Study of Pre-equilibrium Process by Sudden Approximation

在统计假设下导出了预平衡多步复合过程的主方程。其中出现的参数是由固定激发数的吸收势得到的。利用δ相互作用计算了势，进而得到了透射系数。多步复合过程从多步直接过程的哪一步开始一直是一个问题。我们计算了第一阶段和第二阶段的贡献，发现两者同等重要。这与现象学分析的结论是一致的。由于温度固定态是各种激子态的混合态，将温度固定的吸收势分解为各种激子态的吸收势，得到了预平衡过程的吸收势，并在Fermi液体近似下进行了解析计算。另一方面，还进行了有δ相互作用的数值计算，并对两种结果进行了比较。当中间态被限制在束缚组态时，如预平衡过程，随着入射能量的增加，一致性变差，而当中间态不被限制时，一致性很好。计算中考虑了泡利阻塞效应，在矩阵元为随机的情况下，由相互作用的二阶矩得到激子态间的跃迁几率。二阶矩是由吸收势计算的扩展宽度得到的。如果采用半经典近似，那么对于固定的自旋宇称态，扩展宽度是能量的函数。这些结果对于研究预平衡以及动力壳模型是有用的。

Preequilibrium multistep compound process is described by the master equation, which is derived under the statistical assumption. Parameters appeared there are obtained from an absorptive potential with fixed exction number. The potential is calculated by using the delta-interaction and furthermore the transmission coefficients are obtained. From which stage of the multistep direct process the multistep compound process starts had been a question. We calculated contributions from the first stage and the second stage and both are found to be equally important. This agrees with conclusions from phenomenological analyzes. However the Pauli blocking effect are not taken into account in the absorptive potentials.As a temperature fixed state is a mixture of various exciton states, the absorptive potential with fixed temperature is decomposed into ones for various exciton states, and absorptive potential for preequilibrium processes are obtained Under the Fermi liquid approximation the calculation is analytically performed. On the other hand the numerical calculations with delta interaction is also performed, and both results are compared. When intermediates states are limited to bound configurations like in the case of pre-equilibrium process, agreements become worse as the incident energy increases, while if the intermediate states are not restricted agreements are pretty good. In this calculation the effect of Pauli blocking is taken into account.Transition probabilities between exciton states are obtained by the second moment of the interaction if the matrix elements are random. The second moments are obtained from the spreading width, which is calculated from the absorptive potential. If the semiclassical approximation is adopted then the spreading widths are obtained as a function of energy for a fixed spin-parity state. These results are useful for studies of preequilibrium as well as the dynamical shell model.