Ghost orbits in the diamagnetic hydrogen spectrum using harmonic inversion- art. no. 032504

The harmonic inversion method is applied in the case of the hydrogen atom i n a magnetic field to extract classical information from the quantum photo- ionization cross section. The study is made close to a saddle-node bifurcat ion for which the usual semiclassical formulas give diverging contributions . All quantities (actions, stabilities, and Maslov indices) for real orbits above the bifurcation and for complex ghost orbits below the bifurcation, are found to be in excellent agreement with the modified semiclassical pred ictions based on a normal form approach.