Brueckner G matrix for a planar slab of nuclear matter

The equation for the Brueckner G matrix is investigated for planar-slab geo metry. A method for calculating the G matrix for a planar slab of nuclear m atter is developed for a separable form of NN interaction. Actually, the se parable version of the Paris NN potential is used. The singlet S-1(0) and t he triplet S-3(1)-D-3(1) channel are considered The present analysis relies on the mixed momentum-coordinate representation, where use is made of the momentum representation in the slab plane and of the coordinate representat ion in the orthogonal direction. The full two-particle Hilbert space is bro ken down into the model subspace, where the two-particle propagator is cons idered exactly, and the complementary subspace, where the local-potential a pproximation is used, which was proposed previously for calculating the eff ective pairing potential. Specific calculations are performed for the case where the model subspace is constructed on the basis of negative-energy sin gle-particle states. The G matrix is parametrically dependent on the total two-particle energy E and the total momentum P-perpendicular to in the slab plane. Since the G matrix is assumed to be further used to calculate the L andau-Migdal amplitude, the total two-particle energy is fixed at the value E = 2 mu, where mu is the chemical potential of the system under investiga tion. The calculations are performed predominantly for P-perpendicular to = 0. The role of nonzero values of P-perpendicular to is assessed. The resul ting G matrix is found to depend greatly on mu in the surface region. (C) 2 001 MAIK "Nauka/Interperiodica".