同位旋相关的核子—核子散射截面的介质修正研究
|
摘要
输运理论模型作为模拟重离子反应的一种重要工具,已经被广泛应用,而且取得了很大成功。碰撞项作为输运理论的两部分输入量之一,随着反应能量的增大,其贡献也越来越大,尤其是在中能重离子反应中。长期以来,人们对平均场做了大量的研究,通过密度依赖引入了介质效应;而对碰撞项的研究还很少,大多采用的仍然是自由的核子-核子(NN)散射截面(即实验测量得到的NN散射截面)。介质中的NN散射截面无法从直接实验上测量得到,只能依靠理论计算给出。但是,目前理论计算的结果差别很大,不同的理论或相同理论计算细节不同给出的结果存在比较大的差别。这种差别,不仅存在于定量上,而且存在于定性方面:主要是在大小和同位旋依赖方面。为了消除这种差别,亟需通过寻找灵敏实验观测量,通过实验与理论计算的比较,间接获取介质中的NN散射截面的信息。
本工作主要基于改进了的量子分子动力学模型(ImQMD05模型),对介质中的NN散射截面进行了研究。我们研究了入射能量为400AMeV的~(96)Ru+~(96)Ru及~(96)Zr+~(96)Zr两个对称反应系统中出射的自由中子、自由质子和它们的比值n/p,在不同的截面下的动能分布、角分布等,从中寻找了一些敏感的观测量来对介质中的NN散射截面进行约束。关于截面的选取,一方面围绕截面的同位旋依赖的不同,选取R_(iso)~(med)=σ_(np)~(med)/σ_(pp(nn))~(med)=0\0.10\0.1\0.333\1\2\∞七种不同的同位旋依赖的截面;另一方面围绕截面的大小不同,选取R~(med)=σ_(NN)~(med)/σ_(NN)~(free)=1\(1+0.4ρ/ρ_0)\2三种大小不同的截面。
首先,通过对~(96)Ru+~(96)Ru系统出射的自由核子在动量空间的出射数目、经历的最大密度、经历的碰撞次数、达到最大密度的时间等物理量的研究,全面分析了反应系统的出射机制。通过分析发现,受截面直接影响比较大的自由核子,主要从横向出射;由于它们经历的碰撞次数少,所以能量耗散少,出射的动能比较大。
其次,结合出射核子的能谱和角分布的分析得到,在同位旋相关的不同截面下,这部分自由中子与自由质子的比值n/p,敏感地依赖于介质中同位旋相关的NN散射截面;随着R_(iso)~(med)的增加,n/p单调地减小。同时,通过比较~(96)Ru+~(96)Ru及~(96)Zr+~(96)Zr两个系统发现,丰中子系统表现出更为明显的同位旋依赖性。
对截面大小的分析方面,同样结合自由核子的出射机制、能谱、角分布进行分析,发现截面的大小变化对自由核子的中质比(n/p)几乎没有影响,对核阻止本领的影响非常明显。通过对两个阻止本领的观测量Q_(zz)和E_(RAT)进行分析得到,O_(zz)/A随R~(med)的增大单调减小,E_(RAT)随R~(med)的增大单调增大。比较两个不同丰中子程度的系统发现,系统的丰中子程度对阻止本领随截面大小的变化没有影响,只是存在数值上的差别。
Transport theory is an important method to simulate the process ofheavy-ion reactions, and the collision term is one of the input parts in thetransport models. Free nucleon-nucleon cross section has been always used inthe collision term. However, the contributions from nucleon-nucleoncollisions are as important as that from the mean field contributions atintermediate and high energy heavy ion collisions in the transport modelapproaches. The information on the isospin dependence of the in-mediumnucleon-nucleon cross section is very important for us to constrain thedensity dependence of symmetry energy, especially at super-saturationdensities. Up to now, there is not much study on isospin dependence of thein-medium NN cross section through heavy ion collisions and very largeuncertainty exists concerning the isospin dependence of the in-medium NNcross section. Therefore, to find sensitive observables and then to constrainthe isospin dependence of the in-medium NN cross section is necessary forfinally accurately constrain the density dependence of the symmetry energy.The aim of this work is to search for the sensitive observable for the isospindependence of the in-medium nucleon-nucleon cross sections.
The influence of the isospin dependence of in-medium nucleon-nucleoncross sections on the n/p ratios for emitted nucleons in reactions ~(96)Zr+~(96)Zrand ~(96)Ru+~(96)Ru at E/A = 400MeV is investigated by mean of the ImproveQuantum Molecular Dynamics model. The reason for select E/A = 400MeVis that the nucleon-nucleon cross sections are important and elastic collisionchannel is still dominant at this incident energy.
