Scattering-matrix elements for nuclear reactions involving photons

The transformation of scattering-matrix elements from a representation appropriate for particle channels to one that describes photon channels is rederived. Previous derivations have ignored an ambiguity in the relative phase of the vector potential for magnetic and electric multipole radiation. The resultant ambiguity in the S-matrix transformation seems to be a source of confusion about the relative phases of the various terms that contribute to the polarization of particles produced in photonuclear reactions.