Total Compton Cross Section for Arbitrary Spin

Abstract

The magnitude of the total Compton cross section for arbitrary spin is calculated in lowest order by using the absorptive part of the forward scattering amplitude and the unitarity property of the $S$ matrix. To find the general form (for any spin) of the forward amplitude a universal electromagnetic interaction, implying the value 2 for the gyromagnetic ratio, is postulated. The deduced cross section contains as special cases the known cross sections for spinless and Dirac particles. The average of the cross section over all the possible polarization states of the particle is also performed. In the high-energy region the cross section never increases faster than linearly with the energy of the photon. If a development in powers of the photon energy is made, the first and second coefficients are found to be spin independent. The coefficient of the square of the energy is proportional to the square of the modulus of the spin vector.