Z=64 subshell gap in the shell model and the effective boson number in the interacting boson model.

Abstract

The size of the proton subshell gap between the ${\mathit{d}}_{5/2}$ and ${\mathit{h}}_{11/2}$ orbitals is reviewed. The need of revising the microscopic calculations with increased energy gap is reexamined for N\ensuremath{\ge}82 nuclei. Both for occupation probabilities and the nuclear structure of N=82 isotones and the $^{146\mathrm{\ensuremath{-}}154}\mathrm{Sm}$ isotopes, the increased gap at Z=64 is not inconsistent with experiment, except that increased quadrupole strength is required for obtaining the same structure. The use of alternative values of boson numbers in the interacting boson model (IBM) for N88 nuclei is investigated. In a phenomenological IBM calculation there is no a priori need of the use of subshell closure. In the empirical studies for this region the use of the Z=64 subshell does lead to elegant systematics in some cases but it also leads to inconsistencies in other cases. Dependence of collective deformation effect on the slope of particular orbitals, rather than on gap size only, is illustrated.