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The fragmentation of one-nucleon knock-out strength at low energies is considered from the viewpoint of the two particle-one hole ͑and two hole-one particle͒ response propagator. The aim is to deal with particleparticle ͑and hole-hole͒ as well as particle-hole collectivity simultaneously. This is achieved on a Tamm-Dancoff level by the so-called Faddeev approximation of the 2 p1h propagator. Results of this approach illustrate the relevance of this consistent treatment of both particle-particle ͑hole-hole͒ and particle-hole collectivity. A further extension, within the framework of 2p1h RPA which was sometimes applied in the past, has serious unsolved problems, some of which are discussed in detail.

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DifFerent normalization conditions for random phase approximation amplitudes have been obtained recently for use with energy-dependent interactions. These conditions are shown to be equivalent. A third method, which has a wider applicability, is also discussed. PACS number(s): 21.60.Jz, 24.10.CnThe random phase approximation (RPA) [1, 2] is a well-known method to descr'ibe the excitation of manybody systems. As such it has also frequently been applied in nuclear structure theory. In these applications [2], one often adopted phenomenological interactions with a few parameters adjusted so as to reproduce the energies of the most collective excitations. More recently it has been realized that this approach can only yield reasonable results in a unified description of both low-energy excitations and those at higher energies, e.g. , giant resonances, if the interaction is allowed to be energy dependent. The main physical origin of this energy dependence of the effective interaction in the RPA is the induced interaction via medium polarization as well as the dispersive contributions to the particle and hole propagators. These effects are explicitly treated to some extent in the extended RPA (ERPA) method, utilized recently by various authors [3 -6].One of the features of the ERPA method, and of the use of energy-dependent interactions in the RPA in general, is that this energy dependence yields an extra term in the normalization condition for the RPA amplitudes. In Ref.[6], this normalization condition was expressed in the form