Second RPA calculations with a Skyrme force are performed to describe both high-and low-lying excited states in 16 O. The coupling between 1 particle-1 hole and 2 particle-2 hole as well as that between 2 particle-2 hole configurations among themselves are fully taken into account and the residual interaction is never neglected, not resorting 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 standard RPA is addressed and discussed. 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 second RPA due to the huge number of 2 particle-2 hole configurations.A better description of the excitation energies of the low-lying 0 + and 2 + states is obtained with second RPA with respect to RPA.

We make use of a subtraction procedure, introduced to overcome double-counting problems in beyond-mean-field theories, in the second random-phase-approximation (SRPA) for the first time. This procedure guarantees the stability of SRPA (so that all excitation energies are real). We show that the method fits perfectly into nuclear density-functional theory. We illustrate applications to the monopole and quadrupole response and to low-lying 0 + and 2 + states in the nucleus 16 O. We show that the subtraction procedure leads to: (i) results that are weakly cutoff dependent; (ii) a considerable reduction of the SRPA downwards shift with respect to the random-phase approximation (RPA) spectra (systematically found in all previous applications). This implementation of the SRPA model will allow a reliable analysis of the effects of 2 particle-2 hole configurations (2p2h) on the excitation spectra of medium-mass and heavy nuclei.

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