Knowledge Bank

Recently, Harris and $Jungen1$ have shown that the dipolar core of the CaF molecule has an important effect on its Rydberg $states2$. Here the hydrogen atom with an electric dipolar core is treated as a simple model of such a system. The Hamiltonian is separable in spherical polar coordinates, and the angular factor is the same as for the Stark effect of a rigid linear $molecule3$. This must be calculated numerically, but the radial factor is analogous to that of the Kratzer $potential4$, and can be solved analytically. Alternatively, this system provides an interesting example of the direct (or Dalgarno-$Lewis5$) perturbation method. Perturbation formulas will be presented for the electronic energy levels and intensities, and for angular momentum matrix elements. It is hoped that these results will assist in the understanding of the spectra of the rare-gas $hydrides6$.