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Problem of two Coulomb centres at large intercentre separation: asymptotic expansions from analytical solutions of the Heun equation. (English) Zbl 0960.81075
Summary: The case of large intercentre distance in the two Coulomb centres problem is studied by solving separated wave equations with the help of a series of confluent hypergeometric functions. By considering the confluence of two singularities in an auxiliary equation with four regular singularities, new relations between the solutions of the quasi-angular equation are found and used to obtain exponentially small terms in the asymptotic expansion for energy eigenvalues. For some electronic states, energy splittings at pseudocrossings are evaluated, and results are compared with those of earlier asymptotic and numerical calculations.

MSC:
81V55Applications of quantum theory to molecular physics
33C90Applications of hypergeometric functions