of the elliptic flow at midrapidity (bottom panel) on the stiffness of the EOS, parametrized by the incompress- ibility, and on the in-medium nucleon-nucleon scattering cross-section modification factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Unprecedented possibilities are on the hori- zon for studies of the isospin-dependence of the EOS, which is critical for connecting heavy-ion physics measurements to astrophysical obser- vations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The difficulties in using nuclei with significant variations in the isospin asymme- try, along with the paucity of neutron measure- ments at midrapidity, have in the past greatly 12 restricted the capability to put tight constrains on the EOS of asymmetric nuclear matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Fortu- nately, at this time modern neutron detectors are available for heavy-ion measurements in many facilities, including at accelerators performing collisions at high beam energies such as GSI, while radioactive beam measurements are entering a new era at RIKEN and FRIB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' FRIB will provide proton- and neutron-rich beams of not only the highest-intensity worldwide, but also characterized by the widest currently accessible range of the isospin asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Establishing a strong heavy-ion program at FRIB will therefore enable previously inaccessible exploration of the symmetry en- ergy (see Section III B, “Experiments to extract the symmetry energy”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Moreover, the proposed FRIB400 beam energy upgrade would not only allow exploration of densities up to around 2n0, but it would also provide increased resolution of the isospin-dependence of the EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In particular, among observables sensitive to the symmetry energy, both charged pion yields and the absolute magnitude of the elliptic flow (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 4) significantly increase between the current top FRIB energy of 200 MeV/nucleon and the proposed 400 MeV/nucleon [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The increase in available computing power and advances in statistical methods make it possible to perform wide-ranging comparisons of heavy-ion collision simulations with experimental data (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', using Bayesian analysis), allowing one to vary multiple model assumptions at the same time as well as to put robust uncertainties on the obtained constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Furthermore, given the wealth of the upcoming independent data, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', from heavy-ion collision experiments, neutron star observations, and microscopic nuclear theory calculations, global analyses of complementary efforts have likewise a strong potential for putting tight constraints on the EOS (see Section IV, “The EOS from combined constraints”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Beyond the much-needed interpretation of intermediate energy heavy-ion collisions, advances in transport theory can lead to significant contributions to other areas of nuclear physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In particular, recently attention has been given to cross-cutting opportunities for employing state- of-the-art hadronic transport codes in studies supporting space exploration and advanced medical treatments (see Section V A, “Applications of hadronic transport”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Transport theories may also be used in tests of extensions of hydrodynamic approaches supporting far-from-equilibrium evolution (see Section V B, “Hydrodynamics”), which are a focus of intense studies due to their importance for modeling heavy-ion collisions at high energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Finally, constraining the dense nuclear matter EOS through interpretations of heavy-ion collision measurements may have other profound conse- quences, including helping to answer fundamental questions about the possible existence of dark matter in the cores of neutron stars or providing the impetus for studies of nuclear systems in fractional dimensions (see Section VI, “Exploratory directions”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Needs The next-generation experimental measurements of observables sensitive to the nuclear matter EOS are imminent, and further progress in resolving the nuclear matter EOS is contingent on enhanced theory support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In particular, the development of transport theories based on microscopic hadronic degrees of freedom, which are the only means of interpreting measurements from heavy-ion collision experiments at intermediate to high beam energies, must be strengthened and expanded to fully realize the potential of the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' facilities leading the exploration of the dense nuclear matter EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Support for both individual scientists and collaborations, and in particular for viable career pathways for early career researchers, is imperative to maintain the health of and diversify the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' hadronic transport community, and to fully capitalize on the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' efforts exploring the dense nuclear matter EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 13 II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' THE EQUATION OF STATE FROM 0 TO 5n0 Efforts to determine the equation of state (EOS) of nuclear matter are at the forefront of nuclear physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' An EOS contains fundamental information about the properties of a many-body system (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', Section I B), and is, in essence, any nontrivial relation between the thermodynamic properties of a given type of matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In nuclear physics, the form of the EOS that is most often pursued is the relation between energy per baryon or pressure and baryon density nB, isospin excess δ, and temperature T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For symmetric matter, the isospin excess vanishes (δ = 0), and for asymmetric matter the energy per baryon or pressure are commonly partitioned into a part corresponding to symmetric matter and the remainder, which contains all information about the isospin-dependence of the EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Due to the charge invariance of strong interactions, the latter part is (to a very good accuracy) quadratic in the isospin excess δ at densities relevant to nuclear experiments and astrophysical observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The quadratic coefficients in the expansion around δ = 0 are independent of δ, and are often referred to as the symmetry energy (denoted as S(nB) at T = 0) or symmetry pressure, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' These, together with the EOS of symmetric matter, are then sufficient to describe the EOS of nuclear matter at any isospin asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' While many approaches to constraining the nuclear matter EOS are pursued, here we describe three research areas which have the capability to constrain the EOS over wide ranges of density: inferences of the EOS from comparisons of experimental measurements to model simulations of heavy-ion collisions (Section II A), microscopic calculations of the EOS using chiral effective field theory (Section II B), and EOS inferences from neutron star studies (Section II C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Transport model simulations of heavy-ion collisions soft EOS hard EOS temperature [MeV] 0 50 100 150 200 250 300 density nB/n0 0 2 4 6 8 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='8 AGeV 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4 AGeV 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='2 AGeV 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='6 AGeV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='8 AGeV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4 AGeV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='2 AGeV FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Phase diagram trajectories of the central re- gion in Au+Au collisions at zero impact parameter, obtained from UrQMD simulations with a soft or a hard (characterized by K0 = 200 or K0 = 380 MeV, respec- tively) EOS [23, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The trajectories follow the evolu- tion at times when temperature is fairly well-defined, from the moment of the highest compression to densi- ties around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Heavy-ion collisions at very low to interme- diate beam energies provide the means to probe nuclear matter at different densities (from sub- saturation to several times the saturation den- sity), temperatures (from a few MeV to well above one hundred), and neutron to proton ratios (from near symmetric nuclear matter, where Nn/Np ≈ 1, up to Nn/Np ≈ 2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 6 for an illustrative calculation of heavy-ion col- lision trajectories in the T-nB phase diagram from simulations using two schematic EOSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' These wide ranges of system properties ac- cessed in heavy-ion collisions position them as a perfect tool to extract the nuclear matter EOS, test predictions and extrapolations from regions of the QCD phase diagram accessed by other approaches, and provide a necessary input to nuclear theory and nuclear astrophysics calcu- lations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For example, the density-dependence of both the symmetric and asymmetric EOS can shed light on modeling effective nuclear in- teractions in the medium [15, 25–27] or con- strain approaches using the density functional theory [28–30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 14 However, systems created in heavy-ion collisions are short-lived, and their dynamic evolution is out of equilibrium over significant fractions of the total collision time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The evolution of a colliding system depends on the energy and centrality of the collision, and progresses through initial compression, growth of the compression zone, development of flows, and overall decompression with a gradual local equilibration during the process, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The inherent complexity of the evolution means that the corresponding transport equations cannot be solved directly due to their high non-linearity, and therefore detailed inferences from heavy-ion collision experiments, where the non-equilibrium evolution probes nuclear matter over substantial ranges of density, require comparisons to results of collision simulations in transport models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Beyond modeling the dynamics of the collisions, transport models provide a connection to the equilibrium limit allowing for inferring the EOS [31], transport coefficients [32], as well as the in-medium properties and cross-sections of hadrons [33–35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Transport theory At its core, transport theory aims to describe the time evolution of the one-body phase-space distribution function in a semi-classical approximation for a dissipative system composed of a large number of particles, here in particular for a system of two heavy nuclei colliding at an energy per nucleon which is typically larger than the Fermi energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The theoretical foundations of transport theory include the BBGKY hierarchy of coupled equations for reduced density matrices [36] as well as the equations of the nonequilibrium Green’s function theory [37, 38] such as obtained in Martin- Schwinger (also known as Schwinger-Keldysh) formalism for non-equilibrium Green’s function (see also Section V B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' To arrive at transport equations, one employs (among others) a Wigner transformation and coarse-graining as well as a gradient expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The Wigner transformation and coarse-graining nB FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Contour plots of the system-frame baryon density nB (top row) and local excitation energy E∗/A (bottom row) at times t = 0, 5, 10, 15, and 20 fm/c (columns from left to right), obtained from a transport simulation [39] of a 124Sn+124Sn reaction at beam energy Elab = 800 AMeV (√sNN = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='24 GeV) and impact parameter b = 5 fm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The contour lines for the density use increments of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4n0, starting from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1n0, while the contour lines for the local excitation energy correspond to the values of E∗/A = {5, 20, 40, 80, 120} MeV;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' for statistical reasons, contour plots for the energy have been suppressed for baryon densities nB < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 0 100 200 300 dN/dy y (GeV/c) 132Sn+ 124Sn 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1 y IBUU pBUU RVUU SMF IQMD IQMD-BNU IQMD-IMP TuQMD 0.' metadata={'source': 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+page_content='1 y IBUU pBUU RVUU SMF IQMD IQMD-BNU IQMD-IMP TuQMD 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 0 100 200 300 dN/dy y (GeV/c) 132Sn+ 124Sn 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1 y IBUU pBUU RVUU SMF IQMD IQMD-BNU IQMD-IMP TuQMD FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Comparison of results for rapidity distri- butions (top) and transverse flow of nucleons (bot- tom) as functions of the scaled rapidity, obtained with different transport codes (identified in the leg- end) within the TMEP initiative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The results shown were obtained for 132Sn+124Sn collisions at Elab = 270 AMeV (√sNN = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='01 GeV) and impact param- eter b = 4 fm, using controlled input models for the EOS and the cross sections as well as identically ini- tialized nuclei [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' lead to positive-definite phase-space distribu- tions [41] that can be efficiently sampled with Monte-Carlo techniques, while the gradient ex- pansion yields, for each particle species, the force acting on a particle and the particle’s veloc- ity as gradients of its total energy with respect to the spatial position and momentum, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Knowledge of the kinematics of all parti- cles, together with the elementary collision rates, drives the evolution in the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Finally, to arrive at a set of Vlasov-Boltzmann–like equa- tions, one employs the quasi-particle approxima- tion, neglecting details of the spectral functions and treating all particles as on-shell (we note here that while there are some transport codes with off-shell particle treatment, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', [42, 43], this approach is still an outstanding challenge in the transport theory, as will be discussed further below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Alternative approaches to arriving at a transport theory for heavy-ion collisions include using the relativistic Landau quasiparticle the- ory [44] or, in approaches starting from a molec- ular picture, representing the global wavefunc- tion as a product (sometimes antisymmetrized) of single-particle Gaussian wavepackets [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The particle species considered in transport theory depend on the collision energy and may range from nucleons, through pions and the delta resonances, to higher resonances, kaons, and hy- perons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Some transport formulations further in- corporate light clusters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', deuterons, tritons, and 3He nuclei) as independent degrees of free- dom, with recent extensions also including alpha particles [46] which appear abundantly in exper- iments and are of particular importance for colli- sions at fixed-target beam energies on the order of hundreds of MeV/nucleon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In some of these approaches, clusters are produced through multi- particle reactions, as discussed further below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For the lowest energy collisions, nonrelativistic formulations of the transport theory may be employed, but the majority of the available codes are relativistic, with many addressing collisions at energies from tens of MeV/nucleon to at least a few GeV/nucleon (see [35, 47, 48] for reviews).