The third virial coefficient of depolarised-light-scattering spectral moments for moderately quantum systems

By means of the Wigner-Kirkwood (WK) method, the spectral moments of depolarized interaction-induced light scattering (DILS) spectra for a moderately quantum N-body system can be written as asymptotic expansions in powers of ?, whose terms are interpreted as successive corrections to the classical values. At low density, the DILS spectral moments obey a virial expansion, whose second and third coefficient (called respectively two-body and three-body moment) are experimentally accessible. While two-body moments depend, rigorously, only on the pair interaction potential and pair polarizability, three-body moments depend, also, on irreducible three-body potential and polarizability, and are therefore good candidates for the detection of these irreducible effects. We present here a general method for obtaining the two- and three-body spectral moments up to the second significant term in the WK series. We explicitly present, for the first time, the expression for the first quantum correction term to the second three-body spectral moment; this calculation requires one to consider dynamic correlations, in addition to the static corrections to the distribution function. The study of the temperature dependence of the first three classical and quantum-corrected moments is presented, over a large range of temperatures, for systems having different quantum behaviour, in order to infer the limits of applicability of the WK method. The results are presented, in reduced units, for a system of atoms interacting via a Lennard-Jones pair potential, and having dipole-induced-dipole pair induced polarizability.