  The Brueckner G-matrix for a slab of nuclear matter is analyzed in the
singlet $^1S$ and triplet $^3S+^3D$ 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 $^1S$ 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 $E_0=10 \div 20$ MeV for both
the channels under consideration.
