Relativistic Contribution to the Hyperfine Interval of the Metastable Triplet State ofHe3

The relativistic correction to the hyperfine-structure splitting of the metastable $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state of ${\mathrm{He}}^3$, first calculated by Sessler and Foley to be 315 ± 3 ppm, is reevaluated as ${\Delta }_{\mathrm{rel}}=327\mathrm{}\pm 3$ ppm. Using this new value, the theoretical ratio of the hyperfine splitting in the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state of ${\mathrm{He}}^3$ to the hyperfine splitting in the $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state of ${\mathrm{He}}^{3+}$ becomes ${\rho }_{\mathrm{th}}=6.221\mathrm{}1911\pm 0.0000187$ The experimental value for the ratio is 6.221 1384±0.000 0012, and the 8±3 ppm discrepancy is presently unexplained.