Firstly, we investigate the nucleon emission mechanism. Our resultsshow that the emitted nucleons with higher kinetic energies carry clearinformation of the isospin dependence of in-medium NN cross sectionsbecause they experience less two-body scatterings. Therefore, the n/p ratiofor emitted high energy nucleons is selected to study the isospin dependence of the in-medium nucleon-nucleon cross sections.
Secondly, the influences of isospin dependence of in-mediumnucleon-nucleon cross sections on the n/p ratios of emitted nucleons aresystematically analyzed by varying the ratio R_(iso)~(med)=σ_(np)~(med)/σ_(pp(nn))~(med).Thecorrelation between the n/p ratios for emitted nucleons with E_k＞300MeV andR~(med)=σ_(NN)~(med)/σ_(NN)~(free) shows that n/p ratio depends on R_(iso)~(med) and the isospinasymmetry of the reaction system. Therefore, we propose that the n/p ratio ofemitted high energy nucleons in very neutron-rich reaction system at severalhundreds AMeV can be taken as sensitive observable to constrain the isospindependence of in-medium nucleon-nucleon cross sections.
Based on the analysis for the difference of the energy distribution andangular distribution on the NN cross section, we find the very small influenceof the cross section on the free neutron and proton ratios, and the obviousinfluence of the stopping power. The calculation result is that the variableQ_(zz)/A decrease with increasing R~(med) and E_(RAT) increase with increasingR~(med). For the different neutron-rich systems, we obtain the small influence ofthe tendency of stopping power on the NN cross section, and the differenceexists in the calculated values.
本工作主要基于改进了的量子分子动力学模型(ImQMD05模型),对介质中的NN散射截面进行了研究。我们研究了入射能量为400AMeV的~(96)Ru+~(96)Ru及~(96)Zr+~(96)Zr两个对称反应系统中出射的自由中子、自由质子和它们的比值n/p,在不同的截面下的动能分布、角分布等,从中寻找了一些敏感的观测量来对介质中的NN散射截面进行约束。关于截面的选取,一方面围绕截面的同位旋依赖的不同,选取R_(iso)~(med)=σ_(np)~(med)/σ_(pp(nn))~(med)=0\0.10\0.1\0.333\1\2\∞七种不同的同位旋依赖的截面;另一方面围绕截面的大小不同,选取R~(med)=σ_(NN)~(med)/σ_(NN)~(free)=1\(1+0.4ρ/ρ_0)\2三种大小不同的截面。
首先,通过对~(96)Ru+~(96)Ru系统出射的自由核子在动量空间的出射数目、经历的最大密度、经历的碰撞次数、达到最大密度的时间等物理量的研究,全面分析了反应系统的出射机制。通过分析发现,受截面直接影响比较大的自由核子,主要从横向出射;由于它们经历的碰撞次数少,所以能量耗散少,出射的动能比较大。
其次,结合出射核子的能谱和角分布的分析得到,在同位旋相关的不同截面下,这部分自由中子与自由质子的比值n/p,敏感地依赖于介质中同位旋相关的NN散射截面;随着R_(iso)~(med)的增加,n/p单调地减小。同时,通过比较~(96)Ru+~(96)Ru及~(96)Zr+~(96)Zr两个系统发现,丰中子系统表现出更为明显的同位旋依赖性。
对截面大小的分析方面,同样结合自由核子的出射机制、能谱、角分布进行分析,发现截面的大小变化对自由核子的中质比(n/p)几乎没有影响,对核阻止本领的影响非常明显。通过对两个阻止本领的观测量Q_(zz)和E_(RAT)进行分析得到,O_(zz)/A随R~(med)的增大单调减小,E_(RAT)随R~(med)的增大单调增大。比较两个不同丰中子程度的系统发现,系统的丰中子程度对阻止本领随截面大小的变化没有影响,只是存在数值上的差别。
Transport theory is an important method to simulate the process ofheavy-ion reactions, and the collision term is one of the input parts in thetransport models. Free nucleon-nucleon cross section has been always used inthe collision term. However, the contributions from nucleon-nucleoncollisions are as important as that from the mean field contributions atintermediate and high energy heavy ion collisions in the transport modelapproaches. The information on the isospin dependence of the in-mediumnucleon-nucleon cross section is very important for us to constrain thedensity dependence of symmetry energy, especially at super-saturationdensities. Up to now, there is not much study on isospin dependence of thein-medium NN cross section through heavy ion collisions and very largeuncertainty exists concerning the isospin dependence of the in-medium NNcross section. Therefore, to find sensitive observables and then to constrainthe isospin dependence of the in-medium NN cross section is necessary forfinally accurately constrain the density dependence of the symmetry energy.The aim of this work is to search for the sensitive observable for the isospindependence of the in-medium nucleon-nucleon cross sections.
