Year: 2012
Type: article
Abstract: Background: The $R$ matrix formalism of Lane and Thomas has proven to be a convenient reaction theory for solving many-coupled-channel systems. The theory provides solutions for bound states, scattering states, and resonances for microscopic models in one formalism.Purpose: The first purpose is to extend this formalism to the relativistic case so that the many-coupled-channel problems may be solved for systems in which binary breakup channels satisfy a relative Dirac equation. The second purpose is to employ this formalism in a relativistic continuum shell model.Methods: Expressions for the collision matrix and the scattering amplitude, from which observables may be calculated, are derived. The formalism is applied to the 1$p$-1$h$ relativistic continuum shell model with an interaction extracted from relativistic mean-field theory.Results: The simplest of the $\ensuremath{\sigma}+\ensuremath{\omega}+\ensuremath{\rho}$ exchange interactions produces a good description of the single-particle energies in ${}^{16}$O and ${}^{90}$Zr and a reasonable description of proton scattering from ${}^{15}$N.Conclusion: The development of a calculable, relativistic $R$ matrix and its implementation in a $1p\ensuremath{-}1h$ relativistic continuum shell model provide a simple relatively self-consist physically justifiable model for use in knockout reactions.
Source: Physical Review C
Authors: J. Grineviciute, Dean Halderson
Institution: Western Michigan University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W1964294636