Nuclear Electromagnetic Moments of Odd-Mass Nuclei within Skyrme-Hartree-Fock-Bogoliubov and Shell-Model Frameworks
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Abstract
Accurate prediction of electromagnetic moments in odd-A nuclei near doubly magic cores is challenging due to their sensitivity to core polarization and single-particle structure. This study investigates the predictive performance of Skyrme-HFB (SLy4) against shell model (SM) calculations for quadrupole moment (Q20) and magnetic dipole (M10) in the selected nuclei (17O, 17F, 39Ca, 39K, 47Ca, 49Sc, 131In, 133Sb, 133Sn, and 209Bi) near doubly magic cores using the Hartree-Fock-Bogoliubov (HFB) method and the SM method. The SLy4 interaction was used in HFB calculations. On the other hand, SM calculations were performed in sd, sd-pf, fp, and jj shells using USDC, SDPF-U, GXPF1A, jj45pn, and sn100pn interactions. The calculated results of both methods were compared with experimental data from the IAEA/INDC nuclear datasets. For Q20 Skyrme-HFB predicted the correct sign with minor deviations in the value of light nuclei (e.g., 17O, 17F, 39Ca, 47Ca) by about −7% to +6%, but for heavier nuclei like 39K and 49Sc the deviation is much higher about (-88% and -85.7%), and for nuclei around 132Sn and 208Pb cores (131In, 133Sb, 133Sn, 209Bi) the deviation was also high, ranging from -81% to -96%. Meanwhile, the SM Q20 results showed a significant improvement, with a deviation of 1-16% for the whole set. For M10, HFB calculations were close to experiment for light nuclei (17O and 17F) with deviation (0.99% and 1.53%), respectively, and reasonable for nuclei like (47Ca ≈ 4.5% and 39Ca ≈ 11.5%), but deviated strongly for 39K by -73.87%. M10 for heavier nuclei was not evaluated within HFB in the present work. SM calculation reproduced M10 with absolute percent deviations of across the studied nuclei (median ), where the lowest values were 17F (0.03%), 209Bi (0.29%), 39K (0.38%), and 17O (0.87%), while the highest values were 39Ca (29.23%), 133Sn (25.53%), and 133Sb (23.33%).
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