The R-matrix theory

TL;DR

The paper provides a comprehensive pedagogical overview of the R-matrix method, detailing its calculable and phenomenological variants, with applications in atomic and nuclear physics including scattering, transfer, and radiative reactions.

Contribution

It offers a unified, detailed explanation of both variants of the R-matrix method, illustrating their use in diverse physical problems and recent nuclear physics applications.

Findings

Two variants of R-matrix method are explained and contrasted.

Applications include elastic scattering, transfer, and radiative-capture reactions.

The formalism is applied to recent complex nuclear physics problems.

Abstract

The different facets of the $R$-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: $(i)$ The "calculable" $R$-matrix method is a calculational tool to derive scattering properties from the Schr\"odinger equation in a large variety of physical problems. It was developed rather independently in atomic and nuclear physics with too little mutual influence. $(ii)$ The "phenomenological" $R$-matrix method is a technique to parametrize various types of cross sections. It was mainly (or uniquely) used in nuclear physics. Both directions are explained by starting from the simple problem of scattering by a potential. They are illustrated by simple examples in nuclear and atomic physics. In addition to elastic scattering, the $R$-matrix formalism is applied to transfer and radiative-capture reactions. We also present more recent and more ambitious applications of the theory in nuclear physics.