Appraisal of the Kuo-Herling shell-model interaction and application to A=210–212 nuclei

Shell-model calculations are described for A=204–212 nuclei. These calculations use the Kuo-Herling realistic effective interactions for hole states and particle states relative to ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. These interactions contain a bare part and a core-polarization contribution. The contribution of the core polarization was varied to find the best fit to the energy spectra of A=204–206 and 210–212 nuclei. This and other modifications to the Kuo-Herling interaction—designed to give better agreement with experimental energy spectra—are discussed. Aspects of the spectroscopy of ${}_{}{}^{211\mathrm{-}212}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$, ${}_{}{}^{212}{}_{}{}^{}\mathrm{Ra}$, ${}_{}{}^{210}{}_{}{}^{}\mathrm{Bi}$, and ${}_{}{}^{212}{}_{}{}^{}\mathrm{At}$ are presented in order to illustrate the use of the Kuo-Herling particle interaction. Deficiencies in the Kuo-Herling interaction are described and the desirability and possibility of an improved calculation of the interaction is emphasized.