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Transport approaches can be generally divided into those concentrating on a single-particle characterization of the colliding system and those attempting to describe many-particle correla- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Both types of approaches are highly complex and nonlinear, and the relevant equations are solved by simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The single-particle approaches typically solve a set of Boltzmann-Vlasov– type equations [47, 49] (also known as the Boltzmann-Uehling-Uhlenbeck, or BUU equations) in which the evolution of the system is governed by a mean-field evolution of the phase space distribu- tion (Vlasov equations) and a collision term which drives the dissipation (the Boltzmann collision term).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' While, in principle, the Boltzmann-Vlasov equation is deterministic, numerical solutions 16 contain numerically-induced fluctuations due to the fact that the evolution is obtained using the method of test particles, in which the continuous distribution function is represented by a large, but finite, number of test particles sampling the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' To include fluctuations of a physi- cal origin, one can add a fluctuation term to the two-particle collision term, thus arriving at the Boltzmann-Langevin formulation [35, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In contrast, quantum molecular dynamics (QMD) approaches include classical many-body cor- relations in the ansatz of the many-body wave function [47, 51], which is postulated as a product of single-particle wave packets of a fixed width, with the width regulating the amount of fluctuations and correlations in QMD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In Anti-Symmetrized Molecular Dynamics (AMD) [45], the product wave function is anti-symmetrized and the formulation includes Pauli correlations in the propagation as well as in, to a certain extent, the collision term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The fact that hadronic transport approaches are built on firm theoretical foundations has been crucial for the continued development of simulation frameworks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Reaching back to the roots of the nuclear transport theory has made it possible to resolve ambiguities which would be otherwise hard to tackle by purely phenomenological means, including descriptions of cluster production [52], low relative-velocity correlations (Hanbury–Brown-Twiss correlations) [53], and off-shell transport [42, 49, 54, 55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The strong theoretical foundation of transport theory has also been effective in ensuring covariance of the theory and preserving conservation laws in case of interactions that stray beyond outcomes of field-theoretic models, in particular interactions employing energy density functionals [44, 56–58] which are often needed for realistic descriptions of bulk properties of nuclear matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' An important effort to validate conclusions reached from comparing transport model results to data has been recently intensified by the formation of the Transport Model Evaluation Project (TMEP) [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Within this endeavor, predictions from different models are compared in controlled settings (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', ensuring the same physical input such as the EOS, initial densities, and cross sec- tions), oftentimes with comparisons to known results that can be achieved analytically or by other methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Similar controlled comparisons of complex simulations have been done in other fields of physics: from atomic traps, through ultra-relativistic heavy-ion collisions, to core-collapse su- pernova calculations [59–62], and they are known to be very fruitful for their respective fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The TMEP analyses not only enable identifying models that produce outlier predictions, but also determine details of implementation or physical assumptions behind the diverging results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' An ex- ample of such a comparison of codes for simulations of heavy-ion collisions at lower energies, with controlled input, can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 8, showing results for rapidity distributions (left) and the transverse flow (right) [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In general, the codes agree with each other reasonably well, however, differences between the codes are visible and, moreover, can be traced to specific model choices in the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For example, the generally lower values of the transverse flow in the case of QMD codes are a result of an approximation used in the evaluation of a non-linear term in the mean-fields, which becomes relevant when density fluctuations become large, as often occurs in QMD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Beyond identifying this and similar problems, the Project has yielded recommendations for optimal algorithms used in transport codes, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', for ensuring obeying the Pauli principle in elementary two-body collisions [63] or for integration of equations of motion with mean-fields [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Moreover, the project has identified a set of tests for transport codes that ensure their credibility when addressing different heavy-ion collision observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Stringent tests of hadronic transport codes are especially important for studies aimed at constraining the nuclear symmetry energy, which, compared to other model parameters, has a comparatively weak effect on heavy-ion observ- ables and which therefore demands maximal precision from transport simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Below, we will also discuss the role that such comparisons can play in determining the uncertainty of transport model investigations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 17 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Selected constraints on the EOS obtained from heavy-ion collisions A selection of important constraints on the EOS obtained from heavy-ion collisions can be found in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9 for both symmetric matter (pressure as a function of density, left panel) and asymmetric matter (symmetry energy as a function of density, right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' We note here that while many results are reported in terms of constraints on the incompress- ibility K0, in the context of heavy-ion collision studies of the EOS, K0 should be understood as a parameter which specifies the behavior of the EOS in the range of densities probed by a given study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For example, in the case of experiments probing mostly densities above 2n0, constraints on K0 are only indicative of the behavior of the EOS above 2n0, and in particular do not constrain the behavior of the EOS around n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This subtle, and often confusing, point is a consequence of simple parametrizations of the EOS used in many transport codes, where the only parameter con- trolling the behavior of the EOS both around n0 and at higher densities is K0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Recently, flexible parametrizations of the EOS have been developed (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', [57, 58]) and implemented (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', in hadronic transport code SMASH [75, 76]) which allow one to vary the incompressibility K0 and the high-density behavior of the EOS independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The collective behavior of matter created in the collisions, especially the directed and elliptic flow, has been shown to be a very sensitive probe of the EOS [31, 67, 77–79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In contrast to collisions at the Fermi energies, where all nucleons within nuclei participate in the collisions, and unlike in collisions at ultrarelativistic energies, where the evolution of the colliding nuclei can be understood in terms of participant nucleons, at intermediate energies the interplay between the expanding collision zone and the dynamics of the spectators are key ingredients to understanding Le Fèvre et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Lynch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' from Fuchs et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Oliinychenko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Danielewicz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Walecka model Fermi gas pressure [MeV/fm3] 1 10 100 baryon density nB/n0 1 2 3 4 5 HIC(isodiff) HIC(n/p) mass(Skyrme) IAS mass(DFT) PREX II HIC(π) Tsang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' ASY-EOS FOPI-LAND symmetry energy S(nB) [MeV] 0 20 40 60 80 baryon density nB/n0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Left: Selected constraints on the symmetric EOS obtained from comparisons of experimental data to hadronic transport simulations in [31] (region with black horizontal stripes), [65, 66] (region with red forward stripes), [67] (region with blue backward stripes), and [58] (region with green vertical stripes);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' see text for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Also shown are results of analytical calculations for the free Fermi gas (green dotted line) and in the linear Walecka model (pink dashed line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Right: Selected constraints on the symmetry energy obtained from comparisons of hadronic transport simulations to experimental data in [6] (region with purple forward stripes), [68] (region with green backward stripes), [69] (the solid orange region), and [70] (the red circle, square, and triangle symbols).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Also shown are symmetry energy constraints obtained in [70] based on a novel interpretation of analyses of nuclear masses in DFTs [11, 71] (cyan diamond symbol) and in Skyrme models [72] (cyan star symbol), of Isobaric Analog States (IAS) energies [73] (magenta plus symbol), and of PREX-II experiment [74] (blue inverted triangle symbol).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 18 experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' A seminal constraint on the symmetric nuclear matter EOS [31] in the density range (2–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5)n0 was obtained by comparing measurements of collective flow from heavy- ion collisions [80–83] at beam energies Elab = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='15–10 AGeV (corresponding to nucleon-nucleon center-of-mass energies √sNN = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='95–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='72 GeV) with results from hadronic transport simulations using EOSs with different values of the incompressibility at saturation density K0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The outcome of this study suggests a symmetric-matter EOS to lie between those labeled with K0 = 210 MeV and K0 = 300 MeV (see the region with black horizontal stripes in the left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For densities in the range (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5) n0, probed in collisions below Elab <∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 AGeV (√sNN <∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 GeV), the EOS may be inferred from meson yields [84–86].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Indeed, subthreshold production of strange mesons (specifically, K+ and K0), which interact weakly with nuclear matter, depends on the highest densities sampled in the collision, which in turn depend on the stiffness of the EOS [87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In [65], ratios of experimentally measured kaon yields in Au+Au and C+C collisions have been reproduced in hadronic transport simulations with soft mean-field interactions yielding K0 = 200 MeV and an EOS [66] consistent with the constraint from [31] (see the region with red forward stripes in the left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In [67], the elliptic flow data measured at Elab = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 AGeV (√sNN = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='07–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='52 GeV) by the FOPI collaboration [88] were used together with simulations from Isospin Quantum Molecular Dynamics (IQMD) [23, 89] to constrain the incompressibility at K0 = 190 ± 30MeV, again indicating a rather soft EOS (see the region with blue backward stripes in the left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Recently, new measurements by the STAR collaboration from the fixed target (FXT) program at RHIC have become available, providing an opportunity to expand the set of world data utilized to deduce the baryonic EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' A Bayesian analysis study [58], in which the speed of sound was independently varied in specified intervals of baryon density (thus providing a more flexible EOS at higher densities), suggests a tension between the E895 [83, 90–92] and STAR [93, 94] data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Using only the STAR measurements, the study [58] further found that EOSs which simultaneously describe the slope of the directed flow and the elliptic flow, in the considered energy range of Elab = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='9–9 AGeV (√sNN = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 GeV), are relatively stiff at lower densities and relatively soft at higher densities (see the region with green vertical stripes in the left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' However, the model used in that work did not include the momentum dependence of the EOS, which likely results in a spuriously stiff EOS at intermediate densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' As such, the study should be treated as a proof of principle that a tight constraint on the EOS at high densities can be achieved by using a combination of precise data, flexible forms of the EOS used in simulations, state-of-the-art models, and advances in analysis techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The symmetry energy contribution to the EOS can be studied at low collision energies Elab <∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 AGeV (√sNN <∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='32 GeV), where in particular observables such as charged pion yields [95] or neutron and proton flow [96, 97] have been proposed as sensitive to the asymmetric contribution to the EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Some of the constraints derived from such studies are shown in the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9, where, in addition to the usual EOS constraint bands, symbols with uncertainty bars represent results from analyses in which the symmetry