C1 non-integrability of a hydrogen atom in a circularly polarized
2012 - J.L. Guirao, M.A. López, J. A. Vera
Central European Journal of Physics. 10(4), 742-748 (2012)
Barrabés et al. [Physica D, 241(4), 333-349, 2012] consider the problem of the hydrogen atom interacting with a circularly polarized microwave field modeled as a planar perturbed Kepler problem. For different values of the parameter, the authors offer some numerical evidence of the non-integrability of this problem. The objective of the present work is to give an analytical proof of the C1 non-integrability of this problem for any value of the parameter using the averaging theory as a main tool.