Surface Delta Interaction and Single-Closed-Shell Nuclei

The surface delta interaction has been applied in a calculation of the energy levels of isotopes of Pb, Sn and Ni, ${\mathrm{Po}}^{210}$, and nuclei belonging to the 82-neutron shell. The Bogoliubov-Valatin method combined with the Tamm-Dancoff approximation has been utilized. In certain cases, exact shell-model calculations have also been performed. The comparison between the results obtained in these two ways shows that the approximation method works quite well for the two-particle case. For more than two particles outside closed shells, the approximation works relatively well only for the $2_1$+ and $4_1$+ states. The agreement with experiment is fairly good in general. For ${\mathrm{Pb}}^{206}$ the results are even slightly better than those of True and Ford. For ${\mathrm{Pb}}^{204}$ and ${\mathrm{Pb}}^{202}$ it was found necessary to reduce the strength of the interaction about 10%. In Ni and in the 82-neutron nuclei the results are fairly good, but in the isotopes of Sn and in ${\mathrm{Pb}}^{210}$ the 2+ and 4+ states lie somewhat too high.