Effect of Nuclear Motion of the Hyperfine Structure of the Ground Term of Hydrogen

Abstract

The correction factor for the effect of nuclear motion on the hyperfine structure of hydrogen is discussed. It is found that this factor can be represented by ${(1+\frac{m}{M})}^{\ensuremath{-}3}$ to within terms of order $(\frac{m}{M}){\ensuremath{\alpha}}^{2}log\ensuremath{\alpha}$, where $m$, $M$ are, respectively, the masses of the electron and nucleus while $\ensuremath{\alpha}$ is the fine structure constant. It is assumed that the Coulomb potential is that of a point charge for distances greater than ${r}_{0}=\frac{{e}^{2}}{m{c}^{2}}$ and that for distances smaller than ${r}_{0}$ it is of the order $m{c}^{2}$. This assumption makes it possible to treat the problem by means of existing theories. First-order perturbation theory for the effect of the nuclear magnetic field is employed. The reasons for doing the work are explained in the introduction. The calculations for the part of the proton's magnetic moment following from Dirac's equation are described in Section II. Section III is concerned with the effect of the part of the magnetic moment of the proton which is not accounted for by Dirac's equation and is referred to as the Pauli part. The deuteron is also discussed in Section III.