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

The introduction of resonance line width into the QED cyclotron scatte ring amplitudes is considered. It is shown that the width arises from loop corrections to the electron propagator, which also bring about sh ifts in the Landau energy levels. A formalism is developed that allows the dressed electron propagator to be derived. It is shown that the s tates of Herold, Ruder, & Wunner, and of Sokolov & Ternov, which diago nalize the component of the magnetic moment operator parallel to the e xternal magnetic field, are appropriate for calculation of the scatter ing amplitudes, whereas the states of Johnson & Lippmann are not. In a ddition, it is shown that the Breit-Wigner broadening approximation E --> E - iGAMMA/2 is consistent with the perturbation-theoretic order o f 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 t he states of Herold et al. or of Sokolov & Ternov are chosen, but that they do not if the states of Johnson & Lippmann are used.