Eur. Phys. J. A 13, 307-317 (2002)
The local potential approximation for the Brueckner G-matrix and a simple model of the scalar-isoscalar Landau-Migdal amplitude
M. Baldo1, U. Lombardo2, 3, E.E. Saperstein4 and M.V. Zverev41 INFN, Sezione di Catania, 57 Corso Italia, I-95129 Catania, Italy
2 INFN-LNS, 44 Via S. Sofia, I-95123 Catania, Italy
3 Dipartimento di Fisica, 57 Corso Italia, I-95129 Catania, Italy
4 Kurchatov Institute, 123182, Moscow, Russia
baldo@ct.infn.it
(Received: 2 November 2001 Communicated by P. Schuck)
Abstract
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
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
S0(E0) 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
E0 = 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.
21.30.Fe - Forces in hadronic systems and effective interactions.
21.65.+f - Nuclear matter.
21.60.-n - Nuclear-structure models and methods.
© Società Italiana di Fisica, Springer-Verlag 2002