Diatomic molecules with large angular momentum in the Born-Oppenheimer approximation

摘要

The standard Born-Oppenheimer approximation for a diatomic molecule yields an expansion in powers of is an element of for the bound state associated with a given electron energy level, a fixed vibrational quantum number n and a fixed nuclear angular momentum quantum number l. The expansion parameter is an element of 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 is an element of(5) whenever the nuclear angular momentum quantum number satisfies l < k is an element of(-3/ 2). We apply our approximation to the H-2(+) and HD+ ions and compare the results with published rotational-vibrational energies.