Relativistic R matrix and continuum shell model

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 to 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 channels problem 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 1p-1h relativistic continuum shell model with an interaction extracted from relativistic mean-field theory. Results: The simplest of the $\sigma +\omega +\rho$ 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. Conclusions: The development of a calculable, relativistic $R$ matrix and its implementation in a $1p-1h$ relativistic continuum shell model provide a simple relatively self-consist, physically justifiable model for use in knockout reactions.