energy has been determined for the most sensitive density of a given measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' At incident energies below Elab = 100 AMeV (√sNN = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='93 GeV), low densities are probed after the initial impact and compression of the projectile and target [6, 98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Since the symmetry potentials for neutrons and protons have opposite signs, emission of a particular nucleon type is enhanced or suppressed depending on the asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' A comparison of the experimental measurements of isospin diffusion and the ratio of neutron and proton spectra in collisions of 112Sn+124Sn at Elab = 50 AMeV (√sNN = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='90 GeV) to results from ImQMD simulations produced a constraint on the symmetry energy for densities (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='3–1) n0 [6] (see the region with purple forward stripes in the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Collisions at higher energies (Elab > 200 AMeV, or √sNN > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='97 GeV) probe the EOS at n > n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In the FOPI-LAND experiment, constraints on the symmetry energy were obtained from studies of the ratio of the elliptic flow of neutrons and hydrogen nuclei in Au+Au collisions at Elab = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4 AGeV (√sNN = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='07GeV) [68], while the ASY- 19 EOS experiment used neutron to charged fragments ratios measured in Au+Au collisions [69] (see the region with green backward stripes and the solid orange region, respectively, in the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In [70], a comprehensive analysis was performed with the goal of identifying the values of the symmetry energy at densities to which given experiments are most sensitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Using the isospin diffusion in collision systems with different proton to neutron ratios [99], neutron to proton energy spectra in Sn+Sn systems [100], and spectral pion ratios measured by the SπRIT collaboration in Sn+Sn collisions at Elab = 270 AMeV (√sNN = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='01 GeV) [101, 102], that work [70] put constraints on the values of the symmetry energy at about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='2n0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4n0, and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5n0, respectively (see the red circle, square, and triangle symbols in the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Also shown in the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9 are symmetry energy constraints obtained in [70] based on a novel interpretation of the analyses of nuclear masses in DFTs [11, 71] (cyan diamond symbol) and in Skyrme models [72] (cyan star symbol), of the Isobaric Analog State (IAS) energies [73] (magenta plus symbol), and of the PREX-II experiment result [74] (blue inverted triangle symbol).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Challenges and opportunities Selected results presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9 showcase significant achievements in determining the EOS and, simultaneously, the need to develop improved transport models to obtain tighter and more reliable constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Answering this need will require support for a sustained collaborative effort within the community to address remaining challenges in modeling collisions, in particular in the intermediate energy range (Elab ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1–25 AGeV, or √sNN ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='9–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1 GeV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In the following,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' we will address selected areas where we see the need for such developments: (1) comprehensive treat- ment of both mean-field potentials and the collision term in transport codes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' (2) use of microscopic information on mean fields and in-medium cross sections,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' such as discussed in Section II B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' in trans- port,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' (3) better description of the initial state of heavy-ion collisions in hadronic transport codes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' (4) deeper understanding of fluctuations in transport approaches,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' which affect many aspects of simulations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' (5) inclusion of correlations beyond the mean field into transport,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' which is crucial for a realistic description of light-cluster production,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' (6) treatment of short-range-correlations (SRCs) in transport,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' which are tightly connected to multi-particle collisions as well as off-shell transport,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' (7) sub-threshold particle production,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' (8) the study of new observables,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', azimuthally resolved spectra, to obtain tighter constraints on the EOS, (9) the question of quantifying the uncertainty of results obtained in transport simulations, and (10) the use of emulators and flexible parametriza- tions for wide-ranging explorations of all possible EOSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Fortunately, advances in transport theory as well as the greater availability of high-performance computing make many of these improvements possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Support for these developments will lead to a firm control and greater understanding of multiple complex aspects of the collision dynamics, allowing comparisons of transport model cal- culations and heavy-ion experiment measurements to provide an important contribution to the determination of the EOS of dense nuclear matter, which, in particular, cannot be determined by any other method at intermediate densities (1–5)n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Comprehensive treatment of mean-field potentials and the collision term Notably, driven by specific experimental needs over the last two decades, the refinement of hadronic transport codes has diverged into two complementary branches: Codes which were ap- plied to describing experiments at very low to low energies (Elab <∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 AGeV, or √sNN <∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 GeV), such as IQMD, AMD and pBUU, have become progressively better at describing the momentum- and isospin-dependence of the interaction, while codes which were primarily used as afterburners for simulations of ultra-relativistic heavy-ion collisions (Elab >∼ 25 AGeV, or √sNN >∼ 7 GeV), such as SMASH [75] or UrQMD, were developed to offer a fully relativistic evolution as well as scattering 20 and decay modes taking into account all established particle and resonance species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' As heavy-ion collisions are entering an era of precision data on symmetric nuclear matter at higher densities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', in experiments at HADES, BES FXT, and future CBM) and on asymmetric nuclear mat- ter at normal and supranormal densities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', at FRIB and future FRIB400), where features of both diverging branches of hadronic transport codes are important, a vigorous development of transport models is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In particular, numerous studies show the importance of including the momentum-dependence of the interactions, which is observed in elastic scattering of hadrons off nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Moreover, momentum-dependence naturally occurs in microscopic effective interac- tions [38, 103] where it contributes to the calculated mean fields, whether near or away from sat- uration density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Incorporating single-particle energies with momentum dependence different than that in free space, which is often quantified with effective masses, is crucial in hadronic transport both for studies of symmetric nuclear matter [31, 79, 104, 105] as well as studies of the symmetry energy and its relation to effects such as the neutron-proton effective mass splitting [106–108] (see also Section VI E for more discussion on effective masses and the nuclear symmetry energy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Some of the theoretical and implementation solutions have already been established, while others will require devising new approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' When possible, the best practices need to be carried over across the domains, as has been exemplified in, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', the development of the SMASH code, which uses many implementation solutions from pBUU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Microscopic input to transport One of the most prominent opportunities for improvement in transport models concerns imple- mentations of the EOS informed by state-of-the-art many-body studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Such efforts are especially timely given that sophisticated microscopic calculations of the properties of nuclear matter are currently becoming available for large ranges of baryon density, temperature, and isospin fraction (see Section II B for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' To incorporate the effects of the resulting EOSs in hadronic transport calculations, the corresponding Lorentz-covariant single-particle potentials as well as the in-medium interactions (both as functions of density, asymmetry, and momentum) are needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' A particular challenge is to determine the connection between the EOS inferred from a transport calculation and the zero-temperature EOS obtained from microscopic calculations [109], or even the finite-temperature EOSs that are becoming increasingly available [110, 111].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In a heavy-ion collision, the medium progresses through a set of non-equilibrium states that relax toward a local equilibrium, however, the nature of the local equilibrium also evolves during the collision due to the system expansion, so that even if the system approaches a local equilibrium at any given moment of the evolution, that agreement is only temporary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Errors incurred due to differences between non-equilibrium and equilibrium states of high-density matter contribute to the systematic error in inferring the EOS when comparing transport to experimental data (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9 and [31]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Here, the availability of state-of-the-art microscopic calculations at finite temperature could reduce system- atic errors in connecting the finite- and zero-temperature EOSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Moreover, the use of microscopic input would provide a consistency between the effective in-medium cross sections in the collision term and the mean fields used in the propagation of the phase space distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' It could also help address the question of the extent to which nonlocalities in the microscopic theory should be reflected in the propagation and the collision term [112, 113] (where, in particular, departures from standard approaches modify the entropy to take a form different than that obtained in the Landau quasiparticle theory [44, 114]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' To accelerate progress at the interface of the transport description of heavy-ion collisions and microscopic nuclear matter theory, direct collaboration of practitioners in the two research areas is required to assess how the needs of transport simulations can be answered by what can be currently calculated in microscopic theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Conversely, the use of microscopic interactions in transport could validate the many-body theory results in regions of density and temperature which are only accessible by heavy-ion collisions [115].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 21 Initial state Numerous studies point toward the dependence of outcomes of heavy-ion collision experiments on details of the initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In ultrarelativistic heavy-ion collisions, understanding these effects have led to the discovery of higher order flow harmonics [116, 117] and flow fluctuations [118].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' (Interestingly, the importance of the initial state for experimental outcomes also positions heavy-ion collisions at high energies as an unusual, but complementary probe of nuclear structure, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', a white paper on Imaging the initial condition of heavy-ion collisions and nuclear structure across the nuclide chart [119].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=') Given the high sensitivity of flow observables to both the EOS and the initial state of collisions, the impact of the initial conditions on outcomes of heavy-ion collisions needs to be thoroughly understood in order to narrow the constraints on the EOS of both symmetric and asymmetric matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Aspects of initial conditions that need to be considered include event-by-event fluctuations of the initial state [116–118], relative distributions of neutrons and protons and shell effects [120], and correlations tied to deformation [121] or short-range correlations [122].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Some of these elements will be further discussed below in the context of the dynamics of heavy-ion collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Fluctuations Fluctuations of the phase space distribution are an important ingredient of transport simula- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In particular, fluctuations of the one-body density are important for including the conse- quences of the dissipation-fluctuation theorem in the reaction dynamics as well as for describing effects due to the largely unknown, neglected many-body correlations, thus going beyond the mean- field description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The question of how to include them properly and of their consistency with the nucleon-nucleon correlations explicitly implemented in transport theories, however, has not been completely clarified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' As discussed above, fluctuations are included in a different manner in the two families of transport approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' While in the BUU transport fluctuations can be introduced by the Langevin extension of the Boltzmann-Vlasov equation, which adds a fluctuation term to the collision term (and which is still rarely implemented), in the molecular dynamics approach fluctu- ations are introduced in a classical way by using finite-size particles, the width of which regulates the amount of fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Fluctuations then affect the outcome of simulations in many ways, in- cluding by regulating the formation of intermediate-mass fragments (IMFs) which appear through the growth of fluctuations in regions of spinodal instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' It was also shown in box calculations that fluctuations have a strong influence on the efficiency of Pauli-blocking [63] and even on the calculation of the force in the Vlasov term for QMD codes in which non-linear parametrizations of the fields are used [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Correlations Correlations in transport simulations strive to address intermediate-range correlations beyond the mean-field picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Physically, such correlations are also a source of fluctuations, but at the same time have other additional impacts, including, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', influencing the production of light clusters (LCs), that is light nuclei up to the alpha particle which are copiously produced in heavy-ion collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The mean-field models used in transport calculations are usually not detailed enough to realistically describe very light nuclei with their particular spin-isospin structure reflecting strong quantum effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' An additional complication results from the fact that in a collision, clusters often appear in the nuclear medium where their properties are drastically changed (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', the binding energy of clusters is reduced with increasing density until the Mott point, at which they dissolve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Currently, most codes describe the production of clusters by using a cluster-finding algorithm, based on particle proximity in coordinate and/or momentum space (coalescence) toward the end of the evolution, which in more advanced versions also takes into account criteria related to the binding energy of the produced clusters [123].