The influence of the isospin dependence of in-medium nucleon-nucleoncross sections on the n/p ratios for emitted nucleons in reactions ~(96)Zr+~(96)Zrand ~(96)Ru+~(96)Ru at E/A = 400MeV is investigated by mean of the ImproveQuantum Molecular Dynamics model. The reason for select E/A = 400MeVis that the nucleon-nucleon cross sections are important and elastic collisionchannel is still dominant at this incident energy.
Firstly, we investigate the nucleon emission mechanism. Our resultsshow that the emitted nucleons with higher kinetic energies carry clearinformation of the isospin dependence of in-medium NN cross sectionsbecause they experience less two-body scatterings. Therefore, the n/p ratiofor emitted high energy nucleons is selected to study the isospin dependence of the in-medium nucleon-nucleon cross sections.
Secondly, the influences of isospin dependence of in-mediumnucleon-nucleon cross sections on the n/p ratios of emitted nucleons aresystematically analyzed by varying the ratio R_(iso)~(med)=σ_(np)~(med)/σ_(pp(nn))~(med).Thecorrelation between the n/p ratios for emitted nucleons with E_k＞300MeV andR~(med)=σ_(NN)~(med)/σ_(NN)~(free) shows that n/p ratio depends on R_(iso)~(med) and the isospinasymmetry of the reaction system. Therefore, we propose that the n/p ratio ofemitted high energy nucleons in very neutron-rich reaction system at severalhundreds AMeV can be taken as sensitive observable to constrain the isospindependence of in-medium nucleon-nucleon cross sections.
Based on the analysis for the difference of the energy distribution andangular distribution on the NN cross section, we find the very small influenceof the cross section on the free neutron and proton ratios, and the obviousinfluence of the stopping power. The calculation result is that the variableQ_(zz)/A decrease with increasing R~(med) and E_(RAT) increase with increasingR~(med). For the different neutron-rich systems, we obtain the small influence ofthe tendency of stopping power on the NN cross section, and the differenceexists in the calculated values.
引文
[1] 丁大钊 陈永寿 张焕乔.原子核物理进展[M].上海.上海科学技术出版社,1997,440
[2] B A Li, C M Ko and W Bauer. Excitation Functions of Stopping Power and Flow in Relativistic Heavy-Ion Collisions[J]. Nucl Phys A, 1998, 630:556-562
[3] Chen L W, Ko C M and Li B A. Determination of the Stiffness of the Nuclear Symmetry Energy from Isospin Diffusion[J].Phy Rev Lett, 2005, 94:032701
[4] Li Q F, Li Z X, Zhao E G. Density and temperature dependence of nucleon-nucleon elastic cross section[J]. Phys Rev C ,2004,69:017601
[5] W A Friedman. Basis for a Characteristic Temperature in Nuclear Fragmentation[J]. Phys Rev Lett, 1988, 60:2125-2128;Rapid massive cluster formation[J].Phys Rev C,1990,42:667-673
[6] D H E Cross. Statistical decay of very hot nuclei-the production of large clusters Rep[J]. Rep Prog Phys, 1990, 53:605-658
[7] L G Moretto et al. .Are Multifragment Emission Probabilities Reducible to an Elementary Binary Emission Probability[J]. Phys Rev Lett,1995,74:1530-1533
[8] L G Moretto et al.. Reducibility and thermal scaling in nuclear multifragmentation[J].Phys Rep, 1997,287:249-336
[9] L G Moretto et al..Resilient reducibility in nuclear multifragmentation[J].Phys Rev C, 1999, 60:031601
[10] J P Boodorf et al.. Statistical multifragmentation of nuclei[J]. Phys Rep, 1995,133-221
[11] R J Charity. computer code. available via http://wunmr. wustl. edu/～rc/gemini/
