Electron-bound states in the field of dipolar molecules

Abstract

We study Clary's theory for an electron in the field of a dipolar molecule. We find for a molecule of rotor constant $B$ and dipole moment $\ensuremath{\mu}$ that Clary's ``rotationally adiabatic'' molecular potential ${ϵ}_{ad}(r)$ behaves like $\ensuremath{-}64{r}^{4}∕3{\ensuremath{\mu}}^{4}$ near $r=0$ and like $\ensuremath{-}{\ensuremath{\mu}}^{2}∕6B{r}^{4}$ at infinity. We show, using general results about the spectrum of the Schr\"odinger Hamiltonian, that the salient features of the electron bound states spectrum, i.e., the existence of only a few weakly bound states, are a consequence of these asymptotic formulas. We argue that the long-range $(1∕{r}^{4})$ part of the interaction may be interpreted as resulting from the angle-averaged molecular dipole potential at some rotation temperature. Our results should be contrasted with those of Camblong et al. Phys. Rev. Lett. 87, 220402 (2001), who claim that these features arise from the renormalization of the static point dipole interaction.