Hyperfine Structure of Helium-3 in the Metastable Triplet State

The hyperfine structure splitting in the metastable ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state of ${\mathrm{He}}^3$ has been measured recently by the atomic beam magnetic resonance method. The Fermi value of the hfs splitting in this state is computed here using various available wave functions, including the six-term Hylleraas function of Huang. An error estimate for the hfs calculation can be made from a knowledge of the accuracy of the calculated binding energy. In all cases, the actual discrepancy between the computed value of the hfs and the experimental result is consistent with the estimated inaccuracy. In particular, the Hylleraas function yields a value of the negative binding energy of $0.087600\times 4hc{R}_{{\mathrm{He}}^4}$ (experimental value $0.087618\times 4hc{R}_{{\mathrm{He}}^4}$), and hence gives the hfs to about 0.1 percent. Thus the anomalous magnetic moment of the electron should be taken into account. The calculated result, including the order $\alpha$ anomalous moment of the electron and the order $\frac{m}{M}$ reduced mass correction, is 6735.9±4.7 Mc/sec as compared to the experimental value of 6739.71±0.05 Mc/sec. Relativistic, higher order quantum electrodynamic, and nuclear structure effects are somewhat smaller than the uncertainty in our calculation.