Proton Structure and the Hyperfine Shift in Hydrogen

The effect of the electromagnetic structure of the proton upon the hyperfine splitting of $s$ states in hydrogen is determined without recourse to any specialized model for proton interactions. The principal modification of the Fermi formula, derivable nonrelativistically, appears as a multiplicative correction $1-2{a_0}^{-1\mathrm{}}{〈r〉}_{\mathrm{em}}$ where $a_0$ is the Bohr radius and ${〈r〉}_{\mathrm{em}}$ is the first statistical moment of a distribution which characterizes the proton structure. The absence of additional structure corrections of experimental consequence is rigorously demonstrated. The method relies on a phenomenological representation of the proton deduced from the invariance principles of quantum field theory. The size of the proton is estimated from the available bound state data and compared with the size prediction inferred from scattering experiments.