  We perform a variational quantum Monte Carlo simulation of an interacting
Fermi gas confined in a three dimensional harmonic potential. This gas is
considered as the precursor system from which a molecular bosonic gas is
formed. Based on the results of two-body calculations for trapped atoms, we
propose a family of variational many-body wave functions that takes into
account the qualitative different nature of the BCS and BEC regimes as a
function of the scattering length. Energies, densities and correlation
functions are calculated and compared with previous results for homogeneous
gases. Universality tests at the unitarity limit are performed including the
verification of the virial relation and the evaluation of the $\beta$
parameter.
