Previous calculations have shown that the accurate prediction of two-nucleon overlap factors requires the inclusion of very large numbers of highly excited configurations. These "extended basis shell model" calculations treat a pair of nucleons added to an inert core. In the present paper, the two-particle random-phase approximation theory of Vary and Ginocchio is used to generalize the extended basis shell model to include the effect of core correlations. Including them is shown to have a small effect on two-nucleon stripping reactions, such as ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(t, p){}_{}{}^{18}{}_{}{}^{}\mathrm{O}$. However, the random-phase approximation enables us to include the effect of the highly excited single-particle states on the transition amplitudes for the pickup of a pair, e.g., ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(p, t){}_{}{}^{14}{}_{}{}^{}\mathrm{O}$. Because the admixed states have wave functions which are large in the surface and exterior regions, they result in large enhancements of pickup cross sections. We have also studied the breakdown of the random-phase approximation, when eigenvalues become complex. We provide a proof, for an arbitrary two-body interaction, that the potential strength for which the random-phase approximation eigenvalues become complex, is the minimum strength for which nontrivial solutions to the Hartree-Fock-Bogolyubov equations exist.

NUCLEAR REACTIONS Core correlations included in EBSM calculations of two nucleon stripping reactions using particle-RPA; influence of EBSM on two nucleon pickup reactions; breakdown of RPA.

• Received 19 December 1977

DOI:https://doi.org/10.1103/PhysRevC.18.1011