NONLINEAR DIELECTRIC-RELAXATION AND DYNAMIC KERR-EFFECT IN A STRONG DC ELECTRIC-FIELD SUDDENLY SWITCHED ON - EXACT-SOLUTIONS FOR THE 3-DIMENSIONAL ROTATIONAL DIFFUSION-MODEL

The infinite hierarchy of differential-recurrence relations for ensemb le avenges of the spherical harmonics pertaining to the noninertial ro tational Brownian motion of an ensemble of polar and anisotropically p olarizable molecules in a strong external de electric field is derived by averaging the underlying Langevin equation. This procedure avoids recourse to the Fokker-Planck equation, the solution of which involves complicated mathematical manipulations. Exact analytic solutions for the spectra of the relaxation functions and relaxation times for nonli near dielectric relaxation and dynamic Kerr effect of symmetric top mo lecules are calculated for two limiting cases, namely, pure induced di pole moments and pure permanent moments, using the continued fraction method. The general case where both types of moment are taken into acc ount is then considered by using matrix continued fractions. Exact exp ressions for the dielectric and Kerr effect relaxation times are also derived as functions of the parameters xi and sigma characterizing the field-off and the induced dipole moments. Plots of these relaxation t imes are presented for various values of xi and sigma. The nonlinear r elaxation behavior is emphasized in figures showing how the real and i maginary parts of the spectra of the relaxation functions deviate from the Lorentzian profiles.