The resonance absorption probability function for neutron and multiplicative integral

TL;DR

This paper derives a rigorous analytical expression for the resonance absorption probability function for moderating neutrons using multiplicative integral theory, removing previous restrictive assumptions in reactor physics modeling.

Contribution

It introduces a novel, exact analytical derivation of the probability function using Volterra integral theory, improving upon approximate methods.

Findings

Exact expression for resonance absorption probability function derived

Removes restrictive assumptions from previous models

Enhances accuracy of neutron flux density calculations

Abstract

The analytical approximations for the moderating neutrons flux density like Fermi spectra, widely used in reactor physics, involve the probability function for moderating neutron to avoid the resonant absorption obtained using some restrictive assumptions regarding the acceptable resonances width. By means of multiplicative integral (Volterra integral) theory for a commutative algebra an analytical expression for the probability function is obtained rigorously without any restrictive assumptions.