The effect of correlation of inhomogeneous environmental shifts on Raman depolarization ratio dispersion

The magnitude and sense of correlation between the inhomogeneous broadening distributions of two neighboring electronic states is shown to have a sign ificant effect on the dispersion of the depolarization ratio, rho, for Rama n scattered radiation. To examine this effect quantitatively we treat numer ically a model in which two electronic excitations with mutually perpendicu lar transition dipole orientations are represented by shifted one-dimension al harmonic potentials. The inhomogeneous broadening is treated in the stat ic limit as a Gaussian fluctuation in each of the two electronic origins. T he correlation of these shifts is treated as a variable with the fully corr elated and fully anti-correlated limits spanning the uncorrelated case. It is shown that the degree of correlation (and its sign) strongly influences the value of the depolarization ratio in some cases which should be amenabl e to experimental study. Three cases are treated which differ in the separa tion of the electronic origins of the two states from larger than the total transition width, less than the transition width, and zero. If the state d egeneracy is due to symmetry, then in this last case the correlation of the inhomogeneous fluctuations becomes equivalent to symmetric and anti-symmet ric environmental variations.