Two- and four-quasiparticle Tamm-Dancoff theories are applied to study the even-parity states of the even tin isotopes. The residual nucleon-nucleon force is the realistic potential of Tabakin. We investigate the effects of the core neutrons and protons on our $0^{+}$, $2^{+}$, and $4^{+}$ states by including the appropriate BCS and configuration-mixing contributions directly and by the "core polarization" renormalization of Bertsch, Kuo, and Brown. We find the core-polarization corrections most important and generally sufficient to explain the basic experimental data. The summation of the random-phase-approximation bubble and related exchange diagrams to all orders for the core nucleons gives almost the same results as those obtained with only second-order corrections. Such second-order corrections seem to be a sufficient approximation independently of the single-particle basis chosen.

• Received 5 December 1967

DOI:https://doi.org/10.1103/PhysRev.169.983