Influence of quantum defects on recurrence strengths of closed orbits

Abstract

Experimentally obtained Stark-recurrence spectra taken at low principal quantum numbers show unusual degrees of orbit profile asymmetry. To clearly illustrate the semiclassical mechanisms behind this behavior a numerical experiment is performed where orbit profiles (recurrence strength as a function of scaled energy) are found from computed Stark spectra. These spectra are generated for a wide range of quantum defects assuming a highly simplified excitation and core structure which represents a semiclassical system restricted to s-wave scattering. It is noted that at low quantum numbers, the expected dominant nonhydrogenic feature of recurrence spectra is scattered orbits whose scaled actions are unresolved from existing hydrogenic orbits. The semiclassical orbit profiles obtained from absorption spectra are compared with semiclassical closed-orbit theory. Closed-orbit theory successfully predicts the systematic shifting of recurrence strength as a function of quantum defect. In the limited parameter space investigated it is found that the distribution of recurrence strength is influenced primarily by interference with scattered combinations containing a primitive orbit repetition. The systematic shifting of recurrence strength as a function of quantum defect is attributed to a relative phase shift between the contributing orbits.