What is it about?
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.
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Why is it important?
This lays down the mathematical foundations of the Holstein-Herring/Chibisov surface integral method for calculating the elusive exchange energy splittings of the lowest discrete states for diatomic atom-ion systems, the simplest being the Hydrogen Molecular Ion (H_2^+). This energy splitting is of paramount importance in e.g. atmospheric and stellar Physics.
Perspectives
This paper is followed by a later paper producing a general algorithm. The results of calculations for other systems are shown. This approach is by no means exhausted.
Dr Tony Cyril Scott
RWTH-Aachen University
Read the Original
This page is a summary of: Asymptotics of Quantum Mechanical Atom-Ion Systems, Applicable Algebra in Engineering Communication and Computing, September 2002, Springer Science + Business Media,
DOI: 10.1007/s002000200100.
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