ORTHOGONAL TRANSFORMATIONS IN THE LINE SPACE AND MODELING OF ROTATIONAL RELAXATION IN THE RAMAN-SPECTRA OF LINEAR TOPS

Collisional relaxation of linear tops is considered for molecular tens or quantities time-conserved in the ideal gas (angular momentum and it s products). By introducing new bases in the line space (the associate d Laguerre polynomials of a discrete variable), a simpler description of relaxation is attained. In the Markov limit, the relevant time auto correlations are shown to decay slower than given by the mono-exponent ial law; a formula is derived for the correction. Using perturbation t heory (PT), a general 4-state, non-Markovian expression for the relaxa tion matrix Gamma is found and analyzed. Based on this expression, a n ew model of Gamma is proposed and used to calculate the collisional cr oss sections characterizing depolarized Rayleigh scattering and rotati onal 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 approache s appear to have much in common. (C) 1997 Elsevier Science B.V.