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 ${g}_{J}$ $(\mathrm{He},2^{3}S_{1})={g}_{e}(1\ensuremath{-}40.91640\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6})=\ensuremath{-}2.002237379$. This result is in good agreement with the previous theoretical value calculated by Perl and Hughes to order ${\ensuremath{\alpha}}^{2}$. Higher-order corrections (${\ensuremath{\alpha}}^{3} \mathrm{and} {\ensuremath{\alpha}}^{2}\frac{m}{M}$) contribute -0.151 ppm. Combining this result with the calculated value for the atomic hydrogen ${g}_{J}$ factor gives the ratio $\frac{{g}_{J}(\mathrm{He},2^{3}S_{1})}{{g}_{J}(\mathrm{H},1^{2}S_{\frac{1}{2}})}=1\ensuremath{-}23.212\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ with an estimated uncertainty of 3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}9}$. 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, Lalo\e, and Brossel.