Semiclassical nature of planetary atom states

Abstract

The semiclassical quantization of classically stable planetary atom configurations (the so called frozen planet configurations) is discussed in some detail. The existence of (approximate) integrals of motion allows for a torus quantization procedure, the semiclassical limit of which is the Gutzwiller periodic orbit formula reduced to fundamental orbits only. We show that the multi-dimensional torus quantization yields accurate semiclassical energies for the planetary atom states. We compare our results with those obtained by a multipole model of the electron- electron interaction which has been proposed as a more transparent model for describing the frozen planet configurations. We give evidence that this model fails in predicting the energies for large quantum numbers.