Nuclear moments in density functional theory: an analysis of magnetic dipole and electric quadrupole moments within nuclear DFT of one-particle and one-hole neighbours of doubly magic nuclei

The density functional theory (DFT) code, HFODD, was used to calculate magnetic dipole $\mu$ and electric quadrupole $Q$ moments, with emphasis on the former, of the odd neighbours of eight doubly magic nuclei (16O, 40Ca, 48Ca, 56Ni, 78Ni, 100Sn, 132Sn and 208Pb).

In our approach, we made use of pure Hartree-Fock using the Skyrme and Gogny functionals while aligning the angular momenta along the axial-symmetry axis and breaking time-reversal symmetry, which allowed for a full analysis of the spin polarization effects due to the unpaired nucleon. In order to restore the broken symmetries, the projection-after-variation (PAV) method was used which provides us with the spectroscopic moments. Our results were achieved by adjusting one coupling constant in the time-odd mean-field sector of the nuclear functional, namely the time-odd spin-spin isovector Landau parameter g0'. The results were compared with experimental data, where available, to determine the validity of our work.

From the analysis, we have concluded that our approach is promising and stands as a solid base for further work into the area and allowing the opportunity to refine the work through additional approaches e.g. deformed-configuration interaction. We note that as a consequence of our work, we determined that the use of effective charges and effective g-factors are not needed to describe the nuclear moments.