  Theory of the birefringence of the refractive index in atomic diamagnetic
dilute gases in the presence of static electric (optical Kerr effect) and
magnetic (Cotton-Mouton effect) fields is formulated. Quantum-statistical
expressions for the second Kerr and Cotton-Mouton virial coefficients, valid
both in the low and high temperature regimes, are derived. It is shown that
both virial coefficients can rigorously be related to the difference of the
fourth derivatives of the thermodynamic (pressure) virial coefficient with
respect to the strength of the non-resonant optical fields with parallel and
perpendicular polarizations and with respect to the external static (electric
or magnetic) field. Semiclassical expansions of the Kerr and Cotton-Mouton
coefficients are also considered, and quantum corrections up to and including
the second order are derived. Calculations of the second Kerr and Cotton-Mouton
virial coefficients of the helium-4 gas at various temperatures are reported.
The role of the quantum-mechanical effects and the convergence properties of
the semiclassical expansions are discussed. Theoretical results are compared
with the available experimental data.
