Abstract

The scattering term within the Boltzmann equation was for decades approximated either through the Legendre polynomial for deterministic solvers or by $S(\alpha ,\beta )$/free gas model approach for Monte Carlo solvers. This, to some extent, inaccurate approach led to the assumption in several cases that the scattering term can be further “tuned” to simplify complex mathematical solver of the transport equation, mainly by reducing considerably the computation time, assuming no consequences on the physical results.

The introduction of the resonant dependent scattering kernel to MONTE CARLO code and in particular the experimental validation within the resolved resonance range for Uranium and Thorium, in RPI (Renselear Polytechnic Institute), pointed out that the scattering term cannot be taken as a second order negligible term, but rather should be accurately regarded for any solution of the transport equation.

Corollary to the considerable high impact of that “physical” scattering kernel, this study extends its importance beyond the epithermal resolved resonance range and aims to proof that the scattering kernel can and should be accurately dealt also at higher energies at least up to about several tens of keV. Moreover, in the debate between the purely quantum mechanics treatment known as the Optical Model -OM and the Doppler broadening based classical approach, the latter seems to be correct for this extended energy range. Strictly speaking, Newton’s Laws for the scattering kernel evaluation remain intact, yet in accordance to their quantum mechanics based integrated scattering cross section values as was shown for example by the well-known fundamental Breit Wigner formula.

摘要

几十年来，玻尔兹曼方程中的散射项通过确定性求解器的勒让德多项式或通过 $秒(\alpha ,\beta )$用于 Monte Carlo 求解器的 /free gas 模型方法。在某种程度上，这种不准确的方法导致在几种情况下假设散射项可以进一步“调整”以简化传输方程的复杂数学求解器，主要是通过显着减少计算时间，假设对物理结果没有影响.

在 RPI（伦斯利尔理工学院）中，将共振相关散射内核引入 MONTE CARLO 代码，特别是铀和钍的分辨共振范围内的实验验证，指出散射项不能被视为二阶可忽略的项，而是应该准确地考虑传输方程的任何解。

由于“物理”散射核具有相当高的影响，本研究将其重要性扩展到超热分辨共振范围之外，旨在证明散射核也可以而且应该在更高能量下准确处理，至少高达大约几十keV。此外，在被称为光学模型 -OM 的纯量子力学处理与基于多普勒展宽的经典方法之间的争论中，后者似乎对于这种扩展的能量范围是正确的。严格来说，用于散射核评估的牛顿定律保持不变，但根据其基于量子力学的积分散射截面值，如众所周知的基本 Breit Wigner 公式所示。