$α^{2} \ln α^{- 1}$ Recoil Corrections to the Hydrogen Hyperfine Structure and the Proton Polarizability

6 November 1972

journal article
research article
Published by American Physical Society (APS) in Physical Review Letters

Vol. 29 (19) , 1295-1297
https://doi.org/10.1103/physrevlett.29.1295

Abstract

We report a calculation of the order

(\frac{m_{e}}{m_{p}}) α^{2} \ln α^{- 1}

corrections to the hyperfine splitting (

ν_{H}

) of the hydrogen ground state. The result

Δ ν_{H} = \frac{8}{3} {(\frac{m_{e}}{m_{p}})}^{2} {(1 + \frac{m_{e}}{m_{p}})}^{- 5} c α^{4} R_{\infty} \ln α^{- 1} [9 + 7 k (1 + k) - (\frac{m_{e}}{m_{p}}) k (3 + 14 k)] = 0.0016

MHz (1.1 ppm) is used in conjunction with the corresponding formula for the muonium hyperfine interval to obtain an estimate of the proton polarizability.

Keywords

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α2lnα−1Recoil Corrections to the Hydrogen Hyperfine Structure and the Proton Polarizability

Abstract

Keywords

$α^{2} \ln α^{- 1}$ Recoil Corrections to the Hydrogen Hyperfine Structure and the Proton Polarizability