The Local Potential Approximation for the Brueckner G-matrix

Abstract

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, $S^{\prime }$, 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 cut-off 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.

Comments: 13 pages, 9 figures