Theory of the angular distribution of molecular photofragments

Abstract

The theory of the anisotropy of the flux of molecular fragments produced by polarized light has been discussed previously for linear molecules by Zare, Jonah, and Busch and by Wilson but is here analyzed more systematically for an arbitrary molecule. Polarized light creates a cosine squared distribution of excited molecules and the distribution of fragments is given by f(θ) = (1/4π)[1 + βP2(θ)], where θ is the angle between the detection direction and the electric vector of the light. The parameter β depends on the orientation in the molecular framework of the transition dipole moment and the dissociation direction and on the time averaged correlation functions 〈 〈 Dm m′(2) [δ Ω (t)]〉 〉 of the rotating molecules. The correlation functions can be evaluated exactly for linear and spherical top molecules and can be expressed in terms of one dimensional integrals for symmetric tops using the techniques of St. Pierre and Steele. Correlation functions for asymmetric tops have not yet been evaluated. These correlation functions are not only averages over the Boltzmann distribution of rotational energies of the molecules, but they are also averages over the distribution of lifetimes of the excited state. Thus the anisotropy β emerges as a rather complex quantity but numerous formulae for β are given which apply to special cases of practical interest.