Capture into resonance in dynamics of a classical hydrogen atom in an   oscillating electric field
  We consider a classical hydrogen atom in a linearly polarized electric field of slow changing frequency. When the system passes through a resonance between the driving frequency and the Kepler frequency of the electron's motion, a capture into the resonance can occur. We study this phenomenon in the case of 2:1 resonance and show that the capture results in growth of the eccentricity of the electron's orbit. The capture probability for various initial values of the eccentricity is defined and calculated. 
Anatoly Neishtadt and Alexei Vasiliev