[12] T Maruyama et al.. Fragment Mass Distribution in Intermediate Energy Heavy-Ion Collisions and the Reaction Time Scale[J]. Prog Theor Phys,1992,87:1367-1376
[13] Koji Niita et al.. Analysis of the (N, xN' ) reactions by quantum molecular dynamics plus statistical decay model[J]. Phys Rev C, 1995,52:2620-2635
[14] J Aichelin. Quantum molecular dynamics-A dynamicl microscopic n-body approach to investigate fragment formation and the nuclear equation of state in heavy ion collisions[J]. Phys Rep, 1991, 202:233
[15] C Hartnack et al.. Quantum molecular dynamics a microscopic model from UNILAC to CERN energies[J].Nucl Phys A, 1989, 495, 303-319
[16] G F Bertsch et al. .Boltzmann equation for heavy ion collisions[J]. Phys Rev C,1984,29:673-675
[17] J Aichelin et al. .Numerical simulation of medium energy heavy ion reactions[J]. Phys Rev C,1985,31:1730-1738
[18] Bertsch F G and Gupta S D. A guide to microscopic models for intermediate energy heavy ion collisions[J]. Phys Rep, 1988, 160:189
[19] C Gregoire et al.. Semi-classical dynamics of heavy-ion reactions[J].Nucl Phys A, 1987, 465:317-338
[20] Persram D and C Gale. Elliptic flow in intermediate energy heavy ion collisions and in-mediume effects[J]. Phys Rev C,2002,65:064611
[21] A B Larionov, W Cassing, C Greiner and U Mosel.Squeeze-out of nuclear matter in peripheral heavy-ion collisions and momentum-dependent effective interactions[J]. Phys Rev C,2000,62:064611
[22] P Danielewicz, R Lacey and W G Lynch. Determination of the Equation of State of Dense Matter[J]. Science, 2002, 298:1592
[23] A Bohnet et al.. Quantum molecular-dynamics approach to heavy-ion collisions with Brueckner G-matrix cross sections[J].Nucl Phys A, 1989, 494:349
[24] A Faessler. Description of heavy ion reaction with medium dependent forces[J]. Nucl Phys A, 1989, 495:103-113
[25] M Kohno et al.. In-medium nucleon-nucleon cross sections from norelativistic reaction matrices in nuclear matter[J]. Phys Rev C,1998,57:3495
[26] C Fuchs,A Faessler and M El-Shabshiry. Off-shell behavior of the in-medium nucleon-nucleon cross section[J]. Phys Rev C, 2001, 64:024003
[27] Brown B A. Neutron radii in nuclei and the neutron equation ofstate[J]. Phys Rev Lett,2000, 85:5296
[28] Aichelin J and Bertsch G. Numerical simulation of medium energy heavy ion reactions[J].Phys Rev C,1985, 31:1730
[29] J Aichelin,G peilert, A Bohnetetal. Quantum molecular dynamics approach to heavy ion collisions: Description of model , comparison with fragmentation data , and the mechanism of fragment formation[J]. Phys Rev C, 1988, 37:2451
[30] Ning Wang, Xizhen Wu, and Zhuxia Li. Dynamic study of fusion reactions for 40, 48Ca+90, 96Zr around the Coulomb barrier[J].Phys Rev C,2003, 67:024604
[31] Ning Wang,Zhuxia Li, Xizhen Wu, Junlong Tian, Yingxun Zhang,and Min Liu. Further development of the improved quantum molecular dynamics model and its application to fusion reactions near the barrier[J].Phys Rev C,2004,69:034608
[32] Ning Wang, Zhuxia Li, Xizhen Wu. Improved quantum molecular dynamics model and its applications to fusion reaction near barrier[J]. Phys Rev C.2002.65:064608
[33] 王宁.量子分子动力学模型的发展及其在低能重离子反应中的应用(博士毕业论文).中国原子能科学研究院.北京2003
[34] Yingxun Zhang, et al..The influence of cluster emission and the symmetry energy on neutron-proton spectral double ratios[J].Phys Lett B,2008, 664:145-148
[35] Yingxun Zhang, Zhuxia Li,and Pawel Danielewicz. In-medium NN cross sections deteminded from the nuclear stopping and collective flow in heavy-ion collisions at intermediate energies[J]. Phys Rev C,2007,75: 034615
