  We perform a variational quantum Monte Carlo simulation of the transition
from a Bardeen-Cooper-Schrieffer superfluid (BCS) to a Bose-Einstein condensate
(BEC) at zero temperature. The model Hamiltonian involves an attractive short
range two body interaction and the atoms number $2N =330$ is chosen so that, in
the non-interacting limit, the ground state function corresponds to a closed
shell configuration. The system is then characterized by the s-wave scattering
length $a$ of the two-particle collisions in the gas, which is varied from
negative to positive values, and the Fermi wave number $k_F$. Based on an
extensive analysis of the s-wave two-body problem, one parameter variational
many-body wave functions are proposed to describe the ground state of the
interacting Fermi gas from BCS to BEC states. We exploit properties of
antisymmetrized many-body functions to develop efficient techniques that permit
variational calculations for a large number of particles. It is shown that a
virial relation between the energy per particle and the trapping energy is
approximately valid for $-0.1<1/k_Fa<3.4$. The influence of the harmonic trap
and the interaction potential as exhibited in two-body correlation functions is
also analyzed.
