Gross-shell effects in nuclear response functions

Abstract We study nuclear collective vibrations and try to separate contributions from quasi-particle excitations close to the Fermi level from statistically averaged quantities. In this paper we concentrate on the variation coming from the quasi-particle component. As theoretical means we use linear response functions and their semiclassical expansions over trajectories. We study gross-shell effects in vibrating spherical nuclei and evaluate these expansions for the case of an infinitely deep square well, and thus for surface peaked interactions. We calculate strength functions for monopole and quadrupole vibrations. Restricting to only a few dominating terms in the semiclassical expansion we obtain simple expressions which can easily be evaluated numerically. For the case of the quadrupole we find good agreement with available data and with previous computations in the frame of conventional RPA, both for the excitation energies itself as well as their distribution within an energy-weighted sum. The resonance behaviour of the strength function, or its quasi-particle component rather, is determined by the distance between gross shells. The latter is related to the mean period of the shortest periodic orbits.