Saddle-node bifurcation for Rydberg atoms in parallel electric and magnetic fields

A comprehensive study of the hydrogen atom in the presence of parallel electric and magnetic fields is presented from the standpoint of classical mechanics for a nonzero magnetic quantum number $m.\mathrm{}$ The transition from pure Zeeman effect to Stark effect is explored intensively by means of Poincaré surfaces of section for a pair of $m$ values and for different values of the field strengths. It is found that the transition from pure Zeeman effect to Stark effect passes through a saddle-node bifurcation.