Closed-orbit theory and the photodetachment cross section of ${\mathrm{H}}^{\mathrm{-}}$ in parallel electric and magnetic fields

In this paper we obtain a simple analytic formula for the photodetachment cross section of ${\mathrm{H}}^{\mathrm{-}}$ in parallel electric and magnetic fields. The three-dimensional semiclassical approximation predicts oscillations in the spectrum and correlates these oscillations with closed classical orbits. The cylindrical symmetry of the Hamiltonian produces some interesting effects. In particular, at boundary energies the semiclassical approximation fails as a focused cusp approaches the origin.