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' However, these late-stage algorithms do not take into account the dynamic role played by both correlations and LCs in the evolution of the collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' One 22 of the known approaches to this problem has been to consider LCs as separate degrees of freedom, with their own distribution functions and corresponding transport equations, where the collision terms can lead to creation or destruction of clusters (pBUU, SMASH) and which in particular can also take into account the in-medium modifications of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' However, this approach becomes increasingly complex as heavier clusters are characterized by more and more production channels, and consequently it is significantly challenging to include, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', alpha particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Another approach is to modify the phase space of the correlated nucleons according to the Wigner function of the cluster, but then to propagate them after the collision again as nucleons (as is done in, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', AMD [41]), which still requires using a cluster-finding step at the end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In both cases, the production and destruction of clusters necessarily requires multi-particle collisions to ensure energy-momentum conservation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Finally, at lower incident energies the LC production can also be described in terms of the catalyzing effect of spectator nucleons in few-particle collisions [46, 124].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' To explain LC production in high-energy collisions, where LCs are produced in numbers that cannot be obtained through nucleon catalysis due to the relatively few nucleons present in the final stages of these collisions, a similar mechanism of catalysis by pions [52, 125, 126] can be invoked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Short-range correlations A particular aspect of describing correlations in transport simulations is the treatment of short- range-correlations (SRCs), which have been measured in nucleon knock-out experiments [127–130].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Along with the experiments, microscopic many-body calculations show that SRCs introduce a high-momentum tail (HMT) into the nucleon momentum distribution and, moreover, reduce the kinetic symmetry energy relative to the Fermi gas kinetic energy, which is a consequence of the fact that SRCs are more pronounced in symmetric relative to asymmetric matter [131–138] (see also Section VI C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Phenomenological methods have been used to include SRCs in transport models, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', by initializing nuclei with a HMT, but such a procedure does not take into account the dynamic role of SRCs in the initial state, which in the case of the on-shell semiclassical equations of motion results in obtaining nonstationary, excited states of nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In on-shell transport approaches, three- and many-body collisions, incorporated into transport codes within varying approximations, have been suggested as a way of treating SRCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In particular, in an investigation [139] of three-body collisions for pion production processes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', NNN → NN∆), it was found that SRCs between two of the incident nucleons give a noticeable contribution to pion yields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Another approach [140], based on a mean-free-path approximation to the collision integral, observed large effects also on bulk observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The incorporation of n-body collisions in transport equations within a schematic cluster approximation was also studied [141], however, there the effects were found to be rather small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' So far, none of these methods have been widely exploited in the description of heavy- ion reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Since HMTs are tied to the tails of the nucleon spectral functions (away from the quasiparticle peaks), a consistent description of SRCs should involve an off-shell transport formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Dynamical spectral functions of all considered particles, including those which are stable in free space like nucleons, have been accounted for in the off-shell transport approaches implemented, with some differences in detail, in the codes GiBUU [42] and PHSD [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' A subsequent study [142] demonstrated that the momentum distribution automatically develops a HMT within the approach used in GiBUU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Differences in the results from the two approaches have yet to be investigated systematically, including the impact on symmetry energy inferences from heavy-ion collision data based on, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', charged pion subthreshold production yields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Fully quantum transport approaches with SRCs (or equivalent content), without any semi-classical expansions as are present in current off-shell transport approaches, remain a long-term goal, and progress in this area has not ventured yet beyond schematic models [143, 144].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' However, increasing computational power combined with emulation techniques may make such efforts more realistic and enable, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', a seamless integration of the treatment of shell effects in the initial state and collision dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 23 Threshold effects An important influence of mean-field potentials in heavy-ion transport appears in the form of threshold shifts and the related subthreshold production of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Thresholds of particle production are modified in a medium since the mean-field potentials have to be taken into account in the energy-momentum balance of a two-body collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Specifically, when the mean-field potentials are momentum-dependent and/or as a consequence of other model assumptions for the mean-field potentials of the produced particles, the thresholds are shifted away from their free-space values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This may strongly change the production rates of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Moreover, the threshold shifts make it necessary to involve other nucleons, besides the two collision partners in the process, to ensure the energy-momentum conservation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Various schemes to achieve this locally or globally have been in use [115, 145].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Indeed, explaining recent heavy-ion collision subthreshold pion yields, measured by the SπRIT Collaboration [102], required invoking many-body elementary effects in the form of mean-field effects on thresholds in two-particle collisions [86, 101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' However, because the physics invoked in describing the threshold effects is similar to that invoked for other multi-particle effects, alternative multi-particle options remain to be investigated, including producing pion degrees of freedom in multi-particle collisions or in the aftermath of an off-shell propagation between binary collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' (We note here that there is a physics overlap between these mechanisms and the impact of SRCs on pion production [42, 122, 139].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=') Notably, theoretical explorations find sequences of on-shell binary processes to dominate the production at higher beam energies [43, 55, 139], and no comparable difficulties have been encountered in describing the data [146, 147] by transport models without multi-particle effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The contrasting struggles of transport models which do not include threshold or other multi-particle effects of this type [102] , together with expected further theoretical explorations and future measurements of the subthreshold production in heavy- ion collisions, offer exciting possibilities for gaining understanding of the more exotic in-medium processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' New observables Upcoming precision data will further bring unprecedented observables that could be previously considered only in theory, such as triple-differential spectra tied to a fixed orientation of the reaction plane [18, 148–150] not only for protons and most abundant mesons, but also for deuterons,tritons, light nuclei, and hypernuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The potential of such spectra for the determination of the EOS is still to be fully explored, but a preliminary investigation [149] indicates a rich structure with spectra which exhibit a maximum away from the beam direction, characterized by slopes dependent on azimuthal angle and slope discontinuities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Models that might have agreed with each other in describing low-order Fourier coefficients of flow will likely find describing such detailed observables difficult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Challenges remain even at the level of the low-order coefficients, as many models now reproduce proton flow, but not Lambda or pion flow (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Understanding the relations between observables for various particle species will lead to constraints on the physics driving the evolution of heavy-ion collisions in simulations and, through that, to understanding cluster formation, hyperon yields, in-medium interactions with of strange hadrons, and more (see also the white paper on QCD Phase Structure and Interactions at High Baryon Density: Continuation of BES Physics Program with CBM at FAIR [151]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Quantifying uncertainties of transport predictions In the era of multi-messenger physics, where information on the EOS is derived from different areas of physics such as nuclear structure, nuclear reactions, and astrophysics, the ability to assess the uncertainty of a particular result is of crucial importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This problem is especially relevant for evaluations of constraints on the EOS from transport simulations of heavy-ion reactions, since it has been found that using different transport models to describe the same data can lead to very different 24 conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' As found in the TMEP comparisons (see [47] for a review), even with controlled input the results from different models may vary considerably due to different implementation strategies which in themselves are not dictated by the underlying physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In such a situation, calculating the mean and variance of different model predictions is not a reliable way of determining the uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' An approach currently considered for ensuring a robust quality control in combining inferences from different models is to weigh the models with a Bayesian weight which could be based, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', on the performance of a given model in benchmark tests and/or its ability to reproduce all key observables of a given reaction (for example, flow observables, particle multiplicities, and spectra).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Bayesian analysis can be also used for model selection through a comparison of results from a list of available models with data, during which one assigns to each model a probability of being correct based on the quality of the fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' However, this approach implicitly assumes that among the considered models there is at least one “true” model (also known as the M-closed assumption), which is often not fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Efforts have been taken to analyze data with an M-open assumption, where the existence of a perfect model is not assumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For nuclear physics efforts, this is being attempted within the Bayesian Analysis of Nuclear Dynamics (BAND) group [152] by using Bayesian model mixing, where information from different models is combined for inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Emulators and flexible EOS parametrizations Robust explorations of the possible physics underlying various observables often necessitate repeating the calculations many times for different combinations of physics parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' When high event statistics is needed, the computational task can easily overwhelm the available computational resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' An additional computational strain often arises from assessing Bayesian probability distributions for any conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Increasingly, emulators are going to be used for this task, with some steps having been already made [58, 102, 153].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Notably, similar issues emerge in the area of applications of hadronic transport [154] (see also Section V A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For explorations focused on the EOS, it may be of advantage to fit various possible EOSs with flexible relativistic density functionals as suggested in [57, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This approach, given the complete freedom in varying both the functional form of the EOS as well as the EOS parameters, is particu- larly amenable to Bayesian analyses (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', [58] for a Bayesian analysis with a parametrization of the EOS in terms of the functional dependence of the speed of sound on density).