  We outline a partial-fractions decomposition method for determining the
one-particle spectral function and single-particle density of states of a
correlated electronic system on a finite lattice in the non self-consistent
T-matrix approximation to arbitrary numerical accuracy, and demonstrate the
application of these ideas to the attractive Hubbard model. We then demonstrate
the effectiveness of a finite-size scaling ansatz which allows for the
extraction of quantities of interest in the thermodynamic limit from this
method. In this approximation, in one or two dimensions, for any finite lattice
or in the thermodynamic limit, a pseudogap is present and its energy diverges
as Tc is approached from above; this is an unphysical manifestation of using an
approximation that predicts a spurious phase transition in one or two
dimensions. However, in three dimensions one expects the transition predicted
by this approximation to represent a true continuous phase transition, and in
the thermodynamic limit any pseudogap predicted by this formulation will remain
finite. We have applied our method to the attractive Hubbard model on a
three-dimensional simple cubic lattice, and find that for intermediate coupling
a prominent pseudogap is found in the single-particle density of states, and
this gap persists over a large temperature range. In addition, we also show
that for weak coupling a pseudogap is also present. The pseudogap energy at the
transition temperature is almost a factor of three larger than the T=0 BCS gap
for intermediate coupling, whereas for weak coupling the pseudogap and BCS gap
energies are essentially equal.
