Classical theory of magnetic x-ray scattering

A classical derivation is presented for magnetic x-ray scattering from electronic orbital angular momentum. The orbital magnetic scattering factor is identical to that for spin angular momentum, except for the difference in gyromagnetic ratios. Unlike the spin result, which had previously been obtained from both a classical Lagrangian and from quantum mechanics, the classical orbital scattering disagrees with quantum mechanics and with available data. This disagreement between classical and quantum-mechanical results is present for the scattering from a free electron in motion, scattering from an ideal current loop, as well as for scattering from atomic orbital angular momentum.