Nuclear Structure Correction to the Hyperfine Structure in Hydrogen

Abstract

In previous papers, corrections to the hyperfine structure (hfs) in hydrogen of relative order $\frac{\ensuremath{\alpha}m}{M}$ have been calculated by treating the proton as a point particle with an anomalous magnetic moment in addition to its Dirac moment. In this paper the proton is treated as a particle with structure by making use of the high-energy electron-proton-scattering data. Corrections of the previous work in which only a point particle was considered are calculated by using the Feynman formulation of quantum electrodynamics. It is also shown that exactly the same terms may be obtained by using the covariant Bethe-Salpeter equation.The calculated shift of -35 parts per million (including the "recoil corrections") is not in agreement with the combined results of several experiments (-1.4\ifmmode\pm\else\textpm\fi{}18 parts per million). A possible source of this difference is meson corrections to a two-photon form-factor which is taken here as the product of two (Hofstadter) single-photon form-factors.