The Effect of Nuclear Motion on the Hyperfine Structure of Hydrogen

Abstract

The problem is considered from the point of view of a Hamiltonian which is relativistic to order $\frac{{v}^{2}}{{c}^{2}}$. The discussion results in a clearer separation of the non-relativistic correction factor $1\ensuremath{-}\frac{3m}{M}$ from relativistic effects than in previous treatments. The Hamiltonian applies through the interior as well as the exterior of the proton. By means of it the potential energy can be rounded off at small distances without contradiction to relativity, within the order $\frac{{v}^{2}}{{c}^{2}}$. A transformation involving a new effective charge allows the calculation of part of the effect without approximation and it becomes clear that higher order effects are not separable from the so far arbitrary assumptions concerning the proton's radius. Relativistic corrections to the fine structure are reconsidered by means of this transformation and the effect of the acceleration of the proton on the hyperfine structure is discussed.