Effect of core polarization on magnetic dipole moments in deformed odd-mass nuclei

Magnetic properties of deformed odd-mass nuclei are studied within a nonrelativistic mean-field-plus-pairing approach, namely the Skyrme-Hartree-Fock-BCS approach with self-consistent blocking. For an odd number of nucleons these approaches lead to the breaking of the time-reversal invariance. The deviation from the Schmidt values of the isoscalar magnetic dipole moment is known to result from a subtle balance between core-polarization effects and meson-exchange current effects. However, the former are usually calculated in the random phase approximation without time-reversal symmetry breaking at the mean-field level. In this work we show that if one takes into account this symmetry breaking already in the mean-field solution, the correction from core polarization yields a significant contribution to the empirical quenching of the spin gyromagnetic ratios as compared to the free values in deformed odd-mass nuclei. Moreover, we calculate magnetic dipole moments in the Bohr and Mottelson unified-model description with self-consistent blocked mean-field intrinsic states. The obtained results in the $A\sim 100$ and $A\sim 180$ mass regions as well as for three actinide nuclei compare favorably with experimental data.