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

Abstract

Shell corrections to the moment of inertia (MI) are calculated for a Woods-Saxon potential of spheroidal shape. For the statistical equilibrium collective rotations under consideration, 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, the Strutinsky smoothing procedure is used to obtain the average occupation numbers of the particle density using the solutions of the Woods-Saxon eigenvalue problem. We found that these shell components are practically proportional to those of the energy shell corrections, in qualitative agreement with the semiclassical results obtained analytically for the spheroidal cavity within the periodic orbit theory.

Semiclassical shell-structure micro-macroscopic approach for the level density

“…See Ref. [40] for the relation between the MI, δΘ, and energy, δE, shell components within the semiclassical and quantummechanical resolution problems beyond the quantum perturbation cranking model results. These components for small excitation energies and major shell-structure averaging, g−1 ≪ Γ ≪ D sh , of δg are much smaller than the average rigid body value Θ [Eq.…”

“…The so called a "classical rotation" of the spherical nucleus was considered as alignment of nucleons along the symmetry axis on the basis of the periodic orbit theory with a fixed angular momentum projection, see Ref. [38], in contrast to the collective rotation around the perpendicular axis [39,40]. The yrast line was defined as zero excitation energy for a given angular momentum within the cranking model [41,42].…”

“…For a deeper understanding of the correspondence between the classical and the quantum approach, especially their applications to high-spin physics, it is worthwhile to analyze the shell effects in the level density ρ, see Refs. [7,8], in particular in the entropy S and MI, within the semiclassical periodic-orbit (PO) theory (POT) [35,[38][39][40][46][47][48][49][50][51]. This theory based on the semiclassical time-dependent propagator allows to obtain the total level-density, energy, free-energy, and GCE potential in terms of the smooth ETF term and PO-shell corrections [30,35,39,[49][50][51].…”

“…Appendix A: The semiclassical POT So far we did not specify the model for the mean field and, in particular, for nuclear rotation: it can be associated with alignment of the individual angular momenta of nucleons called a "classical rotation" in Ref. [30] -"parallel" to the symmetry axis Oz, in contrast to the collective rotation perpendicular to Oz [40].…”