Comprehensive Formalism for Nuclear-Reaction Problems. III. Calculable Theories with Systematic "Discretization"

Abstract

The comprehensive formalism of earlier papers is specialized in the direction of calculable theories of nuclear reactions especially those based on the shell model such as that of Bloch and Fano. Unlike the basis states used in previous specialization, the shell-model states do not, in general, have the property that ($H+\mathcal{L}$) is Hermitian. We show that this complication is no real obstacle, and that only a weaker Hermiticity condition is needed. The final result is a number of forms of calculable theories of the $R$-matrix kind. No continuum-continuum interaction problems exist, since continua do not occur. This and other merits of the results are discussed from the viewpoint of practical calculations.