Undulations in potential curves analyzed using the Fermi model: LiH, LiHe, LiNe, and ${\mathrm{H}}_2$ examples

The interaction of a Rydberg electron with a ground-state atom is modeled using the Fermi approximation to obtain long-range potentials for various excited diatomic molecules. Particular attention is paid to cases of degenerate and near-degenerate atomic Rydberg levels. Extensive comparisons are performed with recent ab initio calculations for ${}^1{\Sigma }^{+}$ and ${}^3{\Sigma }^{+}$ states of LiH and ${\mathrm{H}}_2,$ also ${}^2{\Sigma }^{+}$ states of LiHe, for up to the ninth state of a specified symmetry. Results for LiNe are also discussed. Overall, good qualitative and in some cases quantitative agreement is found. For isolated states, the undulations in the potentials clearly reflect the nodal pattern of the Rydberg state involved and the magnitude is fixed in the Fermi approach by the electron-ground-state atom scattering length. When several states are close in energy, in the Fermi model because of the factorizable nature of the interaction, only a single nonzero potential emerges from the remaining flat manifold. Such behavior explains, for example, the presence of high barriers at large distances seen in ab initio calculations for the ${}^{1,3}{\Sigma }_{g,u}^{+}$ $n=3\mathrm{}$ states of molecular hydrogen. For the systems involving H the Fermi results are generally better for the weaker, triplet, interactions than the singlets. In the case of near-degenerate levels the weaker interactions are normally described better than the stronger interaction, where avoided crossings (not included in this simple model) may be important. In LiHe, where the interactions are weaker, generally for separations larger than about ${10a}_0$ the Fermi model obtains barrier positions within ${1a}_0$ and maxima within 10 ${\mathrm{cm}}^{\mathrm{-}1}$. For LiNe, because of the very small scattering length for electrons in neon, largely qualitative results are obtained. The Fermi model is also shown to yield a physically sound diabatic approach for excited states of diatomic molecules, allowing for a deeper understanding of the unusual shapes of the adiabatic curves. Limitations of the Fermi model are also discussed.