Line-shape effects in the measurement of the positronium hyperfine interval

Allen P. Mills, Jr.
Phys. Rev. A 27, 262 – Published 1 January 1983
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Abstract

Recently Rich has pointed out that annihilation terms in the effective 4 × 4 Hamiltonian H for n=1 positronium cause the real parts of the Zeeman eigenvalues to be shifted by terms of order (λs4πΔv)2105 relative to the Breit-Rabi eigenvalues. Here λs is the annihilation rate of the singlet state and Δv is the hyperfine interval. Rich observes that the Δv measurements have not correctly dealt with decay. The Zeeman-resonance line shape is calculated here assuming that the non-Hermitian H describes the motion of the four n=1 levels via Schrödinger's equation. The deviations of this line shape from a Lorentzian are exhibited. The asymmetry of the line causes a shift in the line center relative to what one would obtain from a Breit-Rabi plus Lorentzian fit to a measured Zeeman-resonance curve. To take this into account, the measurement of Δv by A. P. Mills, Jr. and G. H. Beaman [Phys. Rev. Lett. 34, 246 (1975)] should be increased by 2.5 ppm to Δv (Mills and Beaman)=203.3875(16) GHz. When the Egan et al. measurement [P. O. Egan, V. W. Hughes, and M. H. Yam, Phys. Rev. A 15, 251 (1971)], which used a different line shape, is reinterpreted in terms of the line shape calculated here, the Egan et al. Δv value increases by 21 ppm to Δv(Egan et al.)=203.3890(12) GHz. The weighted mean of the two corrected measurements is Δv=203.3885(10) GHz.

  • Received 10 November 1981

DOI:https://doi.org/10.1103/PhysRevA.27.262

©1983 American Physical Society

Authors & Affiliations

Allen P. Mills, Jr.

  • Bell Laboratories, Murray Hill, New Jersey 07974

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Vol. 27, Iss. 1 — January 1983

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