Effects of a core electric dipole moment on Rydberg states

Abstract

The problem of a hydrogenic atom with an electric dipolar nucleus is treated as a simple model of the Rydberg states of a molecule with an electric dipolar core. This problem is separable in spherical polar coordinates, and the radial Schrödinger equation can be solved analytically. Alternatively, it provides an interesting example of Dalgarno-Lewis direct perturbation theory. The perturbation solution is used to obtain approximate formulae for various spectroscopically observable effects, including quantum defects, intensity effects, and orbital angular momentum matrix elements. These formulae should be applicable to states with small quantum defects, such as states with higher values of the angular momentum quantum number l, but they are also useful in showing qualitative tendencies for other states.