Dynamics of a Rydberg Hydrogen Atom in a Generalized van der Waals Potential and a Magnetic Field

The classical dynamics of a Rydberg hydrogen atom in a generalized van der Waals potential plus a magnetic field is investigated by using the Poincaré surface of section and phase space trajectories method. The dynamical character of this system depends sensitively on the magnetic field strength. The numerical calculations show that for a certain van der Waals potential, its classical dynamics is regular without the external magnetic field. However, with the addition of the external magnetic field, the dynamical property of the Rydberg hydrogen atom begins to change. With the increase of the magnetic field strength, order-chaos-order-chaos types of transition regions are observed for the hydrogen atom. As the magnetic field strength is very large, nearly all the phase space trajectories are chaotic. Under this condition, only chaotic motion appears. This is caused by the diamagnetic Zeeman effect. Our study provides a different perspective on the dynamical behavior of the Rydberg atom in the van der Waals potential and magnetic field.