Bubble nuclei within the self-consistent Hartree-Fock mean field plus pairing approach

Abstract

The depletion of the nuclear density at its center, called the nuclear bubble, is studied within the Skyrme Hartree-Fock mean field consistently incorporating the superfluid pairing. The latter is obtained within the finite-temperature Bardeen-Cooper-Schrieffer theory and within the approach using the exact pairing. The numerical calculations are carried out for $^{22}\mathrm{O}$ and $^{34}\mathrm{Si}$ nuclei, whose bubble structures, caused by a very low occupancy of the $2{s}_{1/2}$ level, were previously predicted at $T=0$. Among 24 Skyrme interactions under consideration, the MSk3 is the only one which reproduces the experimentally measured occupancy of the $2{s}_{1/2}$ proton level as well as the binding energy, and consequently produces the most pronounced bubble structure in $^{34}\mathrm{Si}$. As compared to the approaches employing the same BSk14 interaction, our approach with exact pairing predicts a pairing effect which is stronger in $^{22}\mathrm{O}$ and weaker in $^{34}\mathrm{Si}$. The increase in temperature depletes the bubble structure and completely washes it out when the temperature reaches a critical value, at which the factor measuring the depletion of the nucleon density vanishes.