Self-Consistent Theory of Nuclear Spectra: The Pairing-Plus-Quadrupole Interaction Model Applied to the Tin Isotopes

The equations of the self-consistent core-particle coupling method, or generalized Hartree-Fock approximation, are derived for the special case of the pairing-plus-quadrupole-quadrupole interaction model. The bases of the approximations of this method are discussed along with the resolution of certain associated technical difficulties. We present, and compare with experiment, results of calculations for the tin isotopes which are completely self-consistent and satisfy all relevant physical constraints. These results include the static quadrupole moments of the first $2^{+}$ states of the even tin isotopes, energies of low-lying states of the odd tin isotopes, and relative spectroscopic factors for ($p,d$) reactions on even targets.