A nonlinear sum rule for atomic hydrogen
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A sum rule for the nonlinear absorption of a probe beam induced by an external light beam is derived for the H atom. Numerical calculations are carried out using the pseudostate summation method and the consistency of the calculation is verified by comparing the length and the velocity gauge. The results confirm the validity of the pseudostate summation method in perturbation theory and give a measure of the strength of nonlinear effects in atomic hydrogen. They are shown to increase by orders of magnitude with increasing the frequency of the external beam. Asymmetries in the nonlinear absorption are expected, with larger negative contributions on the high-frequency side of the spectrum.
PACS 42.65.BpGeneral theory
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