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

TL;DR

This study uses self-consistent mean-field theory with realistic interactions to accurately predict magnetic dipole moments in nuclei near doubly-magic cores, highlighting the importance of spin-isospin and tensor forces.

Contribution

It demonstrates that the M3Y-P6 interaction within SCMF approaches effectively reproduces experimental M1 moments, surpassing some other models and clarifying the role of spin correlations.

Findings

M3Y-P6 reproduces M1 moments well, especially near magic nuclei.

Quadrupole deformation and spin correlations influence M1 quenching.

Discrepancies remain at Z-odd nuclei despite improvements.

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 ($\chi$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 $\chi$EFT-based shell-model results.