An Accurate Method to Interpolate First-Flight Collision Probabilities

Abstract

A method is proposed to approximately calculate first-flight collision probabilities for use in resonance integral calculations with good accuracy and within a short computing time. In the proposed method, collision probabilities at three different energy points are rigorously calculated and stored beforehand. They are used to obtain approximate collision probabilities at an arbitrary energy point by Takahashi's zero-th approximation. Then, these approximate values are used to obtain more accurate values by quadratic interpolation with the neutron total cross section change as an interpolation parameter. The proposed method was applied to the calculation of collision probabilities in a two-region LWR fuel pin cell, and it was found that the collision probabilities can be calculated with an error of less than 1%, a great improvement in accuracy compared to the zero-th approximation, when the total cross section of the fuel region changes 30 times. The proposed method shortens computing time of lattice cell neutronic calculation codes based on the first-flight collision probability method.