Residual interaction in Second RPA with density-dependent forces. Rearrangement terms
AbstractWe derive the expression for the residual interaction to be used in the framework of the Second RPA with density-dependentforces.The adopted procedure is based on a variational approach. It is found that the residual interaction to be used in RPA and beyondRPA matrix elements is not the same as far as the rearrangement terms are concerned. A detailed derivation of the matrix elementscoupling 1 particle-1 hole with 2 particle-2 hole and 2 particle-2 hole among themselves has been done and the correspondingrearrangement terms are shown here. This formal result indicates that both the currently used prescriptions, namely (i) using thesame type of rearrangement terms in RPA and beyond RPA matrix elements or (ii) neglecting the rearrangement terms in beyondRPA matrix elements, are not correct.Keywords: Variational method, second random-phase approximation, residual interactionPACS: 21.30.-x, 21.60.-n, 21.60.JzThe RPA is a widely used microscopic approach adopted tostudy collective modes which can be interpreted in terms of vi-brations. In nuclear physics, the employmentof this model witheﬀective density-dependent interactions allows to successfullydescribe giant resonances and low-lying excitation modes.Thesecond RPA (SRPA) is a natural extension of the RPA where2 particle-2 hole (2p-2h) excitations are included together withthe usual RPA 1 particle-1hole(1p−1h)conﬁgurations,provid-ing in this way a richer description of the excitation modes. Onthe other hand, the manifestation of new exotic modes in unsta-ble nuclei has produced an increasing interest in the context ofnuclear structure and the inclusion of complex conﬁguratio nscoupled among themselves may play a crucial role in the de-scription of these phenomena. Moreover, some low-energy ex-citations like the ﬁrst 0