Magnetic Moments of Odd Nuclei

To understand the grouping of the nuclear magnetic moments a generalization of Schmidt's single-particle model is considered. In the first approximation, the ground state of an odd nucleus is taken to be a doublet state with definite partition quantum numbers, but involving both possible values of the azimuthal quantum number $L$. Only very general assumptions are made concerning the detailed composition of the wave function. On this basis the orbital part of the magnetic moment turns out to be essentially that following from the liquid drop model; the spin part is identical with that of Schmidt. The limits of the magnetic moments, when plotted against $J$, are given by the solid lines on Fig. 1. Next, we have calculated the deviations from the magnetic moments thus obtained which arise from the admixture of states with higher partition quantum numbers to the original wave function. The result is that the magnetic moment is not greatly changed even when the partition quantum numbers are no longer sharp. (Cf. Fig. 2.) The present model fails to explain the near equality of the moments of isotopes which has been found experimentally.