Magnetic and quadrupole moments of bismuth-209: a relativistic configuration-mixing approach
摘要
This theoretical study employs a sophisticated Configuration-Mixing approach within the Nuclear Shell Model framework to calculate the ground-state magnetic dipole moment (µ) and electric quadrupole moment (Q) for isotopes around the 208Pb core, specifically 207Pb, 209Bi, and 210Bi. The work systematically investigates the contributions of core polarization and meson exchange currents (MEC) to resolve the significant discrepancy between the single-particle Schmidt prediction (µSchmidt ≈ + 2.62 µN) and the experimental value (µExp ≈ + 4.092 µN) for 209Bi. Accurate reproduction of the experimental quadrupole moment (Qexp = − 37 µ5 e fm2) for 209Bi requires an enhanced effective proton charge (ep) of 1.60e, quantifying the high polarizability of the 208Pb core and confirming the nucleus’s oblate deformation. Furthermore, the model accurately reproduces the small Qexp (− 7.0 ± 1.0 e fm2) of the p-n coupled 210Bi, demonstrating an 81.1% reduction in magnitude compared to 209Bi due to residual interaction cancellation effects. The study also clarifies that while the spectroscopic quadrupole moment is mathematically zero for J = 1/2 states such as 207Pb, this distinguishes the measured static moment from any underlying intrinsic deformation (Q0). This benchmarking confirms the robustness of the derived effective operators and the chosen model space in describing single-particle and coupled two-particle systems near magic shell closures.