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Au+Au三分裂反应的输运理论研究(42)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(33)
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本报告是欧立博士在博士后工作期间主要研究工作的总结，共分三个部分。第一部分是核子入射核反应中同位旋效应的研究；第二部分是对中高能质子引起的散裂反应的研究；第三部分是利用极限温度对有限温度下不对称核物质核态方程进行约束的研究。
散裂反应的研究在实际应用和理论研究两方面都有很重要的意义。与重离子碰撞相比，散裂反应在入射能量不太高的情况下反应过程的温度比较。所以利用散裂反应核数据抽取到的核物质的核态方程比从重离子碰撞中得到的核态方程更接近零温时的核态方程。本工作中，我们利用改进的量子分子动力学模型ImQMD 结合两种统计衰变模型，GEM2 及GEMINI 研究了能量在1 GeV 以下的质子入射56Fe、136Xe、197Au、208Pb、238U等靶核引起的散裂反应。给出的出射中子、质子双微分截面与实验符合得非常好。同时还给出反应产物的质量、电荷、同位素分布。通过调整统计衰变模型里的参数，ImQMD+GEM2 能够很好地再现重靶上的散裂反应产物的截面，而ImQMD+GEMINI 则很好地再现了轻靶上的散裂反应产物的截面。由于ImQMD 模型没有可调的参数，如果实验能提供足够的精确数据用于GEM2 与GEMINI 中可调参数的系统化，则可以大大地提高模型的预言能力。这对散裂反应的实际应用非常有意义。
在量子分子动力学模型框架下，研究了核子入射112−132Sn 及其相应稳定线上的同量异位素诱发核反应中的同位旋效应。研究表明质子入射112−132Sn 反应截面的体系依赖明显偏离拟合质子入射 稳定核得到的Carlson 经验表达式，并且明显依赖于对称能的硬度。大碰撞参数下质子入射112−132Sn 的弹性角分布对对称能密度依赖形式非常敏感，这完全是对称势的效应而没有混杂核子-核子散射截面的同位旋依赖的效应。在入射能量为100 MeV，碰撞参数7.5 fm 条件下，质子入射与中子入射弹散的弹散角分布峰值对应的角度差对于软的对称能是正值，对于非常硬的对称能是负值，而对于线性的对称能则接近零。这样，大碰撞参数下，能量为100MeV 的质子和中子在丰中子靶核上的弹散角分布峰值对应的角度间的差别可以提供一个非常好的观测量，来约束对称能的密度依赖形式。质子入射Sn 同位素反应截面对体系的依赖对对称能密度依赖敏感而对靶核中子皮厚度变化不敏感，而中子入射Sn 同位素反应截面对体系的依赖对对称能密度依赖不敏感而对靶核中子皮厚度变化敏感。因此，测量低能中子入射丰中子核的反应截面将能够为我们提供中子皮厚度的信息。有限核体系的极限温度，即核体系在破裂前所能承受的最高温度，与核物质的临界温度有关。因此极限温度的实验信息可以用来检验微观理论给出的有限温度下的核态方程，这是其它方法很难实现的。我们从核极限温度出发，研究了有限温度下的不对称核物质的核态方程。采用Skyrme相互作用，结合不同对称能密度依赖的形式，同时考虑不同表面张力的影响，计算了有限核体系极限温度，以及Z=38 的同位素的极限温度，A=93的同量异位素的极限温度。通过与实验比较，对低密区域的对称能的密度依赖形式进行了约束。结果表明软的对称能更为合理。此外，我们用极限温度检验了几套Skyrme 相互作用在有限温度、高不对称度条件下的适用情况。
关键词：散裂反应，双微分截面，核态方程，对称能，同位旋效应，极限温度
This report contains the main postdoctoral work of the author. It consists three parts. The first part is the investigation on dynamical isospin effects in nucleon-induced reactions. The second part is the study on proton-induced spallation reactions by the improved quantum molecular dynamics model plus statistical decay models. The last part is about the investigation on the state of asymmetry nuclear matter at finite temperature constrained from limiting temperature.
It is important to study the spallation reactions both on applications and basic research. Comparing with the temperature in the heavy ion collisions, the temperature in the intermediate energy spallation reaction is lower when the incident energy is not very high. So we can extract the information of the equation of state for nuclear matter which is more close to the zero-temperature case than the one from HIC. Intermediate energy proton-induced spallation reactions with the targets 56Fe、136Xe、197Au、208Pb、238U , etc. are studied by the improved quantum molecular dynamics model (ImQMD) incorporated two statistical decay model GEM2 and GEMINI. The double differential cross sections of emitted protons and neutrons are found to be in good agreement with experimental data. By readjusting two respective parameters in GEM2 and GEMINI, the cross sections for products in proton-induced reactions on heavy targets can be reproduced quite well by both models, especially by the ImQMD+GEM2 model. However, the GEM2 model is not very competent to describe the reactions on light targets compared with the GEMINI model which can describe these reactions quite well. Because there is no adjustable parameter in the ImQMD model, for the future, with more precise experimental data to be available, we expect that the systematic adjustable parameters in GEM2 and GEMINI can be obtained with the present approach to improve the prediction power of this hybrid model. That is very significative for the applications of the spallation reactions.
The isospin effect in nucleon-induced reactions on Sn isotopes has been applied to explore the sensitive observable for the density dependence of the symmetry energy. With the ImQMD model, the various forms of density dependence of the symmetry energies are applied in the calculations. Our study shows that the system size dependence of the reaction cross sections for proton-irradiated 112−132Sn depends sensitively on the density dependence of the symmetry energy, so does the angular distributions of elastic scattering for proton-irradiated 132Sn at large impact parameters, which show that this behavior originates uniquely from the effect of the symmetry potential. Furthermore, The isospin effect in neutron-induced reactions is also studied and it is found that the effect is just opposite to that in proton-induced reactions. The difference between the angular distributions of elastic scattering for proton and neutron-induced reactions at the same incident energy positive for soft symmetry energy, negative for extra-stiff symmetry energy and close to zero for linear density dependent symmetry, which will be possibly very useful for constraining the density dependence of the symmetry energy. Based on the same model, we study the effects of the thickness of neutron skin and symmetry potential on nucleon-induced reactions on Sn isotopes in order to find new sensitive observables to the thickness of neutron skin. The investigation shows that the target size dependence of the reaction cross sections for neutron-induced reactions on Sn isotopes is sensitive to the thickness of neutron skin of target nucleus but not sensitive to the density dependence of the symmetry energy, which may be helpful to extract the thickness of neutron skin of neutron-rich nuclei.
The limiting temperatures of finite nuclei, i. e., the maximum temperatures nuclei can sustain before they become unbound, are correlated with the critical temperature of nuclear matter. Experimental information on limiting temperatures will thus permit tests of microscopic calculations of the nuclear equation of state at finite temperature which cannot be easily obtained by other means. The EOS of asymmetry nuclear matter at finite temperature has been investigated from the view of limiting temperature. With Skyrme effective interaction plusvarious density dependence of symmetry energy, and considering the effect of surface tension on the limiting temperature, we calculated the size dependence of limiting temperature, the isotope distribution of limiting temperature for element of Z=38, and the isobar distribution of limiting temperature for element of A=93. By comparing these results to the experimental data, constraints on the density dependence of symmetry energy at subnormal density are obtained.
The applicability of several Skyrme interactions at finite temperature and large asymmetry degree are test by the view of limiting temperature in this work.
Keywords: spallation reaction, double differential cross section, equation of state, symmetry energy, isospin effect, limiting temperature
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