  The virial expansion method is applied within a harmonic approximation to an
interacting N-body system of identical fermions. We compute the canonical
partition functions for two and three particles to get the two lowest orders in
the expansion. The energy spectrum is carefully interpolated to reproduce
ground state properties at low temperature and the non-interacting large
temperature limit of constant virial coefficients. This resembles the smearing
of shell effects in finite systems with increasing temperature. Numerical
results are discussed for the second and third virial coefficients as function
of dimension, temperature, interaction, and the transition temperature between
low and high energy limits.

Statistical Mechanics;Quantum Gases;Nuclear Theory;Quantum Physics