Spin and orbital $g$ factors with a surface $\delta$ interaction

Using an attractive surface delta interaction we obtain wave functions for two protons (or proton holes) in the $f_{5/2}$ and $p_{3/2}$ shells. We take the single-particle energies to be degenerate. We obtain the remarkable result that the $g$ factors of the lowest $2^{+}$ and the lowest $4^{+}$ states are equal to 1. We find that only the orbital part of the $g$ factors contributes—the spin part cancels out. Shell-model calculations are also performed for these same $g$ factors in a larger model space and with realistic effective interactions.