Asymptotics of quantum mechanical atom-ion systems

We have analyzed and reduced a general (quantum-mechanical) atom-ion diatomic exchange energy formulation into fundamental mathematical forms, namely a particular class of single and. double definite integrals. These are of importance in the charge exchange of molecular processes in atmospheric physics and eventually of interest to matters related to climate. These integrals have been evaluated in terms of asymptotic expansions, with precise schemes for their numerical evaluation. Dividends, for algebraic aspects concerning identities of hypergeometric functions as well as summation techniques for divergent series are also discussed in this context.