# Statistical properties of thermal neutron capture cross section calculated with randomly generated resonance parameters

## TL;DR

This study analyzes the statistical distribution of thermal neutron capture cross sections by sampling resonance parameters from theoretical distributions, revealing asymmetric shapes and good agreement with experimental data.

## Contribution

It introduces a stochastic approach to model the probability distribution of thermal neutron capture cross sections using randomly sampled resonance parameters.

## Key findings

- Distribution is asymmetric with a long tail on the large cross section side.
- Multi-resonance effects reduce the probability of small cross sections.
- Model predictions align well with experimental data for 193 nuclei.

## Abstract

We investigated the probability distribution of the thermal neutron capture cross section ($\sigma_{th}$) deduced stochastically with the resonance parameters randomly sampled from Wigner and Porter-Thomas distributions. We found that the typical probability distribution has an asymmetric shape. While there is a long tail on the large $\sigma_{th}$ side due to a resonance happening to be close to the thermal energy, the multi-resonance contribution considerably reduces the probability on the small $\sigma_{th}$ side. We also found that the probability distributions have a similar shape if nuclei have an average resonance spacing sufficiently larger than an average radiation width. We compared the typical probability distribution with the distribution of the experimental values of 193 nuclei, and found a good agreement between them.