Two pitchfork bifurcations in the polar quadratic Zeeman-Stark effect

In the framework of classical mechanics, a study of the hydrogen atom in the presence of parallel electric and magnetic fields is presented when the magnetic quantum number m is zero. By means of perturbation methods and Poincaré surfaces of section, the existence of the three states experimentally detected by Cacciani et al. (the so-called I, II, and III Cacciani's states), their energy extensions, their evolution and their disappearance are explained as a result of two pitchfork bifurcations. © 1998 Elsevier Science B.V