Second RPA with Skyrme Interaction

The Second Random Phase Approximation (RPA) is a natural extension of RPA obtained by introducing more general excitation operators where two particle-two hole configurations, in addition to the one particle-one hole ones, are considered. Some Second RPA results with Skyrme force in 16O are presented. Different levels of approximation are compared and in particular the quality of the diagonal approximation is tested. The issue of the rearrangement terms to be used in the matrix elements beyond the standard RPA ones, when density-dependent force are used, is briefly discussed. Two approximated, and generally used, schemes are used: the rearrangement terms are neglected in the matrix elements beyond RPA or evaluated with the RPA prescription. 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.