Energy dependence of the potential for interaction of 16O ions with 12C nuclei

Abstract

The moment of inertia for collective rotation is derived analytically for the harmonic-oscillator Hamiltonian within the cranking model for any rotation frequency and at finite temperature. Semiclassical shell-structure moments of the inertia are obtained in terms of the free-energy shell corrections through the rigid-body inertia of the statistically equilibrium rotation of a heated Fermi system by using the periodic-orbit theory. Their analytical structure in terms of the equatorial and 3-dimensional periodic orbits for the axially-symmetric harmonic-oscillator potential is in perfect agreement with quantum results for critical deformations and temperatures.

Keywords

• cranking model
• nuclear rotations
• moment of inertia
• periodic orbit theory
• shell-correction energy
• harmonic oscillator potential.