重离子碰撞量子输运的半经典描述
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摘要
本文介绍了用于模拟中能重离子碰撞的输运模型,包括玻尔兹曼输运模型和量子分子动力学输运模型.前者数值求解单体相空间分布函数基于玻尔兹曼输运方程的演化,后者模拟多体哈密顿量作用下高斯波包描述的核子演化,两类模型对输运模拟的初始化、平均场、核子-核子散射均有不同处理.将输运模拟结果与中能重离子碰撞实验数据相比较,是获取核力及核物质状态方程的重要手段之一.为了减小由于模型依赖性所造成的理论误差,国际输运领域专家进行了不懈的努力,十多年来比较评估了约二十个输运模型对重离子碰撞体系和周期性边界的箱体体系中的模拟计算结果,包括核子之间的碰撞率与泡利阻塞、核子的集体流以及介子的产生等,取得了阶段性的成果.
This article gives a brief review on transport models for the simulations of intermediate-energy heavy-ion collisions,including the Boltzmann transport models and the quantum molecular dynamics transport models. The former solve numerically the evolution of the one-body phase-space distribution function based on the Boltzmann equation, while the latter simulate the evolution of nucleons described by Gaussian wave-packets under the many-body Hamiltonian.Different treatments for the initialization, the mean-field potential, as well as the nucleon-nucleon scatterings are applied in the two type transport models. Comparing transport simulation results with the experimental data of intermediateenergy heavy-ion collisions is one of the main means to extract the information of the nuclear force and the nuclear equation of state. In order to reduce the theoretical uncertainties of transport simulations, continuous efforts have been made by experts of transport models all over the world. In the past decade, simulation results from about twenty transport models are compared and evaluated in systems of heavy-ion collisions and the box with the periodic boundary condition,mainly concentrating on nucleon-nucleon collisions and the Pauli blocking, the nucleon collective flow, and the meson production, etc.
This article gives a brief review on transport models for the simulations of intermediate-energy heavy-ion collisions,including the Boltzmann transport models and the quantum molecular dynamics transport models. The former solve numerically the evolution of the one-body phase-space distribution function based on the Boltzmann equation, while the latter simulate the evolution of nucleons described by Gaussian wave-packets under the many-body Hamiltonian.Different treatments for the initialization, the mean-field potential, as well as the nucleon-nucleon scatterings are applied in the two type transport models. Comparing transport simulation results with the experimental data of intermediateenergy heavy-ion collisions is one of the main means to extract the information of the nuclear force and the nuclear equation of state. In order to reduce the theoretical uncertainties of transport simulations, continuous efforts have been made by experts of transport models all over the world. In the past decade, simulation results from about twenty transport models are compared and evaluated in systems of heavy-ion collisions and the box with the periodic boundary condition,mainly concentrating on nucleon-nucleon collisions and the Pauli blocking, the nucleon collective flow, and the meson production, etc.
