Sharon M. Hughes and George A. Hagedorn
Diatomic Molecules with Large Angular Momentum in the Born-Oppenheimer Approximation
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ABSTRACT.  The standard Born--Oppenheimer approximation for a diatomic molecule yields an expansion in powers of $\eps$ for the bound state associated with a given electron energy level, a fixed vibrational quantum number $n$, and a fixed angular momentum quantum number $l$. The expansion parameter $\eps$ is the fourth root of the ratio of the electron mass divided by the mean nuclear mass. In this paper we present an explicit approximation whose errors are uniformly bounded by~ $C\,\eps^5$~ whenever the angular momentum quantum number satisfies~ $l<\kappa\,\eps^{-3/2}$. 
We apply our approximation to the $H_2^{+}$ and $HD^{+}$ ions and compare the results with published rotational--vibrational energies.