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The above list of issues facing the application of transport theory to heavy-ion collisions high- lights the fact that this approach to putting tighter constraints on the EOS rests on overcoming certain challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In simple terms, one attempts here to use a very dynamic and complex non- equilibrium process to obtain information describing a relatively simple and well-defined system, namely the equilibrated EOS of nuclear matter for different densities, temperatures, and isospin asymmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' To achieve this in a reliable way, multiple complex issues of many-body physics have to be well controlled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' On the other hand, several of the needed improvements are relatively well- understood, and tackling some of the unresolved problems poses an exciting intellectual challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' As a reward for undertaking this effort, one gains the opportunity to obtain information on the EOS in a region which cannot be accessed through any other means: For densities below saturation, there is strongly constraining information from nuclear structure, with significant contributions coming also from low-energy heavy-ion collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Astrophysical observations on neutron stars and neutron star mergers are mainly sensitive to densities above about 3n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The gap between these domains can only be filled with intermediate energy heavy-ion collisions, and transport studies are the essential tool to extract the information on the EOS from experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 25 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Microscopic calculations of the EOS Over the past decade, many-body nuclear theory has made significant progress in deriving microscopic constraints on the nuclear EOS at low densities from chiral effective field theory (χEFT) [155–158].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The progress has been driven by improved two-nucleon (NN) and three-nucleon (3N) interactions, rigorous uncertainty quantification, and algorithmic and computational advances in the frameworks used to solve the many-body Schr¨odinger equation with these interactions (see also the recent white paper on Dense matter theory for heavy-ion collisions and neutron stars [159]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Status Chiral EFT [160–164] provides a systematic way to construct nuclear interactions consistent with the low-energy symmetries of QCD, using nucleons (N’s), pions (π’s), and (in the case of delta-full χEFT), ∆-resonances (∆’s) as the relevant effective degrees of freedoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Nuclear interactions in χEFT are expanded in powers of momenta or the pion mass over a hard scale at which χEFT breaks down;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' this breakdown scale is expected to be of the order of the ρ-meson mass, Λb ≈ 600 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' At each order in the EFT expansion, only a finite number of diagrams enter the description of the interaction according to a chosen power counting scheme, of which the Weinberg power counting has been predominant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For example, at the leading-order (LO) in Weinberg’s power counting one includes contribution from the one-π exchange between two nucleons as well as momentum- independent contact interactions, which allow one to describe key features of the nuclear interaction already at the lowest order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' At next-to-leading-order (NLO), two-π exchanges are included as well as momentum-dependent contact interactions, and similarly, more involved terms appear at higher orders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The various low-energy coupling constants are determined from fits to experimental data, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', the π-N couplings are fit to π-N scattering, while those describing NN short-range interactions are fit to NN scattering data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The advantage of χEFT over phenomenological approaches is that multi-nucleon interactions, such as the important 3N interactions, naturally emerge in the EFT expansion and, moreover, are consistent with the NN sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Forces involving increasingly more nucleons are correspondingly more suppressed, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', the leading contribution to 3N forces (four- nucleon (4N) forces) appears at N2LO (at N3LO) in Weinberg’s power counting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Furthermore, there are only two new low-energy couplings appearing in the three- and four-body forces to N3LO, which govern the strengths of the intermediate- and short-range contribution to the leading 3N forces, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Consequently, χEFT 3N and 4N interactions at N3LO are completely determined by constraints on the coupling constants obtained from NN and π-N scattering”, usually resulting in tight constraints on very neutron-rich matter from χEFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Another key feature of χEFT is that order-by-order calculations in the χEFT expansion have enabled estimation of theoretical uncertainties due to truncating the chiral expansion at a fi- nite order [13, 158, 165, 166].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Quantifying and propagating these EFT truncation errors enables meaningful comparisons between competing nuclear theory predictions, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 10, and/or con- straints from nuclear experiments and neutron-star observations in the multi-messenger astron- omy era [167].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Such comparisons are facilitated by Bayesian methods in a statistically rigorous way [158, 167, 168] to take full advantage of the great variety of empirical EOS constraints we anticipate in the next decade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Chiral EFT also provides nuclear Hamiltonians governing the interactions in nuclear systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' However, to calculate properties of a many-body system, computational methods able to solve the Schroedinger equation for this system are necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Among various frameworks used to solve the nuclear many-body problem in dense matter, quantum Monte Carlo (QMC) methods and many- body perturbation theory (MBPT) have been the main tools employed to study the physics of 26 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Comparison of the energy per particle E/N (left) and the pressure P (right) as functions of density for pure neutron matter in different many-body calculations using interactions from χEFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The left panel also shows low-density QMC results of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' [169] and the conjectured unitary-gas lower bound on the energy per particle of pure neutron matter from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Figure from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' [170].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' neutron-star matter in recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Both methods have recently made tremendous advances in predicting properties of nuclei and calculating the nuclear matter EOS [156, 158, 171–175].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' QMC frameworks, such as the auxiliary field Diffusion Monte Carlo (AFDMC) method, are based on imaginary-time propagation of a many-body wave function and enable us to extract ground-state properties of a nuclear many-body system with high statistical precision [156, 171].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Their nonperturbative nature also allows for the treatment of nuclear interactions at high mo- mentum cutoffs, providing important insights into nuclear interactions at relatively short distances that may help to improve the modelling of χEFT interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' QMC calculations of binding en- ergies, radii, and electroweak transitions of nuclei up to A = 16 [176–182] using χEFT NN and 3N interactions are in very good agreement with experimental data [183–186].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' QMC methods were also used to calculate the EOSs of matter up to about twice the nuclear saturation density n ≈ 2 n0 [187–191].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The calculated EOSs include estimates of systematic truncation uncertainties, and are commonly used to constrain properties of neutron stars [188, 192, 193].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The past decade has also seen a renaissance for many-body perturbation theory (MBPT) calcu- lations in nuclear physics [158, 175].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Key to this development has been the discovery that nuclear potentials with momentum-space cutoffs in the range 400 MeV <∼ Λ <∼ 500 MeV (not to be confused with the breakdown scale of χEFT, Λb) are sufficiently soft to justify the use of perturbation theory methods [194] (see [195] for a Weinberg eigenvalue analysis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Such low-momentum potentials can be obtained from renormalization group methods [196] or by directly constructing chiral effective field theory potentials at a coarse resolution scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Furthermore, recent advances in automatic diagram generation [197] combined with automatic code generation [198] and high-performance computing have led to a fully automated approach to MBPT calculations in nuclear physics [158], in which chiral two- and multi-nucleon forces can be included to high orders in the chiral and MBPT expansions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' MBPT has been demonstrated to be a computationally efficient and versatile tool for studying the nuclear EOS as a function of baryon number density nB, isospin asymmetry δ = (nn −np)/(nn +np), and temperature T [110, 111, 199, 200] with implications for neutron star structure [158] and astrophysical simulations [201];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' here, nn and np correspond to the neutron and 25 5 Hebeler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=',ApJ (2013) Hebeler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=',ApJ(2013) Tews et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=',PRL(2013) Tewsetal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=',PRL(2013) Lynn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=',PRL (2016) Lynn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', PRL (2016) 20 4 Drischler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=',PRL (2019) Drischler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=',PRL (2019) Drischler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=',GP-B (2020) Drischler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=',GP-B (2020) Gezerlis, Carlson, PRC (2010) Unitary gas (s = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='376) 3 fm [MeV 10 P2 5 1 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='2 n [fm-3] n [fm-3]27 proton densities, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In particular, MBPT allows us to compute the EOS of neutron-star (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', β-equilibrated) matter explicitly, which can help improve isospin asymmetry expansions of the low-density nuclear EOS such as the standard quadratic expansion [199, 202–206].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' MBPT also allows us to study nuclear properties other than the nuclear EOS, including the linear response and transport coefficients that could be used to inform more accurate numerical simulations of supernovae and neutron-star mergers [207].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Furthermore, MBPT for (infinite) nuclear matter has been used to construct a microscopic global optical potential with quantified uncertainties based on χEFT NN and 3N interactions [208, 209].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Altogether, MBPT calculations of nuclear matter properties can provide important constraints that enable microscopic interpretations of future nu- clear reaction experiments [210] (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', at the Facility for Rare Isotope Beams) and neutron star observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' To date, theoretical predictions for the nuclear EOS, optical potentials, and in-medium NN scattering cross sections have been computed at finite temperature at various levels of approxi- mation starting from fundamental two- and multi-nucleon forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' These quantities are inputs to transport model simulations [89, 211] of heavy-ion collisions used to extract constraints on the properties of hot and dense nuclear matter (see Section II A for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In transport simu- lations, the EOS, single-particle potentials, and in-medium NN cross sections are usually obtained from effective phenomenological interactions [212, 213] that are fitted to the properties of finite nuclei and cold nuclear matter, and then extrapolated into the finite-temperature regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Recently, some effort has been devoted to benchmarking [109] the temperature dependence of these effective interactions against predictions from χEFT or directly using EFT constraints in fitting effective interactions [207, 214, 215].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' To enable such comparisons, the free energy of homogeneous nuclear matter as a function of temperature, baryon number density, and isospin asymmetry has been cal- culated using χEFT interactions up to second order in many-body perturbation theory [110] and within the Self-Consistent Green���s Function (SCGF) approach [216], which resums particle-particle and hole-hole ladder diagrams to all orders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The resulting EOS has been shown to be consistent with the critical endpoint of the symmetric nuclear matter liquid-gas phase transition [110, 216] as well as the low-density/high-temperature pure neutron matter EOS from the virial expansion [204].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Furthermore, single-particle potentials have been computed at finite temperature at the Hartree- Fock level [217], from G-matrix effective interactions [218], and in SCGF theory [201, 219].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Of particular importance is the associated nucleon effective mass, which is obtained from a momen- tum derivative of the single-particle energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The nucleon effective mass is directly related to the density of states and hence governs entropy generation at finite temperature, with consequences for the dynamical evolution of core-collapse supernovae and neutron star mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Finally, in-medium NN scattering cross sections have been computed at finite density and zero [220] as well as at finite [218] temperature using high-precision nuclear forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In the next decade, the use of effective field theory methods will enable a consistent framework for describing all of these quantities with uncertainty estimates for input into transport simulations of heavy-ion collisions and astrophysical simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Challenges and opportunities To fully capitalize on experimental and observational data and extract key information on fun- damental questions in nuclear physics, continued progress in nuclear theory is crucial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The combi- nation of χEFT with modern computational approaches like machine learning, artifical intelligence, emulators, and Bayesian inference have provided EOS results for a wide range of densities, and at various proton-to-neutron asymmetries and temperatures, with quantified uncertainties [111, 166].