Determination ofgJ(H1, 1S122)gs(e): Test of Mass-Independent Corrections

Abstract

A determination of the ratio of $g$ factors of the electron bound in the hydrogen atom to that of the free electron has been made. For the first time mass-independent terms in the theory are confirmed through the ${\alpha }^3$ radiative correction. Our result is $\frac{g_J({}_{}{}^1{}_{}{}^{}H, 1{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{})}{g_s\mathrm{}\left(e\right)\mathrm{}}=1-17.709\mathrm{}\left(13\right)\mathrm{}\times {10}^{-6\mathrm{}}$.