Third-order spin polarizabilities of the nucleon

We study the structure-constant (polarizability) coefficients of the spin-dependent terms of the nucleon Compton scattering amplitude which are third order in the frequency of the incoming photon. It is shown that these spin-polarizability coefficients can be related to sums of products of electromagnetic transition moments of the nucleon, involving the electric and magnetic dipoles, the electric and magnetic quadrupoles, and the charge electric and magnetic dipole mean-square radii. Three sum rules involving products of the electric dipole transition moments emerge from the calculation.