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Future progress in the development of fundamental interactions, combined with these tools, will 28 increase the precision of the results and enable us to answer open problems in chiral EFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Among these, the most pressing is at which densities and how χEFT breaks down [166, 188].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In particular, for studies of neutron-star mergers it is of great importance to describe dense matter at finite temperatures [200, 201, 204], however, these might influence the breakdown of the theory in dense matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In the next decade, it will be crucial to reliably determine how far one can push the χEFT approach in nucleonic matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' While microscopic calculations have been very successful in calculating properties of nuclei and homogeneous matter at densities up to 1-2 times the nuclear saturation density, we need improved microscopic descriptions of neutron-rich dense matter beyond that regime, at a few times nuclear saturation density and finite temperatures, with quantified uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This can be achieved by employing models derived within relativistic mean-field or density functional theory that are firmly rooted in microscopic theory at lower densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Such models will be very important to connect theoretical calculations within the framework of χEFT to heavy-ion collision experiments at accelerator facilities around the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Heavy-ion collision experiments at intermediate beam energies bridge the low- and high-density regimes of the EOS and provide complimentary informa- tion to that obtained from nuclear structure or neutron-star studies [17] (see Section II A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Robust inferences from the experimental data will require more accurate predictions from transport the- ory, which strongly depend on, among others, mean-field or density functional models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' It will be imperative to test and constrain such models for the EOS with more rigorous microscopic calcu- lations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Beyond their use in hadronic transport simulations, these models are also a crucial input for calculations of properties of neutron star crusts (see Section II C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Additional theoretical constraints might be provided by high-density calculations within the framework of perturbative QCD (pQCD) [221], which can be applied at very high densities of the order of 40 times the nuclear saturation density, where the strong interactions among quarks become perturbative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Constraints on the EOS based on pQCD, together with assumptions on causality and stability, have been used to constrain the EOS at lower densities probed in the core of neutron stars [222–225].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' However, it has been found that the constraining power of pQCD calculations is strongly dependent on the way in which they are implemented [225, 226].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Future studies have to establish to what extent pQCD constraints are robust at densities of the order of several times nuclear saturation density, and how constraining future higher-order calculations may become.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In this regard, improved microscopic calculations of the nuclear EOS using the functional renormalization group [227, 228] will provide important insights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Neutron star theory 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Status Measurements of the EOS, masses of neutron-rich isotopes far from the band of stability, and experimental constraints on nucleon effective masses provide essential input into neutron star mod- els, progressing our understanding of the structure and dynamics of these astronomically important objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Several properties of neutron stars, including the mass-radius relation and their tidal de- formabilities, can be calculated once the EOS is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This, in turn, enables us to constrain the EOS once those properties are observed [229].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Nuclear EOSs for neutron stars can be constructed from, for example, ab initio calculations and density functionals [230–233] or, more schematically, from meta-models [234–236] parameterized by nuclear matter parameters, which can be used to make contact with heavy-ion collisions [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Ab initio calculations take into account more fundamental properties of the nuclear force (see Sec- tion II B), but prohibit the calculation of large ensembles of EOSs spanning the nuclear parameter 29 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Impact of nuclear physics theory and experiment, and different astrophysical measurements on constraining the cold neutron-star EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Blue lines show a family of EOS that are con- strained by chiral EFT at low densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' At higher densities, the EOS can then be constrained using GWs from inspirals of neutron star mergers, data from radio and X-ray observations of pulsars, and electromagnetic signals associated with neutron star mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The indicated boundaries between regions affected by these mea- surements are not strict and depend on the EOS and properties of the astrophysical system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Figure from [237].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Meta-models allow rapid computation of such large ensem- bles, but encode mainly bulk prop- erties of nuclear matter, which ex- cludes them from being used to model finite nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Density func- tionals represent a compromise, al- lowing both rapid computation of EOSs and use in finite nuclear mod- els, and thus are more suited to combining nuclear experimental and astrophysical information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Many of these models can be smoothly extrapolated from the saturation- density to arbitrarily high density, in which case astronomical obser- vations can be used to constrain the saturation-density nuclear mat- ter parameters and their density de- pendence [236, 238].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This extrapo- lation, however, is model-dependent, as different density functionals have different dependence on density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Ad- ditionally, this extrapolation might not be physically well-founded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' As densities inside neutron stars can reach up to several times nuclear saturation density, at some (as-yet not determined) density a description in terms of purely nucleonic degrees of freedom is expected to break down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Heavy-ion collisions can help us constrain that point, and the nature of any phase transitions that occur above saturation density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The nuclear EOSs can be then combined with models describing the EOS at higher densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Models that explicitly include a range of possible high-density degrees of freedom, such as hyperons and quarks, can be constructed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' the predicted neutron star compositions are then dependent on the particular model used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Another approach is to use more general models that give up the explicit dependence on the underlying degrees of freedom, thus losing information on, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', appearance of exotic particles at high densities, in favor of spanning the full space of physically con- sistent EOSs, reducing the model dependence of inferences from astrophysical observations [239].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' These schemes include piecewise polytropes [14, 240–242], line segments [192, 243], speed-of-sound models [188, 189, 244–246], spectral models [247] and non-parametric models generated from Gaus- sian processes (GPs) [168, 248–251] or machine learning techniques [252].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' If these more general approaches are used down to the nuclear saturation density, extra modeling is required to connect them to the microscopic nuclear EOS and nuclear observables [253].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Once the EOS is specified, the solution of the Tolman-Oppenheimer-Volkov equations and their extensions including rotation, determining the structure of a neutron star through balancing the attractive force of gravity and the repulsion coming from the EOS, provide predictions for bulk properties of the neutron star such as radii, tidal deformabilities, moments of inertia, and break-up frequencies of neutron stars as a function of their mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' All of these properties can be compared with multi-messenger observations, including gravitational waves and electromagnetic signals from neutron-star mergers and isolated neutron stars [193].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The systematic construction of neutron star EOS models and statistical inference of EOS pa- 103 8 102 [Mev fm EM: Kilonovae / GRB GWs (post-merger) Pressure 101 GWs (inspiral) Radio and X-ray pulsars 100 Nuclear Physics Experiment and Theory 2 4 6 8 Number density [nsat30 rameters from data is an endeavor that is just over a decade old [14, 240–242].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This effort has matured in the current era of multi-messenger astronomy with a large push to explore the model- dependence of EOS inferences [244, 254] and ways of connecting the EOS with astrophysical and nuclear data [17, 167, 193, 245, 246, 255].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Different choices of which observables to include or infer can be made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For example, astrophysical observations can be used to infer the EOS, which can then be connected to nuclear models to inform their parameters and predict nuclear observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Conversely, nuclear observables can be used to infer nuclear parameters, which can then inform the neutron star models and predict astrophysical observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The future lies in combining more and more sets of data of both types to understand nuclear and neutron star models better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Exciting progress has been made in gathering astrophysical data to constrain our dense matter theories (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 11 for an illustration of density regions affected by different observables).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Neutron- star data from the last 5 years identified the heaviest neutron star known to date with a mass of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='08(7)M⊙ [256, 257] (where M⊙ is the solar mass), while the kilonova AT2017gfo, associated with GW170817, has placed an upper limit on the maximum mass to be on the order of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='3M⊙ [258, 259].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The detection of GW170817 by the LIGO-Virgo Collaboration has enabled us to place constraints on the tidal deformability of this system, ˜ΛGW170817 ≤ 720 [260, 261].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Neutron Star Interior Composition Explorer Mission (NICER) has provided two mass-radius measurements by observing X-ray emission from several hot spots on the neutron star surface, finding a radius of 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='02+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='24 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='06km for a star with mass 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='44+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='15 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='14M⊙ (PSR J0030+0451) and 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='7+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='6 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5km for a star with mass 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='08(7)M⊙ (PSR J0740+6620) in the analyses of Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' [255, 262–264].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' X-ray observations of the temperature of the neutron star in the Cas A supernova remnant have revealed core cooling on the timescale of years, hinting at the possible superfluid properties of the core [265].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' These observations have enabled meaningful constraints on the EOS to be set and have already allowed us fascinating glimpses into the possible properties of high-density matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For example, perturbative QCD predicts that the speed of sound squared approaches the conformal limit of 1/3 from below as the density becomes arbitrarily high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Meanwhile, inferences of the neutron star EOS from observational data indicate that the speed of sound rises in the core to significantly above c2 s = 1/3 [188, 266–269].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Consequently, this suggests that the speed of sound has a non-trivial behavior with increasing density [188, 221, 270].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' At the same time, tentative evidence for quark matter in neutron star cores, which in turn indicates a softening of the EOS, has likewise been suggested [246].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' If we want to leverage the substantial data we have on neutron star cooling and dynamical evolution, additional EOS quantities need to be supplied consistently for each EOS model, such as the effective masses (see also Section VI E) and superfluid neutron and proton gaps, essential for modeling thermal and dynamical properties of neutron stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For example, the mutual friction of the core – the strength of the coupling between the charged particles (electrons, protons) and superfluid neutrons – depends on the effective neutron mass and the proton fraction [271], which both also correlate with the symmetry energy [108].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' A consistent extraction of both symmetry energy parameters and effective masses from heavy-ion collision data is therefore required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In contrast to efforts devoted to systematic, statistically meaningful inferences of the EOS in the cores of neutron stars, modeling the neutron star crust is still in its infancy: The first calculations of large ensembles of systematically parameterized crust models and their use in statistical analysis have only been carried out recently [272–276].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' However, much more nuclear experimental data can be brought to directly bear on crust physics, and we have entered an era where we can access information about the crust with unprecedented fidelity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For example, we have now observed the same neutron-star crust as it first cooled, then became heated by accreted matter, and then cooled again [277–281].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' We have followed a pulsar through a glitch – a sudden change in the rotation period of the pulsar – and glitch recovery with a resolution of a few seconds [282].