Nuclear masses, shell-model and superheavy nuclei (I)

Abstract

Self-consistent field calculations in some closed shell nuclei are presented. A four-parameter, quadratieally velocity-dependent central interaction is used. The parameters are initially adjusted to reproduce mass-formula parameters of Myers and Swiatecki. A spin-orbit field is added and is chosen to be 30 times the Thomas form. A somewhat better fit to binding energies is obtained by a slight adjustment of the surface energy from 18.56 to 19.0 MeV and of the symmetry energy from 28.0 to 32.5 MeV. The spin-orbit strength, when adjusted to fit 48Ca binding energy, is reduced to 27.5. This two-body effective interaction reproduces binding energies reasonably well, but it does not reproduce single-particle energies well (defined as removal energies). The level density is too small, the gaps at closed shells are roughly twice as large as they should be, and states of larger angular momentum are consistently too strongly bound compared to those of smaller angular momentum. The addition of a density-dependent repulsion of short range, to simulate core repulsions in the two-body interaction, improves the single-particle spectrum somewhat. Both interactions give a closed proton shell in 298114 at Z = 114 due to a f 7 2 −f 5 2 splitting of 3 MeV. The N = 184 gap due to the S 1 2 − j 13 2 distance is found to be only 1.5 MeV. However, in 312114 the N = 198 gap is found to be 4.1 MeV due to the j 13 2 − h 11 2 distance. The calculated level structure for these superheavy nuclei is found to be more sensitive to the two-body interactions than is that for the lighter nuclei. The gaps at 298114 and 312114 may therefore be different for a more realistic interaction. The binding energy of the semi-infinite system is also calculated self-consistently, allowing a determination of the surface energy. Comparisons between the liquid drop and the shell-model total binding energies can therefore be made which show that the correction to the former model is several percent. The definition of single-particle energies is discussed at some length.