1mLARGE ORDERS OF THE 1/n-EXPANSION IN ATOMIC PHYSICSm
POPOV V.S., 4mSERGEEV A.V.m
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 email@example.com
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 . 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 .
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  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.,4m97m,8481,1992.
2. POPOV V.S., SERGEEV A.V., Phys.Lett.A, 4m172m, 193, 1993.z"z
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