[36] 张英逊.中能重离子反应中的同位旋效应及核态方程的研究(博士毕业论文).中国原子能科学研究院.北京.2005
[37] 欧立.质子引起的散裂反应及介质内的核子-核子有效相互作用和两体散射截面(博士毕业论文).中国原子能科学研究院.北京.2007
[38] Ning Wang, Zhuxia Li, Xizhen Wu, Engguang Zhao. Search for Possible way of Producing Super-Heavy Elements[J].Mod Phys Lett A, 2005,20:2619-2627
[39] Tian Junlong, Wu Xizhen, Li Zhu-Xia, Zhao Kai. Superheavy fragments produced in the asymmetric strongly damped collision[J].Chin Phys C,2008, 32:34-39
[40] Yingxun Zhang, Zhuxia Li. Probing the density dependence of the symmetry potential with peripheral heavy-ion collisions[J]. Phys Rev C2005, 71:024604
[41] Yingxun Zhang, Xizhen Wu, Zhuxia Li. Connection between the largest Lyapunov exponent, density fluctuation, and multifragmentation in excited nuclear systems[J]. Phys Rev C, 2004, 69:044609
[42] Yingxun Zhang, Zhuxia Li.Elliptic flow and system size dependence of transition energies at intermediate energies[J]. Phys Rev C, 2006,74: 014602
[43] A Bohr and B R Mottelson. Nuclear Structure, Vol. Ⅱ[M]. W A Benjiamin, Inc., Reading, Mass., 1975, pp:137-152
[44] 胡济民 杨伯君 郑春开.原子核理论[M].第一卷,原子能出版社,1987,p:40
[45] David H, Boal and James N Glosi. Quantum collision theory with phase-space distribution functions[J]. Phys Rev C, 1988, 38:1870-1878
[46] Toshiki Maruyama, Koji Niita, and Akira Iwamoto. Quantum collision theory with phase-space distribution functions[J]. Phys Rev C, 1996, 53:297-304
[47] Massimo Papa, Toshiki Maruyama and Aldo Bonasera. Constrained molecular dynamics approach to fermionic systems[J]. Phys Rev C. 2001, 64:024612
[48] Ch Hartnack, Rajeev k Puri and J Aichlin. Modelling the many-body dynamics of heavy ion collisions: Present status and future perspective[J]. Eur Phys J A. 1998, 1:151-169
[49] Toshiki Maruyama, Adlo Bonasera, et al.. Formation and decay of super heavy systems[J].Eur Phys J A, 2002, 41:191-197
[50] M Beiner, H Flocard, N V Giai and P Quentin. Nuclear ground-state properties and selfconsistent calculations with the Skyrme interaction:(Ⅰ). Spherical description[J].Nucl Phys A, 1975, 238:29
[51] E Chabanat, P Bonche, P Haensel, J Meyer and R Schaeffr.A Skyrme parametrization from subnuclear to neutron star densities[J]. Nucl Phys A, 1997,627:710
[52] D Vautherin and D M Brink. Hartree-Fock Calculations with Skyrme' s Interaction. Ⅰ . Spherical Nuclei[J]. Phys Rev C,1972, 5:626
[53] 胡济民 杨伯君 郑春开 卓益忠.原子核物理[M].北京.原子能出版社,1993
[54] 赵凯 李祝霞 吴锡真 王宁 张英逊 田俊龙 张焕乔 刘祖华.~(40,48)Ca+~(90,96)Zr融合反应的动力学模型研究[J].高能物理与核物理,2006,30:26
[55] V S U Maheswari, C Fuchs, A Faessler Z S Wang and D S Kosov. Role of isospin dependent mean field in pion production in heavy ion reactions[J]. Phys Rev C,1998, 57:922
[56] R K Puri,J Aichelin. Simulated Annealing Clusterization Algorithm for Studying the Multifragmentation[j]. Journal of Computational Phys, 2000,160:245-266
[57] W Neubert, A S Botvina. What is the Physics behind the 3He-4He Anomaly ?[J].Eur Phys J A, 2000, 7:101-106
[58] W Cassing, W Metag, U Mosel and K Niita. Production of energetic particles in heavy-ion collisions[J]. Phys Rep, 1990,188:363
[59] J Aichelin, A Rosenhauer, G Peilert, H St(?)cker and W Greiner. Importance of momentum-dependent interactions for the extraction of the nuclear equation of state from high-energy heavy-ion collisions[J]. Phys Rev Lett,1987, 58:1926
[60] M Asakwa, C M Ko, P Levai and X J Qiu.Rho meson in dense hadronic matter[J].Phys Rev C, 1992,46:1159
[61] C M Ko, Q Li and R C Wang. Relativistic Vlasov equation for heavy-ion collisions[J].Phys Rev Lett,1987, 59:1084
