Dynamics of atomic hydrogen in a generalized van der Waals potential

The classical dynamics of a hydrogen atom in a generalized van der Waals potential is investigated. In order to carry out the analytical and numerical investigations for a range of parametric values, we removed the singularity of the problem using Levi-Civita regularization and converted the problem into that of two coupled sextic anharmonic oscillators. We identify the integrable choices of the oscillator system using the Painlevé singularity analysis, and the associated second integrals of motion are derived using the extended Lie transformations. Numerical investigations are carried out for other nonintegrable regions and we observe chaos-order-chaos type of transition regions when one of the system parameters is varied.