Beyond-mean-field study of the possible "bubble" structure of 34Si

TL;DR

This study explores how correlations beyond mean-field approximations affect the predicted bubble structure in 34Si, revealing that these effects tend to smooth out the density depletion and produce a more typical Fermi distribution.

Contribution

It applies a particle-number and angular-momentum projected GCM with Hartree-Fock-Bogoliubov states to analyze density profiles, including charge and transition densities, beyond mean-field.

Findings

Correlations significantly modify the density profile.

Density profile becomes closer to a Fermi-type distribution.

Shape mixing and symmetry restoration impact the density structure.

Abstract

Recent self-consistent mean-field calculations predict a substantial depletion of the proton density in the interior of 34Si. In the present study, we investigate how correlations beyond the mean field modify this finding. The framework of the calculation is a particle-number and angular-momentum projected Generator Coordinate Method based on Hartree-Fock-Bogoliubov+Lipkin-Nogami states with axial quadrupole deformation. The parametrization SLy4 of the Skyrme energy density functional is used together with a density-dependent pairing energy functional. For the first time, the generator coordinate method is applied to the calculation of charge and transition densities. The impact of pairing correlations, symmetry restorations and shape mixing on the density profile is analyzed step by step. All these effects significantly alter the radial density profile, and tend to bring it closer to a Fermi-type density distribution.