Random Matrices and Chaos in Nuclear Physics: Nuclear Reactions

TL;DR

This paper reviews how random-matrix theory models chaotic nuclear reactions, providing a statistical framework that predicts scattering behaviors with minimal parameters and compares well with experimental data.

Contribution

It introduces a random-matrix approach to nuclear scattering, connecting quantum chaos with nuclear reaction modeling and testing its predictions against phenomenological methods.

Findings

RMT provides a robust statistical model for CN reactions.

The theory successfully predicts symmetry violations and invariance properties.

Field-theoretical methods enhance the predictive power of nuclear scattering models.

Abstract

The application of random-matrix theory (RMT) to compound-nucleus (CN) reactions is reviewed. An introduction into the basic concepts of nuclear scattering theory is followed by a survey of phenomenological approaches to CN scattering. The implementation of a random-matrix approach into scattering theory leads to a statistical theory of CN reactions. Since RMT applies generically to chaotic quantum systems, that theory is, at the same time, a generic theory of quantum chaotic scattering. It uses a minimum of input parameters (average S-matrix and mean level spacing of the CN). Predictions of the theory are derived with the help of field-theoretical methods adapted from condensed-matter physics and compared with those of phenomenological approaches. Thorough tests of the theory are reviewed, as are applications in nuclear physics, with special attention given to violation of symmetries (isospin, parity) and time-reversal invariance.