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' These observations have provided very strong evidence that the crust is solid, that there exist superfluid neutrons in the inner crust which can be decoupled from the nuclei in the crustal lattice, and that nuclear 31 reactions from accreted material sinking into the crust provide deep crustal heating [279, 283, 284].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Additionally, models of the neutron star crust predict that, prior to the transition to homoge- neous matter, isolated nuclei in the crust fuse to form cylindrical, planar, and more exotic shapes, termed “nuclear pasta”, that can affect neutron-star observations [285–287].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This crust-core bound- ary region, often referred to as the mantle, is likely a complex fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Density functional theory and molecular dynamics calculations of these structures reveal a complex energy landscape with many coexisting shapes, and correspondingly complex mechanical and transport properties [288–294], which are strongly influenced by the EOS at around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5n0 through the pressure, proton fraction, and surface energy of the structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' These properties can also be studied in multifragmenta- tion reactions, which probe, among others, the competition between nuclear surface energy and Coulomb energy at sub-saturation density [295–297].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Inhomogeneous matter in the crust of a neutron star, including the dripped neutrons expected in the inner crust, can be modeled using a variety of nuclear theory techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' These usually involve calculations within a single, repeating unit (Wigner-Seitz cell) of matter, typically containing a sin- gle nucleus [298–300].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The compressible liquid drop model (CLDM) treats the nuclear matter inside and outside of nuclei as homogeneous and described by the bulk matter EOS, while the surface energy is specified by a separate function with additional parameters [288, 300–303].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The surface parameters and those that define the dimensions of the cell and nucleus are minimized to obtain the ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The Thomas-Fermi model employs the local density approximation, modeling matter with a specified form of the inhomogeneous nuclear matter density in the unit cell;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' here, the parameters of the density distribution are varied to obtain the ground state configuration [304].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Microscopic approaches to describing inhomogeneous nuclear matter, in which individual neutrons and protons are the degrees of freedom, include quantum Hartree-Fock or Relativistic Mean Field models [305–310], and semi-classical molecular dynamics approaches [292, 311].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' There is a great need for nuclear physics input into models of the neutron star crust, which analyses of heavy-ion collision data can provide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For example, the thickness, mass and moment of inertia of the crust depend on the higher-order symmetry energy parameters L, Ksym, and Qsym [272, 274, 312].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Thus measurements of the symmetry energy parameters up to third order in heavy-ion collision experiments are essential to understand the properties of the crust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The symmetry energy, effective masses, and surface energies of nuclear clusters strongly affect the proton fraction on either side of the crust-core transition density, the extent of nuclear pasta near the crust-core boundary, the mechanical and transport properties, the thermal conductivity and specific heat, the electrical conductivity, and the shear modulus of the crust [298, 304, 309, 313].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Nuclear experiment can thus constrain neutron star crust models, and astrophysical observables associated with the crust can measure nuclear observables as well as measurements of neutron star bulk properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For example, the symmetry energy can be constrained by combining nuclear data with crust and core observables, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', through a potential multi-messenger measurement of the resonant frequency of crust-core interface oscillations [276].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Challenges and opportunities The next decade will provide a wealth of new data on neutron stars, as the LIGO-VIRGO- KAGRA detectors are expected to observe many new binary neutron-star mergers, some of them with electromagnetic counterparts [314–316].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' As NICER continues to measure more neutron star masses and radii, next-generation X-ray timing missions such as Strobe-X [317] and radio tele- scopes such as the Square-Kilometer Array will increase the number of pulsars we see and are able to measure by an order of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Long-timescale observations of individual pulsars (using radio timing) and persistent gravitational waves from deformations of neutron stars will lead to 32 measurements of their moments of inertia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' These new data points might enable us to pin down the nuclear matter EOS, to discover or rule out the existence of phase transitions to exotic forms of matter in the cores of neutron stars, and to reliably constrain microscopic interactions between fundamental particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Although model-agnostic extrapolations to higher densities such as through the use of poly- tropes [194, 240], speed of sound schemes [188, 244, 318], Gaussian processes [249, 250] and spectral methods [247], combined with robust data analysis, will eventually allow us to pin down the dense- matter EOS, they cannot answer the question about the relevant microscopic degrees of freedom at high densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Hence, it is crucial to develop improved microscopic models with well-quantified un- certainties in this regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' At the same time, creating ensembles of outer core and crust models that allow for inclusion of astrophysical and nuclear data requires underlying nuclear models to have enough freedom to explore a large region of parameter space, and allow fast computation of relevant quantities that also capture the essential physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Currently, it is energy density functionals like Skyrme, Gogny, and Relativistic Mean Field models that provide these properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Consequently, progress could be made by making a stronger connection between these models and microscopic approaches, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', connecting energy-density functionals to ab initio calculations allowing a more direct link to χEFT [299, 319, 320].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In the same spirit, EFT calculations of the EOS can be used as a “low-density limit” to calibrate higher-density models for neutron stars and heavy-ion collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The crust can be modeled consistently with nucleonic matter in the core using density functional theory to model both.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' When choosing a model, a compromise must be made between accurate modeling of microscopic quantum effects, such as shell effects in the nucleus and surrounding neutron gas, and the computational expediency required to construct large ensembles of crust models needed for statistical inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For example, quantum shell effects strongly determine the evolution of the mass and charge number of nuclei with density, alter the effective mass of dripped neutrons, and drive the complex energy landscape of nuclear pasta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Fully microscopic quantum calculations include shell effects self-consistently, but are computationally expensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The CLDM approach can be used to construct large numbers of crust models, but requires shell effects to be added by hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Future work needs to develop schemes of incorporating such microscopic effects in large ensembles of crust models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The method that may allow that is the Extended Thomas-Fermi method, incorporating shell effects through the Strutinsky Integral: see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', [321].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Models should also incorporate nuclear pasta, as its extended structures may contribute to the mechanical and thermal properties of matter at the crust-core boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' It is computationally demanding to model transport and mechanical properties of the crust microscopically or in simula- tions [322], particularly in the nuclear pasta phases, and it is unrealistic to include these quantities in large ensembles of crust models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Simpler schemes that extrapolate the mechanical and trans- port properties across the parameters space based on microscopic models could be developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Also, representative crust models inferred from data can be used to calculate these crust properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' There is also a need for a balance between accuracy and precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' A model can be accurate but not precise (predicting the correct value of a physical quantity but having large error bars), or precise but not accurate predicting very small error bars, but not predicting the correct value of some physical observable).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Individual crust models can be created from mass models that are precisely fit to data and which predict precise values for, for example, the symmetry energy parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' However, to make accurate inferences of nuclear matter parameters from astrophysical observables, and to include their experimentally measured ranges, ensembles of models spanning the parameter space should be employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Both strategies are important, and the precision-fit models can act as benchmarks against which we assess the outcomes of statistical inferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' When older neutron stars accrete matter in the crust the matter gets gradually pushed down into the core and replaced by the accreted matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The temperatures in the crust are well below the nuclear potential energies, so the replacement crust cannot easily attain nuclear statistical 33 equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Ensembles of accreted crust models are yet to be constructed, but are necessary to correctly account for deep crustal heating and therefore to fully utilize the observations of cooling of accreted crusts in low mass X-ray binaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In all this work, effort must be made to calculate the different observables consistently as well as to combine different data sets in a well-controlled way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This is expanded upon in Section IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' HEAVY-ION COLLISION EXPERIMENTS Establishing the equation of state (EOS) of nuclear matter has been a major focus of heavy-ion collision experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' While very low energy collisions can probe nuclear matter at densities smaller than the saturation density n0, highly-compressed nuclear matter is produced in the laboratory by colliding heavy nuclei at relativistic velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' At even higher energies, in the ultra-relativistic regime, quarks in the colliding nuclei become almost transparent to each other and therefore escape the collision region, which means that matter measured at midrapidity is characterized by a nearly- zero net baryon number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Heavy-ion collision experiments at top beam energies at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) provided convincing evidence that at high temperatures and near-zero baryon density, nuclear matter becomes a quark-gluon plasma (QGP) [323–329], a deconfined but strongly-interacting state composed of color charges, confirming Lattice QCD (LQCD) calculations of the EOS at zero density [330–332].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' While the region of the QCD phase diagram explored in ultra-relativistic heavy-ion collisions is relatively well understood, the EOS of dense nuclear matter at moderate-to-high temperatures and moderate-to-high baryon densities is not known well due to the break-down of first-principle approaches in this regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Answering pressing questions about the QCD EOS in this region, such as whether the quark-hadron transition becomes of first-order at high densities or what is the minimal energy required to produce the QGP, is the driving force behind Phase II of the Beam Energy Scan (BES) program at RHIC, the HADES experiment at GSI, and the future Compressed Baryonic Matter (CBM) experiment at the Facility for Antiproton and Ion Research (FAIR), Germany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This renewed interest in the nuclear matter EOS at high densities,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' accessible in heavy-ion collisions at intermediate energies,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' coincides with an increased effort to constrain the EOS of neutron-rich matter,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' probed in studies of neutron stars and neutron star mergers (see Section II C as well as recent white papers on QCD Phase Structure and Interactions at High Baryon Den- sity: Continuation of BES Physics Program with CBM at FAIR [151] and Dense matter theory for heavy-ion collisions and neutron stars [159]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Furthermore, studies show that heavy-ion collisions in this regime and neutron star mergers probe similar temperatures and baryon densities [333, 334].