Use of a Truncated Hilbert Space in Nuclear Reaction Calculations

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 ${\mathrm{N}}^{15}(n,n^{\prime }){\mathrm{N}}^{15}$ shows good agreement with the results of previous calculations.