[62] J Cugon, D V H(?)te, J Vandermeulen. Simple parametrization of cross-sections for nuclear transport studies up to the GeV range[J].Nuclear Instruments and Methods in Physics Research B,1996,111:215-220
[63] Guangjun Mao, Zhuxia Li,Yizhong Zhuo and Ziqiang Yu. Medium effects on the NN inelastic cross section in relativistic heavy-ion collisions[J].Phys Lett B,1994, 327:183-186
[64] Q Li, Z Li and G Mao. Isospin dependence of nucleon-nucleon elastic cross section[J].Phys Rev C, 2000, 62:014606
[65] F Rami et al., Isospin-tracing: A probe of non-equilibrium in central heavy-ion collisions,Phys. Rev. Lett, 2000, 84:1120-1123
[66] Bao-An Li, Pawel Danielewicz, and William G Lynch. Probing the isospin dependence of the in-medium nucleon-nucleon cross sections with radioactive beams[J]. Phys Rev C, 2005, 71:054603
[67] 卢希庭.原子核物理[M].北京.原子能出版社.2000,第二版,p:102-108
[68] 宁平治 李磊 闵德芬.原子核物理基础[M].北京.高等教育出版社.2003,第一版,P:197-206
[69] Wilmot N Hess. Summary of High-Energy Nucleon-Nucleon Cross-Section Data[J].Rev Mod Phys, 1958, 30:368-400
[2] B A Li, C M Ko and W Bauer. Excitation Functions of Stopping Power and Flow in Relativistic Heavy-Ion Collisions[J]. Nucl Phys A, 1998, 630:556-562
[3] Chen L W, Ko C M and Li B A. Determination of the Stiffness of the Nuclear Symmetry Energy from Isospin Diffusion[J].Phy Rev Lett, 2005, 94:032701
[4] Li Q F, Li Z X, Zhao E G. Density and temperature dependence of nucleon-nucleon elastic cross section[J]. Phys Rev C ,2004,69:017601
[5] W A Friedman. Basis for a Characteristic Temperature in Nuclear Fragmentation[J]. Phys Rev Lett, 1988, 60:2125-2128;Rapid massive cluster formation[J].Phys Rev C,1990,42:667-673
[6] D H E Cross. Statistical decay of very hot nuclei-the production of large clusters Rep[J]. Rep Prog Phys, 1990, 53:605-658
[7] L G Moretto et al. .Are Multifragment Emission Probabilities Reducible to an Elementary Binary Emission Probability[J]. Phys Rev Lett,1995,74:1530-1533
[8] L G Moretto et al.. Reducibility and thermal scaling in nuclear multifragmentation[J].Phys Rep, 1997,287:249-336
[9] L G Moretto et al..Resilient reducibility in nuclear multifragmentation[J].Phys Rev C, 1999, 60:031601
[10] J P Boodorf et al.. Statistical multifragmentation of nuclei[J]. Phys Rep, 1995,133-221
[11] R J Charity. computer code. available via http://wunmr. wustl. edu/～rc/gemini/
[12] T Maruyama et al.. Fragment Mass Distribution in Intermediate Energy Heavy-Ion Collisions and the Reaction Time Scale[J]. Prog Theor Phys,1992,87:1367-1376
[13] Koji Niita et al.. Analysis of the (N, xN' ) reactions by quantum molecular dynamics plus statistical decay model[J]. Phys Rev C, 1995,52:2620-2635
[14] J Aichelin. Quantum molecular dynamics-A dynamicl microscopic n-body approach to investigate fragment formation and the nuclear equation of state in heavy ion collisions[J]. Phys Rep, 1991, 202:233
[15] C Hartnack et al.. Quantum molecular dynamics a microscopic model from UNILAC to CERN energies[J].Nucl Phys A, 1989, 495, 303-319
[16] G F Bertsch et al. .Boltzmann equation for heavy ion collisions[J]. Phys Rev C,1984,29:673-675
[17] J Aichelin et al. .Numerical simulation of medium energy heavy ion reactions[J]. Phys Rev C,1985,31:1730-1738
[18] Bertsch F G and Gupta S D. A guide to microscopic models for intermediate energy heavy ion collisions[J]. Phys Rep, 1988, 160:189
[19] C Gregoire et al.. Semi-classical dynamics of heavy-ion reactions[J].Nucl Phys A, 1987, 465:317-338
