Low-Energy Compton Scattering by Arbitrary-Spin Targets

The classic low-energy theorem for low-energy Compton scattering by spin-½ systems derived in 1954 by Low and by Gell-Mann and Goldberger is generalized to include targets of arbitrary spin. Low's method is used in conjunction with a multipole expansion of the electromagnetic current matrix elements. The multipole expansion is given in the Breit frame (total three-momentum=0) and transformed to the lab system. The result, obtained by replacing the Pauli matrix $\sigma$ in the Low-Gell-Mann-Goldberger result by 2S (where S is the target spin operator), has been derived by Lapidus and Kuang-Chao, but their method of obtaining the current matrix elements is less straightforward than the present one.