引文
1 Bertsch G F,Das Gupta S.A guide to microscopic models for intermediate energy heavy ion collisions.Phys Rep,1988,160:189-233
2 Aichelin J.“Quantum”molecular dynamics-A dynamical microscopic n-body approach to investigate fragment formation and the nuclear equation of state in heavy ion collisions.Phys Rep,1991,202:233-360
3 Fuchs C,Faessler A,Zabrodin E,et al.Probing the nuclear equation of state by K+production in heavy-ion collisions.Phys Rev Lett,2001,86:1974-1977
4 Danielewicz P,Lacey R,Lynch W G.Determination of the equation of state of dense matter.Science,2002,298:1592-1596
5 Steiner A W,Prakash M,Lattimer J M,et al.Isospin asymmetry in nuclei and neutron stars.Phys Rep,2005,411:325-375
6 Baran V,Colonna M,Greco V,et al.Reaction dynamics with exotic nuclei.Phys Rep,2005,410:335-466
7 Lattimer J M,Prakash M.Neutron star observations:Prognosis for equation of state constraints.Phys Rep,2007,442:109-165
8 Li B A,Chen L W,Ko C M.Recent progress and new challenges in isospin physics with heavy-ion reactions.Phys Rep,2008,464:113-281,arXiv:0804.3580
9 Li B A,Ko C M,Ren Z.Equation of state of asymmetric nuclear matter and collisions of neutron-rich nuclei.Phys Rev Lett,1997,78:1644-1647
10 Famiano M A,Liu T,Lynch W G,et al.Neutron and proton transverse emission ratio measurements and the density dependence of the asymmetry term of the nuclear equation of state.Phys Rev Lett,2001,97:052701
11 Tsang M B,Friedman W A,Gelbke C K,et al.Isotopic scaling in nuclear reactions.Phys Rev Lett,2001,86:5023-5026
12 Tsang M B,Liu T X,Shi L,et al.Isospin diffusion and the nuclear symmetry energy in heavy ion reactions.Phys Rev Lett,2004,92:062701
13 Li B A.Neutron-proton differential flow as a probe of isospin-dependence of the nuclear equation of state.Phys Rev Lett,2000,85:4221-4224
14 Li B A.Probing the high density behavior of the nuclear symmetry energy with high energy heavy-ion collisions.Phys Rev Lett,2002,88:192701
15 Xu J,Ko C M,Oh Y.Isospin-dependent pion in-medium effects on the charged-pion ratio in heavy ion collisions.Phys Rev C,2010,81:024910,arXiv:0906.1602
16 Hong J,Danielewicz P.Subthreshold pion production within a transport description of central Au+Au collisions.Phys Rev C,2014,90:024605,arXiv:1307.7654
17 Zhang Z,Ko C M.Medium effects on pion production in heavy ion collisions.Phys Rev C,2017,95:064604,arXiv:1701.06682
18 Ferini G,Gaitanos T,Colonna M,et al.Isospin effects on subthreshold kaon production at intermediate energies.Phys Rev Lett,2006,97:202301
19 Bertsch G F,Kruse H,Gupta S D.Boltzmann equation for heavy ion collisions.Phys Rev C,1984,29:673-675
20 Hartnack C,Li Z,Neise L,et al.Quantum molecular dynamics a microscopic model from UNILAC to CERN energies.Nucl Phys A,1989,495:303-319
21 Xiao Z,Li B A,Chen L W,et al.Circumstantial evidence for a soft nuclear symmetry energy at suprasaturation densities.Phys Rev Lett,2009,102:062502,arXiv:0808.0186
22 Feng Z Q,Jin G M.Probing high-density behavior of symmetry energy from pion emission in heavy-ion collisions.Phys Lett B,2010,683:140-144,arXiv:0904.2990
23 Xie W J,Su J,Zhu L,et al.Symmetry energy and pion production in the Boltzmann-Langevin approach.Phys Lett B,2013,718:1510-1514
24 Kolomeitsev E E,Hartnack C,Barz H W,et al.Transport theories for heavy-ion collisions in the 1 A GeV regime.J Phys G-Nucl Part Phys,2005,31:S741-S757
25 Xu J,Chen L W,Tsang M Y B,et al.Understanding transport simulations of heavy-ion collisions at 100 A and 400 A MeV:Comparison of heavy-ion transport codes under controlled conditions.Phys Rev C,2016,93:044609,arXiv:1603.08149
26 Zhang Y X,Wang Y J,Colonna M,et al.Comparison of heavy-ion transport simulations:Collision integral in a box.Phys Rev C,2018,97:034625,arXiv:1711.05950
