On the damping of giant resonances and the independent propagation of particles and holes

In the literature, damping of nuclear collective motion has been attributed to the imaginary part of the self-energies of particles and holes, when assumed to move independently. We examine this picture within a schematic model adapted to the case of giant resonances. In this model we take degenerate 1p-1h states and dress them by a simple analytical form for the self-energies. We are able to calculate the intrinsic response function analytically and thus to study various approximations. We demonstrate that the on-shell approximation appreciably overestimates the widths of the collective vibrations.