Studies of Stripping and Pickup Reactions on the Basis of the Pairing Plus Quadrupole-Quadrupole Interaction Model

Abstract

Cross sections for ($d, p$) and ($d, t$) reactions in units of the single-particle cross sections (the spectroscopic factors) are calculated for spherical nuclei. It is assumed that the protons fill a closed shell and that only neutrons in an unfilled shell interact with each other through the pairing and quadrupole-quadrupole interactions. First the pairing interactions problem is solved by introducing quasi-particles according to Belyaev. Next the quadrupole-quadrupole interaction is diagonalized, taking into account two quasi-particle states for the first excited state of even-even nuclei. Using these wave functions the spectroscopic factors are obtained in simple form, and are evaluated numerically for the case of the Sn isotopes. Comparison is made with experiments for the transitions to the ground states of even-even and even-odd isotopes as well as to the vibrational states of even-even isotopes. Agreement in both cases is fairly good.