As a continuation of our efforts to calculate the total Compton cross section (to order α² in the presence of an arbitrary homogeneous magnetic field, we here report the result for the spin-1/2 case. The motion of the incident photon is restricted to lie along the direction of the field, but otherwise our result is quite general. Special limiting cases corresponding to classical and weak-field limits are discussed.
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Milton et al. (1974) studied this question.
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