V. Bach, J. Froehlich, A. Pizzo
An Infrared-Finite Algorithm for Rayleigh Scattering Amplitudes, and Bohr's Frequency Condition
(491K, Postscript)

ABSTRACT.  In this paper, we rigorously justify Bohr's frequency condition in atomic spectroscopy. Moreover, we construct an algorithm enabling us to calculate the transition amplitudes for Rayleigh scattering of light at an atom, up to a remainder term of arbitrarily high order in the fine structure constant. Our algorithm is constructive and circumvents the infrared divergences that invalidate standard perturbation theory.