Resonances and Recurrences in the Absorption Spectrum of an Atom in an Electric Field

We use closed-orbit theory to study the absorption spectrum of an atom in an electric field. In previous work we examined absorption spectra above the zero-field ionization threshold. Only one closed orbit exists there, and it is unstable. Now we examine the situation below threshold. Here, the orbit parallel to the electric field is stable and, as the energy decreases, many other closed orbits bifurcate out of it. These closed orbits have simple patterns, and the associated recurrences are most clear if the absorption spectrum is measured using a scaled-variables method. The relation between the semiclassical Einstein-Brillouin-Keller-Marcus (EBKM) theory and periodic-orbit or closed-orbit theory is examined: they are complementary methods in the same sense that energy and time are complementary variables in quantum mechanics. Our numerical calculations show that sinusoidal fluctuations contributed by the closed orbits combine into peaks, and these peaks are in the locations predicted by EBKM theory