Modification of the Porter-Thomas distribution by rank-one interaction

TL;DR

This paper analytically investigates how a rank-one interaction modifies the classic Porter-Thomas distribution of nuclear resonance widths, providing explicit formulas that align well with numerical simulations and experimental deviations.

Contribution

It introduces an analytical solution for the modified distribution accounting for rank-one interactions, extending the standard random matrix model for nuclear resonances.

Findings

Derived explicit formulas for the modified PT distribution.

Demonstrated good agreement between analytical results and numerical simulations.

Provided potential explanations for experimental deviations from the standard PT distribution.

Abstract

The Porter-Thomas (PT) distribution of resonance widths is one of the oldest and simplest applications of statistical ideas in nuclear physics. Previous experimental data confirmed it quite well but recent and more careful investigations show clear deviations from this distribution. To explain these discrepancies the authors of [PRL \textbf{115}, 052501 (2015)] argued that to get a realistic model of nuclear resonances is not enough to consider one of the standard random matrix ensembles which leads immediately to the PT distribution but it is necessary to add a rank-one interaction which couples resonances to decay channels. The purpose of the paper is to solve this model analytically and to find explicitly the modifications of the PT distribution due to such interaction. Resulting formulae are simple, in a good agreement with numerics, and could explain experimental results.