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We develop a new approximation method for determining resonance properties of atomic systems interacting with intense photon beams. This method, based on an improved iteration procedure, leads to analytic expressions for the atomic density matrix from which positions of the resonances are determined. Our iteration procedure is more rapidly convergent than the continued-fraction method, and already in its second step reproduces the Bloch-Siegert shift of the one-photon resonance within 1 ppm.
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Białynicki‐Birula et al. (1976) studied this question.
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