The Local Potential Approximation for the Brueckner G-matrix

The Brueckner G-matrix for a slab of nuclear matter is analyzed in the singlet 1 S and triplet 3 S + 3 D channels. The complete Hilbert space is split into two domains, the model subspace S 0 , 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 1 S pairing problem. A set of model spaces S 0 (E 0) with different values of the cutoff energy E 0 is considered, E 0 being the upper limit for the single-particle energies of the states belonging to S 0. The independence of the G-matrix of E 0 is assumed as a criterion of validity of the local potential approximation. Such independence is obtained within few percent for E 0 =10 ÷ 20 MeV for both the channels under consideration.