SEMICLASSICAL APPROACH TO FEW-BODY PROBLEMS - THE HELIUM ATOM

We report on recent progress in the semiclassical description of two-e lectron atoms. We show that the classical dynamics for the helium atom is of mixed phase space structure, i.e. regular and chaotic motion co exists. Semiclassically, both types of motion require separate treatme nt. Stability islands are quantized via the Einstein-Brillouin-Keller torus-quantization procedure, whereas a periodic-orbit cycle expansion approach accounts for the states associated with hyperbolic electron pair motion. The results are compared with highly accurate ab initio q uantum calculations, some of which are reported here for the first tim e.