Random-phase-approximation calculations and residual interactions in the sigma tau channel.

Abstract

We compare numerical results for renormalized spin-isospin matrix elements within the random phase approximation. Extended calculations are carried out for a pionlike excitation in a finite nucleus; the effects of contact versus momentum-dependent residual interactions, and of \ensuremath{\Delta}-h configurations, are demonstrated. We point out the implications of our results on nuclear structure calculations, where such effects are sometimes neglected. The role of the finite geometry of the system is crucial in determining the features of the spin-isospin responses. We emphasize that a crucial test of the theory can only be achieved through a direct comparison of the longitudinal and transverse channels.