Institute of Theoretical and Experimental Physics,

Bol'shaya Cheriomushkinskaya 25, Moscow, 117259 Russian Federation

S.I.Vavilov State Optical Institute, Tuchkov per. 1, Saint

Petersburg, 199034 Russian Federation, e-mail sergeev@soi.spb.su

The energy of atoms is expanded as a power series in 1/n, where

n is the principal quantum number. We assume that

while . In an essence, such an expansion is

equivalent to the recently developed dimensional expansion [1]. It

is a semiclassical method, which is rather similar to the methods

of molecular vibration analysis. The problem reduces to Rayleigh -

Schrödinger perturbation theory for anharmonic oscillator. Some

difficulties arise from the divergence of the 1/n-expansion. To

sum the divergent series, various methods are used, such as Padé -

Borel approximants. To take full advantage of them, one should

take into account the divergent large-order behaviour of the

expansion responsible for the nearest singularity to the origin in

the Borel function [1].

Typically, the coefficients in the expansion grow as

factorials, , with . We found that the

parameter coincides with the reciprocal of the action

integral, the constants and are also calculable.

Here we extend our recent results [2] to multidimensional

effective potentials for treating nonspherically symmetric and two

-electron atoms. In this case, the determination of the most

probable escape path which minimizes the classical action becomes

a nontrivial task. We examine the parameter for Stark and

Zeeman effects in a hydrogen atom, ion, and helium

isoelectronic sequence. The results may be incorporated into

summation schemes in order to yield highly accurate energies.

1. GOODSON D.Z.,LÓPEZ-CABRERA M.et al, J.Chem.Phys.,›4m97›m,8481,1992.

2. POPOV V.S., SERGEEV A.V., Phys.Lett.A, ›4m172›m, 193, 1993.›z›"z


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