Theory of excitons in liquids. IV. A Simplified treatment of the shift and damping of polarization waves

A simplified theory of the scattering of polarization waves in a liquid arising from the thermal motion of the atoms is presented. The treatment departs somewhat from the general lines of the formal exciton theory in disordered systems set up in the previous papers of this series. Most important, some additional approximations designed to simplify the analysis are introduced. The frequency-dependent lifetime of the transitions is calculated using second-order perturbation theory. From this, an expression is deduced for the damping coefficient of excitation waves, both in the case of an impurity atom in a host liquid and in the case of a pure liquid. In both calculations, the thermal motion of the atoms is represented as a small step diffusion or by using a linear-trajectory approximation. A rough numerical estimation of the level broadening produces the expected orders of magnitude for the lifetimes of states in Ar. Finally, an alternative approach to the exciton problems is discussed in much the same spirit as the Zwanzig treatment of elementary excitations in classical liquids. In the absence of scattering, we demonstrate that this approach leads to the correct form of the exciton dispersion relation.