The first detailed comparison of the low-momentum interaction V_low k with G matrices is presented. We use overlaps to measure quantitatively the similarity of shell-model matrix elements for different cutoffs and oscillator frequencies. Over a wide range, all sets of V_low k matrix elements can be approximately obtained from a universal set by a simple scaling. In an oscillator mean-field approach, V_low k reproduces satisfactorily many features of the single-particle and single-hole spectra

more »

... closed-shell nuclei, in particular through remarkably good splittings between spin-orbit partners on top of harmonic oscillator closures. The main deficiencies of pure two-nucleon interactions are associated with binding energies and with the failure to ensure magicity for the extruder-intruder closures. Here, calculations including three-nucleon interactions are most needed. V_low k makes it possible to define directly a meaningful unperturbed monopole Hamiltonian, for which the inclusion of three-nucleon forces is tractable.