When one of the electrons in a diatomic molecule is highly excited, the molecular system is, in many respects, similar to a hydrogen atom; a single electron moves in the field of a small, singly charged core. These states, called Rydberg states of the diatomic molecule, can essentially be characterized by hydrogenic quantum numbers $n$ and $l$, provided that $n$ is large enough so that the orbital radius of the Rydberg electron is large compared to the dimensions of the ion core. However, unlike the hydrogen atom, the ionic core generates not only a Coulomb field, but higher multipole potentials as well. In addition, the ionic core can be vibrationally and rotationally excited with excitation energies greater than the binding energy of the Rydberg electron. When this happens, auto-ionization can occur. This process is very similar to the nuclear internal-conversion process in which an excited nucleus, instead of emitting a $\gamma$ ray, de-excites by giving up its energy directly to an atomic electron. By taking advantage of the similarity between the autoionization and internal-conversion processes, auto-ionization lifetimes for Rydberg states of ${\mathrm{H}}_2$ and HD are calculated. These results are compared with experimental results and with those obtained from an alternative approach.

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