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Journal of Physics B Atomic and Molecular Physics

Analytical expressions for the positions of the longitudinal and transverse resonances in radio-frequency spectroscopy

S. Swain

Published Dec 1, 1974• 34 citations
Publisher

Abstract

Exact equations determining the positions of the longitudinal and transverse magnetic resonances of a doublet are derived. These equations are simply related. Analytical expressions for the Bloch-Siegert shift and the first three transverse resonances are given which apply over the whole range of RF field strengths with 1% accuracy. The expressions for the three quantum resonances are correct to 3%.

DOI
10.1088/0022-3700/7/17/021

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Exact equations determining the positions of the longitudinal and transverse magnetic resonances of a doublet are derived. These equations are simply related. Analytical expressions for the Bloch-Siegert shift and the first three transverse resonances are given which apply over the whole range of RF field strengths with 1% accuracy. The expressions for the three quantum resonances are correct to 3%.
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The Bloch-Siegert-type shifts and multiple-quantum resonance shifts of a spin-one system subjected to an oscillating radio-frequency applied at right angles to a DC field have been calculated to sixth order in V, the amplitude of the oscillating field, for the single-quantum resonance, and to fourth order in V for the higher resonances. The level crossing criterion appropriate to two-level systems cannot be used here, and a resonance condition based on a previously derived analogue of Shirley's equation for spin-one systems is used instead. The calculation uses degenerate continued-fraction perturbation theory. Numerical calculations were performed in order to obtain the shape of the resonances, and partially check the analytic results. The atomic levels were assumed to be completely stable; the corrections due to finite atomic lifetimes are expected to be small.