Quantum theory of light scattering with environmental perturbations and finite temperatures

The quantum theory of the optical birefringence induced in molecular gases by external fields is discussed in a general setting. The scattering of light by molecules is expressed by the generalized Kramers-Heisenberg formula for the R-matrix element, and the Stokes parameter formalism is used to relate this scattering amplitude to the birefringence observables. Our approach is motivated by Van Vleck's quantum mechanical treatment of the Langevin-Debye formula; for a gas at finite temperature the relationship between the characteristics of the system perturbed by the external field and the unperturbed system can be obtained using thermodynamic perturbation theory. This is conveniently combined with the form of the scattering amplitude obtained in linear response theory, since the thermodynamic averaging and the effects of the external field can be treated in a unified way. We compare this Dyson series expansion method with the more traditional Rayleigh-Schrodinger perturbation theory approach and show how they generate equivalent representations of the scattering amplitude. The quantum thermodynamic average and its classical approximation are discussed in detail.