2 Aichelin J.“Quantum”molecular dynamics-A dynamical microscopic n-body approach to investigate fragment formation and the nuclear equation of state in heavy ion collisions.Phys Rep,1991,202:233-360
3 Fuchs C,Faessler A,Zabrodin E,et al.Probing the nuclear equation of state by K+production in heavy-ion collisions.Phys Rev Lett,2001,86:1974-1977
4 Danielewicz P,Lacey R,Lynch W G.Determination of the equation of state of dense matter.Science,2002,298:1592-1596
5 Steiner A W,Prakash M,Lattimer J M,et al.Isospin asymmetry in nuclei and neutron stars.Phys Rep,2005,411:325-375
6 Baran V,Colonna M,Greco V,et al.Reaction dynamics with exotic nuclei.Phys Rep,2005,410:335-466
7 Lattimer J M,Prakash M.Neutron star observations:Prognosis for equation of state constraints.Phys Rep,2007,442:109-165
8 Li B A,Chen L W,Ko C M.Recent progress and new challenges in isospin physics with heavy-ion reactions.Phys Rep,2008,464:113-281,arXiv:0804.3580
9 Li B A,Ko C M,Ren Z.Equation of state of asymmetric nuclear matter and collisions of neutron-rich nuclei.Phys Rev Lett,1997,78:1644-1647
10 Famiano M A,Liu T,Lynch W G,et al.Neutron and proton transverse emission ratio measurements and the density dependence of the asymmetry term of the nuclear equation of state.Phys Rev Lett,2001,97:052701
11 Tsang M B,Friedman W A,Gelbke C K,et al.Isotopic scaling in nuclear reactions.Phys Rev Lett,2001,86:5023-5026
12 Tsang M B,Liu T X,Shi L,et al.Isospin diffusion and the nuclear symmetry energy in heavy ion reactions.Phys Rev Lett,2004,92:062701
13 Li B A.Neutron-proton differential flow as a probe of isospin-dependence of the nuclear equation of state.Phys Rev Lett,2000,85:4221-4224
14 Li B A.Probing the high density behavior of the nuclear symmetry energy with high energy heavy-ion collisions.Phys Rev Lett,2002,88:192701
15 Xu J,Ko C M,Oh Y.Isospin-dependent pion in-medium effects on the charged-pion ratio in heavy ion collisions.Phys Rev C,2010,81:024910,arXiv:0906.1602
16 Hong J,Danielewicz P.Subthreshold pion production within a transport description of central Au+Au collisions.Phys Rev C,2014,90:024605,arXiv:1307.7654
17 Zhang Z,Ko C M.Medium effects on pion production in heavy ion collisions.Phys Rev C,2017,95:064604,arXiv:1701.06682
18 Ferini G,Gaitanos T,Colonna M,et al.Isospin effects on subthreshold kaon production at intermediate energies.Phys Rev Lett,2006,97:202301
19 Bertsch G F,Kruse H,Gupta S D.Boltzmann equation for heavy ion collisions.Phys Rev C,1984,29:673-675
20 Hartnack C,Li Z,Neise L,et al.Quantum molecular dynamics a microscopic model from UNILAC to CERN energies.Nucl Phys A,1989,495:303-319
21 Xiao Z,Li B A,Chen L W,et al.Circumstantial evidence for a soft nuclear symmetry energy at suprasaturation densities.Phys Rev Lett,2009,102:062502,arXiv:0808.0186
22 Feng Z Q,Jin G M.Probing high-density behavior of symmetry energy from pion emission in heavy-ion collisions.Phys Lett B,2010,683:140-144,arXiv:0904.2990
23 Xie W J,Su J,Zhu L,et al.Symmetry energy and pion production in the Boltzmann-Langevin approach.Phys Lett B,2013,718:1510-1514
24 Kolomeitsev E E,Hartnack C,Barz H W,et al.Transport theories for heavy-ion collisions in the 1 A GeV regime.J Phys G-Nucl Part Phys,2005,31:S741-S757
25 Xu J,Chen L W,Tsang M Y B,et al.Understanding transport simulations of heavy-ion collisions at 100 A and 400 A MeV:Comparison of heavy-ion transport codes under controlled conditions.Phys Rev C,2016,93:044609,arXiv:1603.08149
26 Zhang Y X,Wang Y J,Colonna M,et al.Comparison of heavy-ion transport simulations:Collision integral in a box.Phys Rev C,2018,97:034625,arXiv:1711.05950