$\frac{1}{R}$ Expansion for $H_{2}^{+}$ : Analyticity, Summability, Asymptotics, and Calculation of Exponentially Small Terms

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26 March 1984

journal article
research article
Published by American Physical Society (APS) in Physical Review Letters

Vol. 52 (13) , 1112-1115
https://doi.org/10.1103/physrevlett.52.1112

Abstract

The

\frac{1}{R}

perturbation series for

H_{2}^{+}

has a complex Borel sum whose imaginary part determines the asymptotics of the perturbed energy coefficients

E^{(N)}

. The full asymptotic expansion for the energy includes complex, exponentially small terms:

{E (R) \sim Σ E^{(N)} {(2 R)}^{- N} +, e^{- \frac{R}{n}} Σ a^{(N)} {(2 R)}^{- N}} {+ e^{- \frac{2 R}{n}} [Σ d^{(N)} {(2 R)}^{- N} + log R terms] \pm i e^{- \frac{2 R}{n}} Σ c^{(N)} {(2 R)}^{- N} + \dots}

Keywords

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