Rotationally inelastic cross sections and the parameters of the potential

Abstract

The dependence of rotationally inelastic cross sections on the parameters of the interaction potential has been investigated for a model system consisting of a homonuclear diatomic molecule and an atom. The potential, V( r, θ) = C e −α r[1 + Σ 40 l = 2 a l P l (cos θ)] has been employed and the computations have been performed by the modified infinite-order sudden approximation. It is found that σ(0→ l) = Ac 2 l , where c l = b l /(1 + Σ| b l |), with ▪, and A is a constant that does not depend on a l and l. The limitations of this result with the variation in l, a l and energy have also been studied. The results are discussed to explain the existence of scaling and fitting laws, and to show the importance of expressing the potential in terms of a set of orthonormal functions, ▪, in place of the Legendre polynomials, P l (cos θ).