Magnetic dipole moments adjacent to doubly-magic nuclei in self-consistent mean-field theory with realistic spin-isospin and tensor forces

Abstract

Magnetic dipole ($M1$) moments in nuclei neighboring the doubly-magic core are investigated by the self-consistent mean-field (SCMF) approaches that allow for the breaking of the time-reversal symmetry. By the SCMF calculations with the M3Y-P6 interaction, which keeps realistic spin-isospin and tensor channels, the $M1$ moments are well reproduced, particularly those in the nuclei adjacent to $jj$-closed magicity. The results are in better agreement with the data than those with the Gogny-D1S interaction, slightly better than those of UNEDF1 supplemented by a spin-isospin channel adjusted to the $M1$ moments themselves, and comparable to the shell-model results with the chiral effective-field-theory ($χ$EFT) interaction. Analyses via quadrupole moments, occupation numbers and the lowest-order perturbation theory elucidate the cooperative effects of quadrupole deformation and spin correlation on the displacement from the Schmidt values, which has been known in terms of the quenching of the spin matrix elements. It is shown that a significant portion of the spin correlation is carried by the spin-isospin and tensor channels in the effective interaction. However, while agreement is remarkable at $^{131}$Sn$^m$, $^{133}$Sn and $^{209}$Pb, discrepancies remain at the $Z=\mathrm{odd}$ nuclei $^{133}$Sb, $^{207}$Ti and $^{209}$Bi, as in the $χ$EFT-based shell-model results.

Figures (12)

• Figure 1: $\varDelta\mu$ values in nuclei adjacent to $\ell s$-closed shell. Nuclides and spin-parities are shown at the top and bottom of the figure. Red circles and blue triangles represent the present results with M3Y-P6 and D1S, respectively. Skyblue diamonds and orange inverse triangles are the $J$-projected results with D1S and UNEDF1 quoted from Ref. ref:SDBG22. Green pluses are $\chi$EFT results of Ref. ref:MCSB24. Experimental data are taken from Ref. ref:INDC-0794 and shown by black crosses.
• Figure 2: Upper panel: $\varDelta\mu$ values in nuclei adjacent to the doubly-magic nuclei, having $\ell s$-closed $Z$ and $jj$-closed $N$, and vice versa. See Fig. \ref{['fig:mu_ls-ls_A-odd']} for conventions. Experimental data are taken from Refs. ref:INDC-0794 and ref:IGIT23 (for $^{21}$O). Lower panel: Calculated $\varDelta\mu$ values relative to $\varDelta\mu^\mathrm{exp.}$. Red and blue bars are the current results with M3Y-P6 and D1S, respectively. The $J$-projected results with D1S and UNEDF1 quoted from Ref. ref:SDBG22 are also presented by skyblue diamonds and orange inverse triangles, for reference.
• Figure 3: Upper panel: $\varDelta\mu$ values in odd-$N$ nuclei adjacent to the $jj$-closed shell. See Fig. \ref{['fig:mu_ls-ls_A-odd']} for other conventions. Experimental data are taken from Refs. ref:INDC-0794ref:INDC-0816 and ref:RBBB20 (for $^{133}$Sn). Lower panel: Calculated $\varDelta\mu$ values relative to $\varDelta\mu^\mathrm{exp.}$ when $\mu^\mathrm{exp.}$ is available. See Fig. \ref{['fig:mu_ls-jj_A-odd']} for conventions.
• Figure 4: Upper panel: $\varDelta\mu$ values in odd-$Z$ nuclei adjacent to the $jj$-closed shell. See Fig. \ref{['fig:mu_ls-ls_A-odd']} for conventions. Experimental data are taken from Refs. ref:INDC-0794ref:INDC-0816 and ref:VGMB22 (for $^{131}$In). Lower panel: Calculated $\varDelta\mu$ values relative to $\varDelta\mu^\mathrm{exp.}$. Green bars represent the $\chi$EFT results of Ref. ref:MCSB24. See Fig. \ref{['fig:mu_ls-jj_A-odd']} for other conventions.
• Figure 5: $Q_p/R^2$ values in nuclei of Fig. \ref{['fig:mu_ls-ls_A-odd']}. Single-particle values ($Q_n/R^2$ for odd-$N$ nuclei) are shown by brown pluses. Other symbols are common to Fig. \ref{['fig:mu_ls-ls_A-odd']}. Experimental data are taken from Ref. ref:Stone16.