Spin resonance strengths for radiative polarization and vertical momentum recoils using the spin response formalism

The radiative polarization of electrons and positrons in storage rings includes spin resonances driven by vertical momentum recoils due to spin flip photon emissions. This is in addition to the spin resonances driven by longitudinal momentum recoils. The underlying physics for the vertical momentum recoils is similar to the perturbations induced by a radial field (rf) dipole spin flipper. This paper derives the spin resonance strengths driven by the vertical momentum recoils using known techniques for spin flippers, such as the spin response formalism.