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arXiv:physics/0410063 · Physics Letters A

Sum rules in the oscillator radiation processes

R. Casana, G. Flores-Hidalgo, B. M. Pimentel

Published Jan 27, 2005• 7 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2005.01.031

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Abstract First evaluations of the blackbody-radiation (BBR)-induced shift and broadening of highly excited Rydberg states were based on the account of only the first term of the expansion for the Planck’s distribution in powers of the ratio of the BBR-photon energy to the environmental thermal energy. The corresponding asymptotic expression for the shift is proportional to a sum rule for the oscillator strengths, which is identical for all states, independently of their principal and angular-momentum quantum numbers. The broadening appeared proportional to the sum of the oscillator-strength first moments, which is dependent on only the principal quantum number, being independent of the state’s angular momentum. In this article, we demonstrate that the account of higher-order terms of the Planck’s distribution expansion provides corrections revealing the dependence of asymptotic shift and broadening on the Rydberg-state principal and angular-momentum quantum numbers. The strongest corrections are observed for states with low angular momenta, in agreement with earlier performed numerical calculations. Sum rules for higher moments of oscillator strengths are used for evaluating the corrections for the BBR-induced broadening and shift of Rydberg-state energy levels in neutral atoms and ions of arbitrary nuclear charge Z .
Recently derived sum rules for nonlinear optics are shown to be relevant to a number of experiments in atomic and solid-state physics. To interpret the experiments on atomic transitions and exciton transitions in solids, we analyze the three-level model and examine the modification of the optical spectrum induced on a probe light by the presence of an additional intense light beam. We show that the nonlinear sum rules explain the known experimental data and predict anomalous asymmetry in the nonlinear line shape. We also consider the cases of vibrational states of diatomic molecules and of optical modes of polar crystals and treat them with the model of the anharmonic oscillator. The nonlinear sum rules are shown to be obeyed, thus clarifying the processes of nonlinear absorption.