2 00 3 Pairing in nuclear systems with effective Gogny and V low k interactions

The pairing properties of nuclear systems are a sensitive probe of the effective nucleon-nucleon interactions. We compare the 1 S 0 pairing gaps in nuclear and neutron matter derived from the phenomenological Gogny interaction and a renormal-ization group motivated low-momentum V low k interaction extracted from realistic interactions. We find that the pairing gaps predicted by these interactions are in an excellent agreement in a wide range of sub-nuclear densities. The close agreement between the predictions of the effective forces remains intact in the case where the single particle spectra in neutron and nuclear matter are renormalized by nuclear interactions. The effective nuclear forces are the key ingredients in the nuclear structure studies of finite nuclei within the Hartree-Fock-Bogoliubov and related mean field theories. Well-known examples are the zero-range Skyrme [1] and finite-range Gogny [2,3] forces that have extensively been used in the large scale numerical calculations of finite nuclei over several decades. The effective forces are commonly adjusted to the bulk properties of nuclear systems after a mean-field variational minimization of the ground state energy of a collection of nuclei within the density dependent Hartree-Fock or Hartree-Fock-Bogoliubov theories. A distinctive feature of the finite range Gogny forces, which will be discussed below, is that these were adjusted by minimizing the Hartree-Fock-Bogoliubov energy functional that is a function of the pairing fields [2,3]. Thus, the pair-ing correlations in the system, seen experimentally in the odd-even staggering effects caused by the pairing in the isospin T = 1 states, are encapsulated in