各向同性中子场中介质中子自屏蔽特性的数学公式
Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field
摘要：
中子输运现象的复杂性给产生或使用中子的每个物理系统投下了阴影。在目前的研究中，从头推导的中子自屏蔽因子，以解决的问题，中子通量的减少，因为它渗透到一个材料放置在一个各向同性的中子场。我们从斯图亚特公式出发，采用了稳态中子输运理论。根据用户可根据各种变量（如中子通量分布和当前模拟的几何形状）采用的积分截面参数推导出简单的公式。得出的自屏蔽因子的公式包括一个倒S形函数归一化的权重表示的宏观总的和散射截面的介质之间的比率。一般的凸体积几何形状减少到一组弦长，而体积内的中子相互作用概率参数化的超热和热中子能量。从中子输运公式的简化版本中推导出反S形函数的参数。因此，所得到的一般公式成功地给出了不同元素和不同几何形状的实验中子自屏蔽因子的值。
英文摘要：
The complexity of the neutron transport phenomenon throws its shadows on every physical system wherever neutron is produced or used. In the current study, an ab initio derivation of the neutron self-shielding factor to solve the problem of the decrease of the neutron flux as it penetrates into a material placed in an isotropic neutron field. We have employed the theory of steady-state neutron transport, starting from Stuart's formula. Simple formulae were derived based on the integral cross-section parameters that could be adopted by the user according to various variables, such as the neutron flux distribution and geometry of the simulation at hand. The concluded formulae of the self-shielding factors comprise an inverted sigmoid function normalized with a weight representing the ratio between the macroscopic total and scattering cross-sections of the medium. The general convex volume geometries are reduced to a set of chord lengths, while the neutron interactions probabilities within the volume are parameterized to the epithermal and thermal neutron energies. The arguments of the inverted-sigmoid function were derived from a simplified version of neutron transport formulation. Accordingly, the obtained general formulae were successful in giving the values of the experimental neutron self-shielding factor for different elements and different geometries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
