Effects of the Proton Radius on Nuclear Motion Correction for the Hyperfine Structure of Hydrogen

Contributions to the hyperfine structure of the ground state of hydrogen resulting from the assumption of a non-vanishing proton radius are evaluated in this paper. These effects occur because of the assumed modification of the Coulomb potential inside the proton and the consequent change in the wave function the above assumption implies. Since the proton radius and the shape of the potential function in the interior are not known, there occur uncertainties of relative order $\frac{{\alpha }^{2}m}{M}$ in the hyperfine structure arising from nuclear mass motion.