[20] Persram D and C Gale. Elliptic flow in intermediate energy heavy ion collisions and in-mediume effects[J]. Phys Rev C,2002,65:064611
[21] A B Larionov, W Cassing, C Greiner and U Mosel.Squeeze-out of nuclear matter in peripheral heavy-ion collisions and momentum-dependent effective interactions[J]. Phys Rev C,2000,62:064611
[22] P Danielewicz, R Lacey and W G Lynch. Determination of the Equation of State of Dense Matter[J]. Science, 2002, 298:1592
[23] A Bohnet et al.. Quantum molecular-dynamics approach to heavy-ion collisions with Brueckner G-matrix cross sections[J].Nucl Phys A, 1989, 494:349
[24] A Faessler. Description of heavy ion reaction with medium dependent forces[J]. Nucl Phys A, 1989, 495:103-113
[25] M Kohno et al.. In-medium nucleon-nucleon cross sections from norelativistic reaction matrices in nuclear matter[J]. Phys Rev C,1998,57:3495
[26] C Fuchs,A Faessler and M El-Shabshiry. Off-shell behavior of the in-medium nucleon-nucleon cross section[J]. Phys Rev C, 2001, 64:024003
[27] Brown B A. Neutron radii in nuclei and the neutron equation ofstate[J]. Phys Rev Lett,2000, 85:5296
[28] Aichelin J and Bertsch G. Numerical simulation of medium energy heavy ion reactions[J].Phys Rev C,1985, 31:1730
[29] J Aichelin,G peilert, A Bohnetetal. Quantum molecular dynamics approach to heavy ion collisions: Description of model , comparison with fragmentation data , and the mechanism of fragment formation[J]. Phys Rev C, 1988, 37:2451
[30] Ning Wang, Xizhen Wu, and Zhuxia Li. Dynamic study of fusion reactions for 40, 48Ca+90, 96Zr around the Coulomb barrier[J].Phys Rev C,2003, 67:024604
[31] Ning Wang,Zhuxia Li, Xizhen Wu, Junlong Tian, Yingxun Zhang,and Min Liu. Further development of the improved quantum molecular dynamics model and its application to fusion reactions near the barrier[J].Phys Rev C,2004,69:034608
[32] Ning Wang, Zhuxia Li, Xizhen Wu. Improved quantum molecular dynamics model and its applications to fusion reaction near barrier[J]. Phys Rev C.2002.65:064608
[33] 王宁.量子分子动力学模型的发展及其在低能重离子反应中的应用(博士毕业论文).中国原子能科学研究院.北京2003
[34] Yingxun Zhang, et al..The influence of cluster emission and the symmetry energy on neutron-proton spectral double ratios[J].Phys Lett B,2008, 664:145-148
[35] Yingxun Zhang, Zhuxia Li,and Pawel Danielewicz. In-medium NN cross sections deteminded from the nuclear stopping and collective flow in heavy-ion collisions at intermediate energies[J]. Phys Rev C,2007,75: 034615
[36] 张英逊.中能重离子反应中的同位旋效应及核态方程的研究(博士毕业论文).中国原子能科学研究院.北京.2005
[37] 欧立.质子引起的散裂反应及介质内的核子-核子有效相互作用和两体散射截面(博士毕业论文).中国原子能科学研究院.北京.2007
[38] Ning Wang, Zhuxia Li, Xizhen Wu, Engguang Zhao. Search for Possible way of Producing Super-Heavy Elements[J].Mod Phys Lett A, 2005,20:2619-2627
[39] Tian Junlong, Wu Xizhen, Li Zhu-Xia, Zhao Kai. Superheavy fragments produced in the asymmetric strongly damped collision[J].Chin Phys C,2008, 32:34-39
[40] Yingxun Zhang, Zhuxia Li. Probing the density dependence of the symmetry potential with peripheral heavy-ion collisions[J]. Phys Rev C2005, 71:024604
[41] Yingxun Zhang, Xizhen Wu, Zhuxia Li. Connection between the largest Lyapunov exponent, density fluctuation, and multifragmentation in excited nuclear systems[J]. Phys Rev C, 2004, 69:044609
[42] Yingxun Zhang, Zhuxia Li.Elliptic flow and system size dependence of transition energies at intermediate energies[J]. Phys Rev C, 2006,74: 014602
[43] A Bohr and B R Mottelson. Nuclear Structure, Vol. Ⅱ[M]. W A Benjiamin, Inc., Reading, Mass., 1975, pp:137-152
