Calculation of thegJFactor for the2S13State of Helium

Abstract

The $g_J$ factor for the excited $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state of helium has been calculated from a generalized Breit equation which includes radiative corrections. The result is $g_J$ $(\mathrm{He},2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{})=g_e(1-40.91640\mathrm{}\times {10}^{-6\mathrm{}})=-2.002237379\mathrm{}$. This result is in good agreement with the previous theoretical value calculated by Perl and Hughes to order ${\alpha }^2$. Higher-order corrections (${\alpha }^3 \mathrm{and} {\alpha }^2\frac{m}{M}$) contribute -0.151 ppm. Combining this result with the calculated value for the atomic hydrogen $g_J$ factor gives the ratio $\frac{g_J(\mathrm{He},2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{})}{g_J(\mathrm{H},1\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{})}=1-23.212\mathrm{}\times {10}^{-6\mathrm{}}$ with an estimated uncertainty of 3 × ${10}^{-9\mathrm{}}$. This value is in agreement with the old experimental and theoretical values of Hughes et al., and improves upon the accuracy of the latter, but disagrees with a recent experimental value obtained by Leduc, Laloë, and Brossel.