Use of a truncated Hilbert space in nuclear reaction calculations

Abstract

This formulation of nuclear reaction calculations stays as close as possible to the usual bound-state shell-model calculations. The Hilbert space used in the bound-state calculations is enlarged by adding the scattering states only at that energy for which the reaction is calculated. This Hilbert space is finite-dimensional. The eliminated Hilbert space is partly accounted for by an effective interaction. A variational principle is used to derive the equations for the K and the S matrix, which are then solved by algebraical methods. The numerical application of this method to the reaction N15(n,n′)N15 shows good agreement with the results of previous calculations. © 1968 The American Physical Society.