Generalized shells in nuclei: Hartree-Fock calculations for bubble nuclei

Hartree-Fock calculations in the bubble degree of freedom have been performed on a variety of spherical nuclei. Of particular importance are incipient bubble configurations in ³⁶Ar, ⁶⁸Se, ⁸⁴Se, ¹⁰⁰Sn, ¹¹⁶Ce, ¹³⁸Ce and ²⁰⁰Hg, each of which possesses a binding energy which is comparable to that of the normal spherical closed-shell configuration. The densities of the above nuclei display strong deviations from a uniform shape, and give rise to depletions in the nuclear interior. These nonuniformities are due both to the absence of low angular momentum states in otherwise normally occupied spherical shells, and also to strong self-consistency effects. The nonuniformities in the mass density are further enhanced for nuclei whose neutron and proton densities have depressions or peaks at approximately the same distance from the center of the nucleus. A depression of the central density is most pronounced in the nuclei ³⁶Ar, ¹³⁸Ce and ²⁰⁰Hg. Interior depletions of the density are associated with the relatively higher energies of low angular momentum single-particle levels as compared to high angular momentum single-particle levels. This effect can give rise to moderately large gaps at the Fermi surface. Finally, it is shown that in a bubble configuration, the spin-orbit splitting of low lying doublets is sometimes reversed, and that this effect is especially pronounced for levels with low angular momentum.