Contribution of forbidden orbits in the photoabsorption spectra of atoms and molecules in a magnetic field

In a previous work [Phys. Rev. A 66, 013410 (2002)], we noted a partial disagreement between quantum R matrix and semiclassical calculations of photoabsorption spectra of molecules in a magnetic field. We show that this disagreement is due to a nonvanishing contribution of processes, which are forbidden according to the usual semiclassical formalism. Formulas to include these processes are obtained by using a refined stationary phase approximation. The resulting higher order in $ħ$ contributions also account for previously unexplained “recurrences without closed orbits.” Quantum and semiclassical photoabsorption spectra for Rydberg atoms and molecules in a magnetic field are calculated and compared to assess the validity of the first-order forbidden orbit contributions.