STRONG-FIELD CYCLOTRON SCATTERING .1. SCATTERING-AMPLITUDES AND NATURAL LINE-WIDTH

The introduction of resonance line width into the QED cyclotron scattering amplitudes is considered. It is shown that the width arises from loop corrections to the electron propagator, which also bring about shifts in the Landau energy levels. A formalism is developed that allows the dressed electron propagator to be derived. It is shown that the states of Herold, Ruder, & Wunner, and of Sokolov & Ternov, which diagonalize the component of the magnetic moment operator parallel to the external magnetic field, are appropriate for calculation of the scattering amplitudes, whereas the states of Johnson & Lippmann are not. In addition, it is shown that the Breit-Wigner broadening approximation E --> E - iGAMMA/2 is consistent with the perturbation-theoretic order of the calculation, if the former basis states are chosen, but not the latter. It is further shown that the decay rates obey the expected '' time dilation '' scaling relation GAMMA(Lab) = gamma-1GAMMA(Rest) if the states of Herold et al. or of Sokolov & Ternov are chosen, but that they do not if the states of Johnson & Lippmann are used.