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Semiclassical and quantum shell-structure calculations of the moment of inertia

Shell corrections to the moment of inertia (MI) are calculated for a Woods-Saxon potential of spheroidal shape and at different deformations. This model potential is chosen to have a large depth and a small surface diffuseness which makes it resemble the analytically solved spheroidal cavity in the semiclassical approximation. For the consistent statistical-equilibrium collective rotations, the MI is obtained within the cranking model in an approach which goes beyond the quantum perturbation approximation based on the non perturbative energy spectrum. For the calculation of the MI shell corrections $δΘ$, the Strutinsky smoothing procedure is used to obtain the average occupation numbers of the particle density generated by the resolution of the Woods-Saxon eigenvalue problem. One finds that the major-shell structure of $δΘ$, as determined in the adiabatic approximation, is rooted, for large as well as for small surface deformations, in the same inhomogenuity of the distribution of single-particle states near the Fermi surface as the energy shell corrections $δE$. This fundamental property is in agreement with the semiclassical results $δΘ\propto δE$ obtained analytically within the non perturbative periodic orbit theory for any potential well, in particular for the spheroidal cavity, and for any deformation, even for large deformations where bifurcations of the equatorial orbits play a substantial role. Since the adiabatic approximation, $ω\ll Ω$, with $\hbar Ω$ the distance between major nuclear shells, is easily obeyed even for large angular momenta typical for high-spin physics at large particle numbers, our model approach seems to represent a tool that could be useful for the description of such nuclear systems.