Collective nuclear excitations with Skyrme-second random-phase approximation

Abstract

Second random-phase approximation (RPA) calculations with a Skyrme force are performed to describe both high- and low-lying excited states in $^{16}\mathrm{O}$. The coupling between one particle-one hole and two particle-two hole as well as that between two particle-two hole configurations among themselves are fully taken into account, and the residual interaction is never neglected; we do not resort therefore to a generally used approximate scheme where only the first kind of coupling is considered. The issue of the rearrangement terms in the matrix elements beyond the standard RPA will be considered in detail in a forthcoming paper. Two approximations are employed here for these rearrangement terms: they are either neglected or evaluated with the RPA procedure. As a general feature of second RPA results, a several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions. A much more important fragmentation of the strength is also naturally provided by the second RPA owing to the huge number of two particle--two hole configurations. A better description of the excitation energies of the low-lying ${0}^{+}$ and ${2}^{+}$ states is obtained with the second RPA than with the RPA.