Random-matrix approach to the statistical compound nuclear reaction at low energies using the Monte-Carlo technique

TL;DR

This paper employs a random-matrix and Monte-Carlo approach to simulate compound-nucleus reactions at low energies, validating statistical models and establishing criteria for averaging intervals, with results aligning with theoretical predictions.

Contribution

It introduces a Monte-Carlo method to generate scattering matrices, compares results with analytic and statistical models, and defines criteria for energy-averaging in nuclear reactions.

Findings

Perfect agreement with GOE triple integral

Established criteria for energy-averaging intervals

Validated statistical approaches against Monte-Carlo simulations

Abstract

Using a random-matrix approach and Monte-Carlo simulations, we generate scattering matrices and cross sections for compound-nucleus reactions. In the absence of direct reactions we compare the average cross sections with the analytic solution given by the Gaussian Orthogonal Ensemble (GOE) triple integral, and with predictions of statistical approaches such as the ones due to Moldauer, to Hofmann, Richert, Tepel, and Weidenm\"{u}ller, and to Kawai, Kerman, and McVoy. We find perfect agreement with the GOE triple integral and display the limits of validity of the latter approaches. We establish a criterion for the width of the energy-averaging interval such that the relative difference between the ensemble-averaged and the energy-averaged scattering matrices lies below a given bound. Direct reactions are simulated in terms of an energy-independent background matrix. In that case, cross sections averaged over the ensemble of Monte-Carlo simulations fully agree with results from the Engelbrecht-Weidenm\"{u}ller transformation. The limits of other approximate approaches are displayed.