Notes on thej−jCoupling Shell Model

A study of the nuclear shell model based on the hypothesis of strong spin-orbit coupling yields a number of interesting results for even-even and odd-odd nuclei. To secure simple relations all calculations are based on the extreme limiting situation of complete $j-j$ coupling. Maximum symmetry in the space wave function and $j-j$ coupling are generally in sharp conflict. On occasion there is no conflict and then the consequences of the $j-j$ coupling model are found to agree with experiment (notably the spin and magnetic moment of ${\mathrm{B}}^{10}$ and the sign of the magnetic moment of ${\mathrm{K}}^{40}$). The $j-j$ coupling model yields good results for the magnetic moments of ${\mathrm{N}}^{14}$ and ${\mathrm{Ne}}^{22}$, but in both cases the agreement may be illusory because the computed moments are nearly independent of the amount of singlet wave function in the representation of the ground state. Also the model favors $I=5\mathrm{}$ for the ground state of ${\mathrm{Na}}^{22}$.