the unitary correlation operator method (UCOM) [@FNR1998; @NeF2003; @RNH2004]. Although constructed following different formalisms, the two potentials have similar low-momentum matrix elements. In this work we focus on the UCOM potential.

Within the UCOM, the major short-range correlations, induced by the strong repulsive core and the tensor part of the bare NN potential, are described by a state-independent unitary correlation operator. This can be used to introduce correlations into an uncorrelated many-body state or, alternatively, to perform a similarity transformation of an operator of interest. Applied to a realistic NN interaction, the method produces a “correlated" interaction, $\text{V}_{\text{UCOM}}$, which can be used as a universal effective interaction, for calculations within simple Hilbert spaces.

The aim of the UCOM is to treat explicitly only the state-independent short-range correlations; long-range correlations should be described by the model space. This tells us already that the UCOM-based HF is not enough, since a Slater-determinant wavefunction is unable to describe correlations. It was found indeed that, although bound nuclei were obtained using the $V_{\text{UCOM}}$ already at the HF level, the binding energies were underestimated by about 4 MeV per nucleon. Second-order perturbation theory, however, constitutes a tractable and adequate extension to the “zero-order" description provided 