Extended second random phase approximation applied to metallic clusters

The coupling to two particle-two hole configurations is at the basis of the calculations of the spreading width of the collective excitations that in random phase approximation (RPA) are described as superpositions of one particle-one hole elementary modes. Second RPA (SRPA) is just the extension of RPA including both kinds of configurations. In SRPA use is made of the quasiboson approximation (QBA) as in RPA. It has been found that this is at the origin of the fact that the coupling among them strongly lowers the RPA collective excitations, both in metallic clusters and in nuclei. When the coupling of the two particle-two hole configurations among themselves is also included, as it has to be done in order to be consistent, this effect is even enhanced. Thus the reasonably good description of the collective vibrational states obtained at the RPA level (as expected on physical grounds, for example, for the dipole modes) is completely spoiled in SRPA. In the present paper we show quantitatively, for metallic clusters, that this disturbing behavior is eliminated when no use is made of QBA and a better description of ground-state correlations is introduced.