General mathematical formulation of scattering processes in atom–diatomic collisions in the RmatReact methodology

Accurately modelling cold and ultracold reactive collisions occurring over deep potential wells, such as D + + H 2 → H + + HD , requires the development of new theoretical and computational methodologies. One potentially useful framework is the R -matrix method adopted widely for electron–molecule collisions which has more recently been applied to non-reactive heavy-particle collisions such as Ar–Ar. The existing treatment of non-reactive elastic and inelastic scattering needs to be substantially extended to enable modelling of reactive collisions: this is the subject of this paper. Herein, we develop the general mathematical formulation for non-reactive elastic and inelastic scattering, photoassociation, photodissociation, charge exchange and reactive scattering using the R -matrix method. Of particular note is that the inner region, of central importance to calculable R -matrix methodologies, must be finite in all scattering coordinates rather than a single scattering coordinate as for non-reactive scattering. This article is part of a discussion meeting issue ‘Advances in hydrogen molecular ions: H 3 + , H 5 + and beyond’.