A shell-model calculation of the odd-mass tin isotopes

Abstract

A shell-model Hamiltonian with a residual two-nucleon interaction of Gaussian form is used to calculate the states of the odd-mass tin isotopes. The Bogolyubov-Valatin quasi-particle transformation is made and the residual interaction is diagonalized in a one- and three-quasi- particle space. The spurious states must be projected out. Various approximations to this procedure, such as perturbation theory and a phonon approximation, are studied. Perturbation theory is adequate for low states. The phonon approximation is correct qualitatively, but not quantitatively. The parameters of the residual interaction and the single-particle energies are determined by requiring good agreement with the experimental energies. Magnetic moments, electromagnetic transition rates and spectroscopic factors are calculated and agree well with the experimental values.