  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.
