THE EFFECT OF THE BREAKDOWN OF THE BORN-OPPENHETMER APPROXIMATION ON THE DIPOLE MOMENT AND QUADRUPOLE MOMENTS OF A DIATOMIC MOLECULE

Abstract

In the Born-Oppenheimer approximation the dipole moment of a vibronic level of a diatomic molecule can be expressed as a power series in $(v + \frac{1}{2})$ where v is the vibrational quantum number, i.e. $$ \mu_{v} = \mu^{(0)}+\mu^{(1)} \left[(B_{e}/ \omega_{e})\left(v + \frac{1}{2}\right)\right]+\mu^{(2)}\left[(B_{e}/ \omega_{e})\left(v + \frac{1}{2}\right)\right]^{2}+ \cdots $$ In this paper the effect of the breakdown of the Born-Oppenheimer approximation on the expression for $\mu_{v}$ for an isolated ground state $(^{1}\Sigma)$ of a diatomic molecule is determined. The main effect is to greatly increase the isotopic dependence of $\mu^{(0)}$ and a similar conclusion follows for the isotopic dependence of eqQ values. The theory is applied to the data available for HCl and HD.