Review of Classical Analytical Results for the Motion of a Rydberg Electron around a Polar Molecule under Magnetic or Electric Fields of Arbitrary Strengths in Axially Symmetric Configurations

Abstract

We review classical studies of the oscillatory-precessional motion of an electron in the field of an electric dipole (the latter representing the polar molecule) with or without external magnetic or electric fields. The focus is on the most recent studies. In one study (at zero external field), it was shown that, generally, the oscillations being in the meridional direction and the precession being along parallels of latitude can take place on the same time scale—contrary to the statement from the previous literature. In another study, it was shown that a magnetic field enables new ranges of the bound oscillatory-precessional motion of the Rydberg electron and that in one of the new ranges, the period of the θ-oscillations has the non-monotonic dependence on primary parameter of the system. This is a counterintuitive result. In yet another study, it was shown that under the electric field there are two equilibrium circular states of a positive energy and one equilibrium state of a negative energy. The existence of the equilibrium state of the negative energy is a counterintuitive result since at the absence of the field, the bound state was possible only for the zero energy. Thus, it is a counterintuitive result that in this case the electric field can play the role of a stabilizing factor.

On Invariant Vectors in the Presence of Electric and Magnetic Fields

“…From a more-general viewpoint, the author discussed the conditions for the introduction of the concept of a "generalized" linear (angular) momentum in analogy with the concept of mechanical energy. Oks reviewed classical studies of the oscillatory-precessional motion of an electron in the field of an electric dipole (the latter representing the polar molecule) with or without external magnetic or electric fields [134]. In future work, we plan to discuss the case of the anisotropic harmonic oscillator and, especially, its connections with the effect of an external electric field on the energy levels of a hydrogen atom [135,136].…”