Abstract
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.
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