Semiclassical photoionization cross section of the hydrogen atom in a magnetic field

We test the accuracy of the semiclassical approximation for a completely chaotic system, the strongly magnetized hydrogen atom. We study a quantity of direct experimental interest, the photoabsorption cross section. The standard semiclassical approximation using periodic orbits is used (without any additional trick to improve convergence) and is shown to agree very well with a fully resolved ab initio quantum ``exact'' calculation. We also study the families of periodic orbits giving the dominant contributions to the spectrum.