[44] 胡济民 杨伯君 郑春开.原子核理论[M].第一卷,原子能出版社,1987,p:40
[45] David H, Boal and James N Glosi. Quantum collision theory with phase-space distribution functions[J]. Phys Rev C, 1988, 38:1870-1878
[46] Toshiki Maruyama, Koji Niita, and Akira Iwamoto. Quantum collision theory with phase-space distribution functions[J]. Phys Rev C, 1996, 53:297-304
[47] Massimo Papa, Toshiki Maruyama and Aldo Bonasera. Constrained molecular dynamics approach to fermionic systems[J]. Phys Rev C. 2001, 64:024612
[48] Ch Hartnack, Rajeev k Puri and J Aichlin. Modelling the many-body dynamics of heavy ion collisions: Present status and future perspective[J]. Eur Phys J A. 1998, 1:151-169
[49] Toshiki Maruyama, Adlo Bonasera, et al.. Formation and decay of super heavy systems[J].Eur Phys J A, 2002, 41:191-197
[50] M Beiner, H Flocard, N V Giai and P Quentin. Nuclear ground-state properties and selfconsistent calculations with the Skyrme interaction:(Ⅰ). Spherical description[J].Nucl Phys A, 1975, 238:29
[51] E Chabanat, P Bonche, P Haensel, J Meyer and R Schaeffr.A Skyrme parametrization from subnuclear to neutron star densities[J]. Nucl Phys A, 1997,627:710
[52] D Vautherin and D M Brink. Hartree-Fock Calculations with Skyrme' s Interaction. Ⅰ . Spherical Nuclei[J]. Phys Rev C,1972, 5:626
[53] 胡济民 杨伯君 郑春开 卓益忠.原子核物理[M].北京.原子能出版社,1993
[54] 赵凯 李祝霞 吴锡真 王宁 张英逊 田俊龙 张焕乔 刘祖华.~(40,48)Ca+~(90,96)Zr融合反应的动力学模型研究[J].高能物理与核物理,2006,30:26
[55] V S U Maheswari, C Fuchs, A Faessler Z S Wang and D S Kosov. Role of isospin dependent mean field in pion production in heavy ion reactions[J]. Phys Rev C,1998, 57:922
[56] R K Puri,J Aichelin. Simulated Annealing Clusterization Algorithm for Studying the Multifragmentation[j]. Journal of Computational Phys, 2000,160:245-266
[57] W Neubert, A S Botvina. What is the Physics behind the 3He-4He Anomaly ?[J].Eur Phys J A, 2000, 7:101-106
[58] W Cassing, W Metag, U Mosel and K Niita. Production of energetic particles in heavy-ion collisions[J]. Phys Rep, 1990,188:363
[59] J Aichelin, A Rosenhauer, G Peilert, H St(?)cker and W Greiner. Importance of momentum-dependent interactions for the extraction of the nuclear equation of state from high-energy heavy-ion collisions[J]. Phys Rev Lett,1987, 58:1926
[60] M Asakwa, C M Ko, P Levai and X J Qiu.Rho meson in dense hadronic matter[J].Phys Rev C, 1992,46:1159
[61] C M Ko, Q Li and R C Wang. Relativistic Vlasov equation for heavy-ion collisions[J].Phys Rev Lett,1987, 59:1084
[62] J Cugon, D V H(?)te, J Vandermeulen. Simple parametrization of cross-sections for nuclear transport studies up to the GeV range[J].Nuclear Instruments and Methods in Physics Research B,1996,111:215-220
[63] Guangjun Mao, Zhuxia Li,Yizhong Zhuo and Ziqiang Yu. Medium effects on the NN inelastic cross section in relativistic heavy-ion collisions[J].Phys Lett B,1994, 327:183-186
[64] Q Li, Z Li and G Mao. Isospin dependence of nucleon-nucleon elastic cross section[J].Phys Rev C, 2000, 62:014606
[65] F Rami et al., Isospin-tracing: A probe of non-equilibrium in central heavy-ion collisions,Phys. Rev. Lett, 2000, 84:1120-1123
[66] Bao-An Li, Pawel Danielewicz, and William G Lynch. Probing the isospin dependence of the in-medium nucleon-nucleon cross sections with radioactive beams[J]. Phys Rev C, 2005, 71:054603
[67] 卢希庭.原子核物理[M].北京.原子能出版社.2000,第二版,p:102-108
[68] 宁平治 李磊 闵德芬.原子核物理基础[M].北京.高等教育出版社.2003,第一版,P:197-206
[69] Wilmot N Hess. Summary of High-Energy Nucleon-Nucleon Cross-Section Data[J].Rev Mod Phys, 1958, 30:368-400