Langmuir's Helium-Like Models Revisited

Abstract

Abstract Classical two-electron configurations, proposed by Langmuir in the days of Old Quantum Theory as models for helium-like atoms, have been examined making use of modern semiclassical theory for the periodic orbits quantization. Combining both analytical and numerical investigations, energy spectra for the rotor-like and oscillator-like models have been evaluated, for the nuclear charges Z = 1, 2, 3, 6. No essential improvement of the original result (for Z = 2) is obtained, signifying that either configuration turns out to be inferior to the simple Bohr's planetary model. Stability of these systems with respect to small perturbations has been examined and a general criterion for selecting classical models as candidates for atomic orbitals within the semiclassical theory is discussed.