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Journal of Physics B Atomic and Molecular Physics

Power series expansion for the RF resonance shift

Stig Stenholm

Published Sep 1, 1973• 24 citations
Publisher

Abstract

The author derives an exact semiclassical expression for the generalized Bloch-Siegert shift of the main RF resonances in the limit of vanishing natural line width. Its power series expansion is found to agree with quantum electrodynamic calculations, but a truncated continued fraction expression is shown to represent the exact values much better.

DOI
10.1088/0022-3700/6/9/005

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Journal of Physics B Atomic and Molecular Physics•Jun 21, 1976•10 citations
The author derives an exact semiclassical expression for the generalized Bloch-Siegert shift of the main RF resonances in the limit of vanishing natural line width. Its power series expansion is found to agree with quantum electrodynamic calculations, but a truncated continued fraction expression is shown to represent the exact values much better.
We present a semiclassical solution for a Zeeman-split, optically pumped, spin-\textonehalf{} system interacting with a strong radio-frequency field. The method of solution presented here is based upon a matrix continued-fraction expansion, and can explain any resonance phenomena which occur for arbitrary geometrical configurations of the pumping beam or the rf field polarization axis. Theoretical predictions of line shapes for some cases are reported and discussed. The solution can also explain some deviations of the observed Bloch-Siegert shift at high rf power from the behavior predicted by a previous semiclassical theory, which can account for simple geometrical configurations only.
Expressions are presented for the Bloch-Siegert shift appropriate to electric dipole resonance experiments between excited states, when the maximum change in lifetime due to the applied field is used as the criterion for determining the resonance centre. The results differ from those reported by Silverman and Pipkin (1972) in the magnitude of the power shift, and in that the present authors predict an additional power-independent shift. The effect of neighbouring levels on the power shift is calculated, and shown to be substantial in certain cases.