Magnetic moments of nuclei with closed j- j shells plus or minus one nucleon

The correction to the Schmidt moment of ²⁰⁹Bi calculated with the Hamada-Johnston potential is shown to be 0.8 n.m. to first order in perturbation theory. This improvement on the zero-order Schmidt moment is compared with previous, smaller first-order corrections calculated with other potentials. A discrepancy with experiment of 0.66 n.m. still remains for this nucleus if one stops at first-order perturbation theory. We also perform complete second-order calculations for ²⁹Si and ²⁰⁹Bi which worsen agreement between theory and experiment. The second-order correction for ²⁰⁹Bi is -0.21 n.m. and for ²⁹Si -0.06 n.m. (compared with a +0.73 n.m. first-order correction for the latter nucleus). Finally certain Tamm-Dancoff and RPA type diagrams which turn out to be important in the second-order calculations are summed to all orders. Our second-order calculations are performed with the Kallio-Kollveit potential.