  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.
