Calculations of Bell and Leinaas and Derbenev and Kondratenko for radiative electron polarization

Derbenev and Kondratenko calculated the equilibrium degree of radiative electron polarization in 1973 (Ya. S. Derbenev and A. M. Kondratenko, Zh. Eksp. Teor. Fiz. 64, 1918 (1973) [Sov. Phys.---JETP 37, 968 (1973)]), and more recently Bell and Leinaas did likewise for a more limited model, but following a different approach [J. S. Bell and J. M. Leinaas, Nucl. Phys. B 284, 488 (1987)]. They report a different resonance structure. In this paper the notations, formalisms, and viewpoints of the two sets of authors are compared, and the connection between their treatments is explained. The formula for the polarization, taking into account vertical fluctuations, is derived following the Derbenev-Kondratenko approach and is generalized to strong-focusing machines. It is also combined with the Derbenev-Kondratenko result into a unified formula.