Excitation of zero, two and four quasi-particles in tamm-dancoff theories of even-parity states of even tin isotopes

Abstract

The quasi-particle second Tamm-Dancoff (QSTD) theory is applied to the study of even-parity states of even tin isotopes, and compared with the quasi-particle Tamm-Dancoff (QTD) theory. Numerical computations were performed with several Gaussian andP2 residual interaction potentials. In contrast to our previous results with a delta force, here our reasonable finite-range forces permit accounting for the 0+ states as well as for the 2+ and 4+ states. Four quasi-particle correlations are included in the ground state. The spurious states of the nucleon number operator are projected out. While the first excited 21+ and 41+ states are generally of almost pure two-quasi-particle character, the first excited 0+ state is quite of the 2qp–4qp mixed type. TheE2-transition probabilities andQ2, the quadrupole moments of the 21+-states are calculated and discussed. The QSTD values ofQ2 can be quite large because of the most important contributions of the mixed 2qp–4qp terms. For one of our Gaussian forcesQ2 (A=116)=+ 0.15 b, a value lying within the limits of the experimental errors. The theory is based on the spherical-shell model.