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.
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