Orthogonal transformations in the line space and modelling of rotational relaxation in the Raman spectra of linear tops

Collisional relaxation of linear tops is considered for molecular tensor quantities time-conserved in the ideal gas (angular momentum and its products). By introducing new bases in the line space (the associated Laguerre polynomials of a discrete variable), a simpler description of relaxation is attained. In the Markov limit, the relevant time autocorrelations are shown to decay slower than given by the mono-exponential law; a formula is derived for the correction. Using perturbation theory (PT), a general 4-state, non-Markovian expression for the relaxation matrix Gamma is found and analyzed. Based on this expression, a new model of Gamma is proposed and used to calculate the collisional cross sections characterizing depolarized Rayleigh scattering and rotational energy relaxation in nitrogen. Though on the rotational momentum scale the validity domains of the PT (high Js) and the infinite-order sudden approximation (low Js) complement each other, the structures of the expressions for the Gamma matrix elements given by both approaches appear to have much in common. (C) 1997 Elsevier Science B.V.