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

Recently Rich has pointed out that annihilation terms in the effective 4 x 4 Hamiltonian H for n = 1 positronium cause the real parts of the Zeeman eigenvalues to be shifted by terms of order (lambda/sub s//4..pi delta nu..)/sup 2/roughly-equal10/sup -5/ relative to the Breit-Rabi eigenvalues. Here lambda/sub s/ is the annihilation rate of the singlet state and ..delta nu.. is the hyperfine interval. Rich observes that the ..delta nu.. 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 = 2 levels via Schroedinger'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 ..delta nu.. (A. P. Mills, Jr. and G. H. Beaman, Phys. Rev. Lett. 34, 246 (1975)) should be increased by 2.5 ppm to ..delta nu.. (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.more » A 15, 251 (1971)), which used a different line shape, is reinterpreted in terms of the line shape calculated here, the Egan et al. ..delta nu.. value increases by 21 ppm to ..delta nu.. Egan et al. = 203.3890(12) GHz. The weighted mean of the two corrected measurements is ..delta nu.. = 203.3885(10) GHz.« less