Thermal energy scattering of alkali atoms from halogen atoms and molecules: the effect of curve crossing

Abstract

A semi-classical theory for the effects of curve crossing on the thermal energy differential elastic scattering cross section for alkali-halide and alkali atom-halogen molecule systems is developed. It is shown how in the M-X case the cross section goes over from being determined by the ‘covalent’ potential curve to being determined by the ‘ionic’ curve as the interaction between the states increases. The first, and probably most important effect in practice, is the loss of low angle scattering and the appearance of some high angle structure. In the M-X₂ case the possibility of chemical reaction leads to a progressive loss of high angle scattering as the interaction increases. The loss of elastic scattering provides a measure of the reaction cross section σ(E) and hence of the reaction rate constant k. Expressions for σ(E) and k, which are decreasing functions of E and T respectively, are given in terms of only two parameters, the position of the crossing point r_x , and a quantity with dimensions of energy, U = ½mA ⁴[2π/ħ(F ₁ - F ₂)]², where F ₁ and F ₂ are the slopes of the potential curves at the crossing point.