Surface corrections to the moment of inertia and shell structure in finite Fermi systems

The moment of inertia for nuclear collective rotations is derived within a semiclassical approach based on the Inglis cranking and Strutinsky shell-correction methods, improved by surface corrections within the nonperturbative periodic-orbit theory. For adiabatic (statistical-equilibrium) rotations it was approximated by the generalized rigid-body moment of inertia accounting for the shell corrections of the particle density. An improved phase-space trace formula allows to express the shell components of the moment of inertia more accurately in terms of the free-energy shell correction. Evaluating their ratio within the extended Thomas-Fermi effective-surface approximation, one finds good agreement with the quantum calculations.

Figure 1

MI shell components $\delta {\mathrm{\Theta }}_x$ (in TF units) as function of $N^{1/3}$ at deformation $\eta =b/a=1.2$ obtained in a quantum-mechanical (QM) and a semiclassical calculation, including surface corrections (${\mathrm{ISPM}}_{+}$) for smaller [upper part (a)] and larger [lower part (b)] particle numbers.

Figure 2

Same as Fig. 1 but for a deformation of $\eta =2.0$.

Figure 3

Comparison between the MI shell components $\delta {\mathrm{\Theta }}_x$ (in TF units) obtained with (${\mathrm{ISPM}}_{+}$) and without (${\mathrm{ISPM}}_{-}$) surface corrections as function of $N^{1/3}$. For comparison the quantum result (black solid line) is also shown. The deformation is $\eta =1.2$.

Figure 4

Same as Fig. 3 but for $\eta =2.0$.