Birefringence induced by a static electric field gradient

Abstract

A quantum theory of the birefringence induced in a molecular gas by a static electric field gradient is presented; it is an application of the finite temperature perturbation theory to molecular light scattering described in the preceding paper. The kinematics of the experiment are dealt with explicitly through the use of a space-fixed frame based on a set of canonically conjugate variables for the centre-of-mass and internal motions of the molecule. This leads to a definition of the molecular multipoles that is different from the conventional one and there are no ‘origin-dependence problems’ at any stage of the calculation. The susceptibility that governs the birefringence is analysed in the spirit of Van Vleck's quantum mechanical account of polarity in terms of the magnitude, relative to k _B T, of the energy level separations associated with the dominant matrix elements of the external field V and the current operator j(k). As in previous treatments, the main contribution is inversely proportional to the temperature, and there is also a temperature independent term. The birefringence depends on the matrix elements of the molecular quadrupole moment operator; in the framework used here, this has a definition independent of the polarity of the molecule.