Odd-Parity States of Even Tin Isotopes in the Quasiparticle Second Tamm-Dancoff Approximation

The negative-parity $3^{-}$, $5^{-}$, $6^{-}$, and $7^{-}$ states of the even isotopes of tin are studied with the quasiparticle second Tamm-Dancoff (QSTD) theory which treats the two- and four-quasiparticle excitations on the same footing. The static magnetic moments and the $E\lambda$ transition probabilities are calculated. The QSTD eigen-values, and particularly the QSTD eigenvectors, obtained with phenomenological residual nuclear forces are found to be more sensitive to the residual nuclear force and to the unperturbed single-particle energy levels assumed than are the corresponding results for the even-parity states of the same isotopes. It is shown, however, that a semiquantitative agreement of the QSTD predictions with experiment can be achieved. In particular, rather good agreement is obtained in one of our cases with the observed values of the static magnetic moments of the $5_1^{-}$ states of ${\mathrm{Sn}}^{116}$ and ${\mathrm{Sn}}^{120}$. Corresponding calculations with a realistic nucleon-nucleon potential are most desirable.