Low-Energy Theorem for Compton Scattering

Abstract

The low-energy theorem for Compton scattering on arbitrary spin targets is derived. Knowledge of the Born term of the amplitude, which is calculated explicitly, enables us to prove Singh's lemma, which allows us to calculate the threshold value of the amplitude from the gauge condition. Every multipole moment of the target is written down explicitly in terms of the low-energy limit of the amplitude. Up to linear order in photon energy $\omega$, this theorem becomes a generalization to arbitrary spin of the theorem derived by Low and by Gell-Mann and Goldberger. To describe the spin-nonflip amplitude up to order ${\omega }^2$, we need two structure-dependent parameters in addition to the charge and magnetic moment.