  We study the virial relations for ultracold trapped two component Fermi gases
in the case of short finite range interactions. Numerical verifications for
such relations are reported through the BCS-BEC crossover. As an intermediate
step, it is necessary to evaluate the partial derivatives of the many body
energy with respect to the inverse of the scattering length and with respect to
the interaction range. They are found to have extreme values at the unitary
limit. The virial results are used to check the quality of the variational wave
function involved in the calculations.

Quantum Gases