Rydberg states of the hydrogen atom interacting with a metal surface and a perpendicular magnetic field

Abstract

The interaction between Rydberg atoms and a metal surface can be described by the instantaneous van der Waals potential for larger atom–surface distances. This interaction breaks the spherical symmetry of free atom and, due to the lack of a third integral of motion, the problem is non-integrable. A similar situation occurs for the hydrogen atom in a constant magnetic field. We show, however, that in a combined case with the magnetic field perpendicular to the surface, this system becomes integrable at a given atom–surface distance for a specific value of the field.