Scattering of Low-Energy Photons by Particles of Spin ½

The first two terms in a frequency expansion of the photon scattering amplitude are considered in the case where the scatterer is a particle of spin \textonehalf{}. It is shown that an exact calculation in quantum field theory gives results identical with those obtained by classical methods or else by use of the Dirac equation with an anomalous Pauli moment. The results depend only on the charge, mass, and magnetic moment of the scatterer. In the case of the proton, the second term, arising from scattering by the magnetic moment, appears to be negligible in comparison with effects due to Thomson and Rayleigh scattering.