Electrodynamics of helium with retardation and diffusion along the center manifold of Wannier orbits

Abstract

We show that an extra complex constant of motion with an analytic form can exist in the neighborhood of some discrete Wannier orbits of helium, when one includes retardation and self-interaction effects. The energies of these discrete Wannier orbits are in the correct atomic magnitude. The highest frequency in the stable manifold of one such orbit agrees with the highest frequency sharp line (2P-1S) of parahelium to within two percent. The generic term of the frequency in the stable manifold to higher orbits is also in agreement with the asymptotic form of quantum mechanics for helium.