Projected BCS-Tamm-Dancoff Approximation for Even Tin Isotopes

Abstract

A model for even "superconductor" nuclei is proposed and developed. In this model the ground state is approximated by the component of a Bardeen-Cooper-Schrieffer (BCS) state corresponding to a fixed particle number. The low-lying excited states are then obtained by diagonalizing the nuclear Hamiltonian in the space spanned by the particle-hole elementary excitations and, for $J=0\mathrm{}$, by the ground state itself. Expressions for the matrix elements of the electromagnetic operators are also given. In the final section, the results obtained from this model for some even tin isotopes are compared with the experimental results and the corresponding results of an ordinary BCS-Tamm-Dancoff approximation. Thus, we are able to give a direct evaluation of the effects of the particle-number nonconservation in the Tamm-Dancoff approximation.