ANALYTIC CALCULATION OF THE AFTEREFFECT SOLUTION AND CORRELATION TIMEOF THE INDUCED DIPOLE KERR-EFFECT

The exact analytic aftereffect functions for the Kerr-effect relaxatio n of an assembly of symmetric top molecules having induced dipole mome nts only are calculated from the rotational diffusion equation (Smoluc howski equation). The solution is obtained in the case where the molec ules are acted on by a strong de field E(c), superimposed on which is a weak probe: field E(1)(t) suddenly snitched off at time t=0. By calc ulating the Laplace transforms of these aftereffect functions, two nor malized autocorrelation functions are established, thus allowing one t o express the corresponding birefringence ac responses by using linear response theory in the manner derived by Coffey er al. [Phys. Rev. E 49, 1869 (1994)] for the longitudinal susceptibility of single-domain ferromagnetic particles. The connection between aftereffect and ac res ponses holds insofar as only one matrix relaxation function is needed for describing the induced dipole Kerr effect. Then, exact expressions for the correlation time and the effective relaxation time are derive d in terms of Kummer functions and compared. It is shown that as soon as the dc field parameter g(c) exceeds 3, the birefringence decay proc ess is no longer dominated by the first nonvanishing eigenvalue of the differential matrix set (solution of the Smoluchowski equation) unlik e dielectric relaxation, but by the second one. Moreover, dispersion p lots and Cole-Cole diagrams as well as phase angles for the second har monic component are presented for various values of g(c) in order to s ee how they deviate from the Debye-like spectra.