# General Mathematical Formulation of Scattering Processes in Atom-Diatomic Collisions in the RmatReact Methodology

## TL;DR

This paper extends the R-matrix method to model complex atom-diatomic collision processes, including reactive scattering, by developing a comprehensive mathematical framework suitable for ultracold collision scenarios.

## Contribution

It introduces a general mathematical formulation for reactive and non-reactive scattering within the R-matrix framework, addressing the challenges of finite inner regions and complex coordinate sets.

## Key findings

- Formulated the R-matrix approach for reactive scattering processes.
- Addressed the mathematical challenges of finite domain integrals.
- Extended the methodology to include charge exchange and photo-processes.

## Abstract

Accurately modelling cold and ultracold reactive collisions occuring over deep potential wells, such as \ce{D+ + H2 -> 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, photo-association, photo-dissociation, 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. % The choice of coordinate set and basis function is these cases becomes more complexThis introduces substantial challenges to the basis sets utilised in practical calculations as integrals over finite domains are often much more challenging than over infinite domains for this problem.