results for nuclear collective states.

To this end we use a renormalized version of the RPA, developed in Refs. [@CPS1996; @CGP1998; @VKC2000], where excited states are built on top of the true RPA ground state. It is formulated in the single-particle basis which diagonalizes the one-body density matrix, i.e., the natural-orbital basis, and its equations are solved iteratively. Following Ref. [@VKC2000], we will call it Extended RPA (ERPA). The term has been used in the literature to describe also higher-order RPA models (such as SRPA), but this is not the case here. Renormalized formulations of the RPA, such as the ERPA, consider explicitly the depletion of the Fermi sea in the ground state due to RPA correlations. Besides corrected excitation properties, the ERPA allows us to evaluate also corrected ground-state properties, namely single-particle energies and occupation numbers. It is derived using the number-operator method, which, contrary to the quasi-boson approximation, does not suffer from double-counting the second-order contributions [@Row1968b; @VKC2000].

This paper is organized as follows. In Sec. \[ScorrH\] we outline the UCOM method and introduce the correlated Hamiltonian. In Sec. \[Serpa\] we present the ERPA method and the formalism used to evaluate ground-state properties and transition strengths. In Sec. 