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Zbl 0960.81075
Bogush, A.A.; Otchik, V.S.
Problem of two Coulomb centres at large intercentre separation: asymptotic expansions from analytical solutions of the Heun equation. (English)
[J] J. Phys. A, Math. Gen. 30, No.2, 559-571 (1997). ISSN 0305-4470

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 2000:: *81V55 Appl. of quantum theory to molecular physics
33C90 Appl. of hypergeometric functions

Keywords: two Coulomb centres problem; separated wave equations; confluent hypergeometric functions; asymptotic expansion; energy eigenvalues; electronic states; energy splittings at pseudocrossings

Cited in: Zbl 1092.81019

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