Jp. Salas et V. Lanchares, SADDLE-NODE BIFURCATION FOR RYDBERG ATOMS IN PARALLEL ELECTRIC AND MAGNETIC-FIELDS, Physical review. A, 58(1), 1998, pp. 434-439
A comprehensive study of the hydrogen atom in the presence of parallel
electric and magnetic fields is presented from the standpoint of clas
sical mechanics for a nonzero magnetic quantum number rn. The transiti
on from pure Zeeman effect to Stark effect is explored intensively by
means of Poincare surfaces of section for a pair of m values and for d
ifferent values of the field strengths. It is found that the transitio
n from pure Zeeman effect to Stark effect passes through a saddle-node
bifurcation.