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' However, while matter created in collisions of heavy-ions has comparable numbers of protons and neutrons, matter inside neutron stars is neutron-rich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Establishing the much needed connection between the studies of the nuclear EOS as probed in heavy-ion collisions and as inferred from neutron star observations is possible by leveraging the experimental capabilities of the newly com- missioned Facility for Rare Ion Beams (FRIB), where energetic beams of proton- and neutron-rich nuclei can be produced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Heavy-ion collision experiments at FRIB can put tight constraints on the dependence of the nuclear matter EOS on the relative proton and neutron abundances [22], and thus enable a description of both dense nuclear and dense neutron-rich matter within a unified framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Indeed, if we assume that the core of a neutron star is composed of mostly uniform nucleonic matter, then nuclear matter and neutron stars should be described by a common EOS, specifying the relationship between the pressure and the temperature, density, and isospin content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The theoretical construct of symmetric nuclear matter consisting of equal amounts of neutrons and 34 Number density Astro HIC(asym) Nuclei properties Theory Crust HIC(SNM) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This schematic plot illustrates the approximate density ranges that are explored in the studies of chiral effective field theory, nuclei properties, heavy-ion collision experiments, and observations of neutron stars and their crusts in astronomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' protons has been successful to derive properties of symmetric matter such as the saturation density and bind- ing energy, however, an additional term in the EOS is needed to de- scribe nuclear matter with unequal neutron-proton composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' This second term depends on the asymme- try δ, defined as δ = (nn − np)/nB, where nn, np, and nB are the neu- tron, proton, and total baryon densi- ties, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Consequently, one can view the asymmetry as the neu- tron excess fraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Mathematically, the energy per nucleon can be then expressed as a sum of two terms: ϵ(nn, np) = ϵSNM(n) + S(n)δ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Here, the first term represents the energy per nucleon of symmetric nuclear matter, while the second term accounts for the correction needed when δ ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Therefore, δ is a crucial parameter that distinguishes neutron stars (with δ >∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='8) from most nuclei (with δ <∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Given the relatively small values of the asymmetry δ for nuclei, in heavy-ion collision experiments it is easier to constrain the coefficients of the EOS of symmetric matter, ϵSNM(nB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In contrast, the energy contribution from the asymmetric term, also known as the symmetry energy, constitutes a small fraction of the total energy of a nucleus even for neutron-rich heavy radioactive isotopes (< 5% in the liquid drop model), and its determination requires precise measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Furthermore, because the isospin effects in any observable tend to diminish with temperature, it may be difficult to measure the symmetry energy at very high densities, which require high-energy heavy-ion reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Therefore, symmetry energy is best probed in heavy-ion collisions of highly asymmetric isotopes at low to intermediate energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 12 shows schematically the baryon density regions explored by different areas in nuclear physics studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Recent breakthroughs in astronomical observations with state-of-the-art instru- ments led to the first detection of a binary neutron-star merger and the unprecedented radii mea- surements of neutron stars with accurately known masses (see Section II C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The neutron star mass-radius relationship provides an insight into the EOS at high densities above twice saturation density (>∼ 2n0), as represented by the red arrow (labelled “Astro”) in the upper right corner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Labo- ratory experiments, especially those using heavy-ion collisions, are essential to provide information on the dependence of the EOS on density and the asymmetry (see also Section II A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' High-energy heavy-ion collisions can provide insight into the symmetric nuclear matter EOS as represented by the gold right-pointing arrow (labeled “HIC(SNM)”), while current probes of the symmetry energy are more suited for measurements of lower energy heavy-ion reactions (<∼ 600 AMeV) as represented by the left-pointing gold arrow (labeled “HIC(asym)”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Many properties of nuclei, such as masses and radii, have been shown to be mainly sensitive to densities around (2/3)n0, however, with a careful selection of nuclear observables, the symmetry energy has been probed over densities of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='3n0 < nB < n0 using Pearson correlation methods [12, 335] (green left-pointing arrow).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Recent advances in chiral effective field theory (see Section II B) enabled extrapolations of the EOS to be extended up to ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5n0 [13], but the uncertainty increases exponentially with density for densities that are higher than n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' It is not clear what is the maximum density up to which such extrapolations can succeed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Finally, one of the most interesting regions is at very low densities (<∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5n0), corresponding to the crust of a neutron star where matter is not uniform (see Section II C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' There, matter changes with increasing density from a Coulomb-dominated lattice to L 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='035 nuclear pasta and, ultimately, to uniform matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The density and nature of these transformations are again dictated largely by the EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Measurements made in heavy-ion collisions at intermediate energies, probing high densities or, equivalently, small nucleon separations, will yield key insights into the nature of the nuclear force, including the density-dependence of the nuclear symmetry energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Experimental efforts to determine the EOS for symmetric matter and the symmetry energy are described in Section III A and III B, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Please note that all beam energies Elab quoted in this section are the single-beam kinetic energies per nucleon, in units of AMeV or AGeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' (Alternatively, Elab is also sometimes denoted by other authors as E/A, with units of MeV or GeV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Additionally, while many results are reported in terms of their constraints on the incompressibility K0, one should refrain from interpreting them as constraining the behavior of the EOS around the saturation density (see Section II A 2 for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Experiments to extract the EOS of symmetric nuclear matter Heavy-ion collision experiments worldwide have extensively studied the EOS of symmetric nuclear matter at supra-saturation densities over the past four decades.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Experiments based at the Schwerionensynchrotron-18 (SIS-18) ring accelerator at the GSI Helmholtz Centre for Heavy Ion Research (GSI) have probed Au+Au collisions at energies between Elab = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='09–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5 AGeV (√sNN = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='92–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='52 GeV), corresponding to fireball densities 1–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Further experimental efforts with Au+Au collisions were carried out at higher energies, Elab = 2–10 AGeV (√sNN = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='70– 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='72 GeV), at the Alternating Gradient Synchrotron (AGS) at the Brookhaven National Laboratory (BNL) to probe fireball densities 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5–5n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Complementing the densities reached at AGS-BNL is the Beam Energy Scan (BES) program of the Solenoidal Tracker at RHIC (STAR) experiment at RHIC in BNL, where high-statistics Au+Au collisions were performed at energies between Elab = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='9– 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 AGeV (√sNN = 3–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='7 GeV) in the fixed-target mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' A selection of constraints on the EOS extracted from the above experiments is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Below, we describe the observables stud- ied to extract the symmetric nuclear matter EOS, experiments probing the aforementioned density ranges, and inferences for the hadronic transport codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Measurements sensitive to the EOS Collisions of heavy nuclei at relativistic energies lead to a rapid compression and heating of matter trapped in the collision region, followed by its dynamic expansion and cooling (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The EOS governs both the compression as well as the expansion of the hot and dense nuclear matter, which in turn affect measured particle distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' For example, a stiffer EOS (characterizing matter that is more incompressible) leads to a relatively smaller compression and, consequently, smaller heating, but a faster transverse expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The smaller temperatures reached in the fireball lead to smaller thermal dilepton and photon yields (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', [336–338]), while the faster expansion manifests itself in relatively higher mean transverse momenta (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=', [24]) and a shorter lifetime of the fireball, the latter of which can be probed by a combination of the femtoscopic radii, R2 out − R2 side, shown to be proportional to the duration of particle emission [339, 340].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The EOS also plays a large role in the interplay between the initial geometry of the system, the expansion of matter originating from nucleons trapped in the collision zone (participants), and the propagation of nucleons which are either still incoming into the collision region or whose trajectories do not directly cross the collision region (spectators).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In systems colliding at beam energies for which the speed of the fireball expansion is comparable with the speed of the spectators, 36 the resulting complex dynamical evolution affects the transverse expansion of the system and, therefore, the angular particle distributions in the transverse plane dN/dφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In particular, moments of the angular momentum distribution, known as the collective flow coefficients and defined as vn = � dφ cos(nφ) (dN/dφ)/ � dφ (dN/dφ), describe the collective motion of the system and are highly sensitive to the EOS, as shown in numerous hydrodynamic [77, 341–346] and hadronic transport [31, 67, 78, 79, 347, 348] models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' At the same time, collective flow observables can be measured with high precision, making them primary observables used to constrain the EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In off-central collisions, the initial collision zone has an approximately elliptical shape, and the pressure gradients within the collision zone are larger along its short axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' If the spectator nucleons move out of the way before the fireball expands, the pressure gradients in the collision zone lead to particle distributions around midrapidity which have maxima coincident with the reaction plane (“in-plane” emission).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' If, however, the spectators stand in the way of the fireball expansion, this leads to a preferential emission along the long axis of the collision zone (“out-of-plane” emission, also referred to as “squeeze-out” due to the role that the spectators play in the expansion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The preferential emission in either in-plane or out-of-plane direction is described by the second Fourier coefficient of flow v2, also known as the elliptic flow, which is positive in the former case and negative in the latter case (see the lower panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The magnitude of the elliptic flow, as well as the energy at which v2 changes sign, are intrinsically connected to the stiffness of the EOS: for example, a stiffer EOS results in both a faster expansion and a more forceful blocking by spectators, which leads to a larger squeeze-out and a more negative v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The rapidity-dependence of the first Fourier coefficient of flow, the directed flow v1, is also sensitive to the EOS as it measures the degree of spectator deflection due to the interaction with the collision zone [349].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In the center-of-mass frame, the spectators from a nucleus moving in the positive beam direction will be deflected to one side, while the spectators from the other nucleus, moving in the negative beam direction, will be deflected to the opposite side, resulting in a positive v1 at positive rapidities and a negative v2 at negative rapidities (here, the sign of v1 is a matter of convention;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' see [58] for a more detailed explanation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The magnitude of the directed flow in each region and, therefore, its slope at midrapidity are directly related to the EOS: for example, a softer EOS leads to a smaller deflection and a smaller slope of v1 at midrapidity, where in particular a sufficiently soft EOS can even lead to a negative slope of v1 [343, 350].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' We note that spectators are necessary to obtain substantial magnitudes of the slope of the directed flow, as can be seen by its small values at high collision energies (see the upper panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Beyond the collective flow phenomena, the EOS also has an effect on hadron production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In particular, much attention has been given to production of hadrons in heavy-ion collision at energies below the nominal production threshold in NN reactions (“sub-threshold” production), which requires multiple sequential hadron-hadron collisions to occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' The probability of these collisions is significantly higher in the high-density regions, and consequently the yield of sub-threshold probes is expected to be substantially enhanced if higher densities are reached in the collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Of particular importance for the EOS studies is sub-threshold production of K+ mesons, which undergo few final-state interactions with the nuclear medium and therefore mostly leave the fireball unperturbed, making them a sensitive probe of the highest densities reached and, consequently, of the nuclear EOS [87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' Experiments probing densities between 1–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='5n0 As described above, sub-threshold particle yields can be used as probes of the EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content=' In partic- ular, due to their low in-medium cross-section, K+ mesons produced at energies lower than the production threshold of Elab = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='58 GeV (√sNN = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='55 GeV) can carry unperturbed informa- 37 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='6 Elab [GeV] 1 2 3 4 5 6 7 (MK+/A)Au+Au / (MK+/A)C+C 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='6 Elab [GeV] 1 2 3 4 5 6 7 (MK+/A)Au+Au / (MK+/A)C+C soft EOS, pot ChPT hard EOS, pot ChPT soft EOS, IQMD, pot RMF hard EOS, IQMD, pot RMF KaoS soft EOS, IQMD, Giessen cs hard EOS, IQMD, Giessen cs ❑HM ▲ SM FOPI Au+Au protons 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89FQT4oBgHgl3EQfIjX8/content/2301.13253v1.pdf'} +page_content='25 beam energy (A GeV)