Allowed and forbidden transition probabilities have been computed using a variational many-electron theory (Jauregui, Bunge and Ley-Koo, Phys. Rev. A55 (1997) 1781) incorporating positive-energy and negative-energy orbitals without ambiguities, and absolutely free from variational collapse. The results agree with experiment and give results very closely but not exactly to other calculations based on the no-pair Hamiltonian where ad hoc negative-energy orbitals occur in first-order corrections to the wave functions.