Classical view of the properties of Rydberg atoms: Application of the correspondence principle

The properties of Rydberg atoms are contrasted with those of hydrogen atoms using both classical and quantal points of view. It is shown that, classically, the effects of the ionic core of the Rydberg atom produce a precession of the otherwise Keplerian elliptical orbit of the excited electron, and that this precession is responsible for the nonhydrogenic properties. Using the correspondence principle, classical properties are then related to quantum mechanical properties by correlating the precession frequency with the quantum defect δ_l. The linear and quadratic Stark effects are also discussed and it is shown that a negative polarizability of the atom is a consequence of a positive ∂δ_l/∂l. In the Appendix, the ‘‘gravitational defect’’ associated with the precession of the perihelion of the Keplerian orbit of the planet Mercury is presented.