The local potential approximation for the Brueckner G-matrix and a simple model of the scalar-isoscalar Landau-Migdal amplitude

Abstract

The Brueckner G-matrix for a slab of nuclear matter is analyzed in the singlet 1S and triplet 3 S + 3 D channels. The complete Hilbert space is split into two domains, the model subspace S0, in which the two-particle propagator is calculated explicitly, and the complementary one, S', in which the local potential approximation is used. This kind of local approximation was previously found to be quite accurate for the 1S pairing problem. A set of model spaces S 0(E 0) with different values of the energy E0 is considered, E0 being the upper limit for the single-particle energies of the states belonging to S0. The independence of the G-matrix on E0 is assumed as a criterion for the validity of the local potential approximation. It turns out that such an independence holds within few percents for E 0 = 10-20 MeV, for both channels under consideration. The G-matrix within the local potential approximation is used for justifying a simple microscopic model for the coordinate-dependent scalar-isoscalar component f (r) of the Landau-Migdal amplitude in terms of the free T-matrix.