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Second Order in Mass Ratio Radiative-Recoil Corrections to Hyperfine Splitting in Muonium
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abstract
Radiative-recoil corrections to hyperfine splitting in muonium of orders $\alpha(Z\alpha)(m/M)^2E_F$ and $(Z^2\alpha)(Z\alpha)(m/M)^2E_F$ are calculated. These corrections are of the second order in the small electron-muon mass ratio. An analytic expression $[(-6 \ln2- \frac{3}{4})\alpha (Z\alpha) - \frac{17}{12} (Z^2 \alpha) (Z\alpha)](\frac{m}{M})^2 E_F$ is obtained. Numerically the correction is equal to $-0.0351\:\mbox{kHz}$ and is of the same order of magnitude as the expected accuracy of the current Los Alamos experiment to measure the hyperfine splitting.
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Cited by 1 Pith paper
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One more radiative-recoil correction to the Lamb shift in muonium
The muon-line radiative-recoil correction to the muonium Lamb shift at order α^6(m/M)^2 m is found to be π² times the common prefactor, replacing a previously quoted (139/32−2 ln2) coefficient.
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