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Journal of Physics B Atomic and Molecular Physics

Analytical expressions for the Bloch-Siegert shift

Peter Hannaford, David Thomas Pegg, George William Series

Published Aug 1, 1973• 54 citations
Publisher

Abstract

Analytical expressions are obtained for the Bloch-Siegert shift in magnetic resonance experiments using results derived previously by Shirley (1965) Series (1973) from semiclassical theory. These expressions together cover the whole range of the shift from 0 to 100%.
DOI
10.1088/0022-3700/6/8/009

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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.
A semi-classical approach developed by Pegg and Series (1970, 1973) is used to study higher order effects in magnetic resonance produced by an oscillating magnetic field perpendicular to a static field as the oscillating field strength is increased. It is shown that the well-known 'multiple quantum' transitions arise from a semi-classical theory, being transformed into 'single quantum' transitions induced by field harmonics in the most appropriate reference frame for treating the problem. Higher order terms in the Bloch-Siegert shift support those derived by Shirley (1965) by means of Floquet theory, and are in gross disagreement with those derived by Chang and Stehle (1971) from quantum electrodynamics, particularly at very high field intensities where the results are not even qualitatively similar. It should be possible to decide easily between the two approaches by experiment.