Direct Reduction to Talmi Integrals Without Use of Transformation Brackets

Abstract

The two-body shell-model matrix elements for central and tensor forces can be expanded as linear combinations of Talmi integrals. A closed form, which does not involve vector-coupling coefficients or transformation brackets, is obtained for the coefficients appearing in this expansion. For the case that all the oscillator constants are the same, the result is simple enough to allow tabulation. A table of these coefficients for matrix elements involving the shell-model states $0s$, $0p$, and $0d$ is included. The main advantage of this method over the Talmi-Brody-Moshinsky method is discussed.