Effect of a tensor force on the proton bubble structure of ${}^{206}\mathrm{Hg}$

The proton density distribution of ${}^{206}\mathrm{Hg}$ is calculated in the framework of the Skyrme-Hartree-Fock approach with the SLy5, SLy5 + T, and SLy5 + ${\mathrm{T}}_w$ interactions. It is shown that the central density drops strongly with the SLy5 and SLy5 + T interactions due to the vacancy of the $3s_{1/2}$ orbital. This means that the density depression in the interior of the nucleus is not so much influenced by the tensor force of the SLy5 + T interaction. However, with the SLy5 + ${\mathrm{T}}_w$ interaction the bubble structure does not exist because the tensor force effect of this interaction leads to the inversion between the single-proton states $3s_{1/2}$ and $1h_{11/2}$ $(3s_{1/2}-1h_{11/2}$ inversion) so that the $3s_{1/2}$ state is fully occupied by protons. In addition, a detailed discussion on the antibubble effect from the pairing interaction is performed by using the Skyrme-Hartree-Fock-Bogoliubov approach. It is found that a proton bubble structure in ${}^{206}\mathrm{Hg}$ is unlikely to appear because of the paring correlation.

Figure 1

Proton density distributions of ${}^{206}\mathrm{Hg}$ by the SHF approach with the SLy5, SLy5 + T, and SLy5 + ${\mathrm{T}}_w$ interactions.

Figure 2

Single proton energies of ${}^{206}\mathrm{Hg}$ given by the SHF approach with the SLy5, SLy5 + T, and SLy5 + ${\mathrm{T}}_w$ interactions.

Figure 3

Proton density distributions of ${}^{206}\mathrm{Hg}$ by the SHFB approach for different $t_0^{{}^{\prime }}$ values in the cases of the SLy5, SLy5 + T, and SLy5 + ${\mathrm{T}}_w$ interactions.