Variational approach to the moment of inertia

We derive an approximate expression for the moment of inertia $\theta$ in the framework of the cranked Hartree-Fock theory. Our method allows for a detailed study of the role of spin-orbit and two-body nuclear potentials. In particular it is shown that in ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ the two-body interaction lowers by 30% the rigid value of $\theta$. The irrotational and rigid values for the moment of inertia are obtained as special cases of the present approach.