Higher-order QED corrections to the hyperfine splitting in ${}^3$He

We present a calculation of the hyperfine splitting of the $2^{3}S$ state in the ${}^3$He atom with inclusion of all QED effects up to ${\alpha }^3{E}_F$, where $E_F$ is the Fermi splitting. Using the experimental value of the $1S$ hyperfine splitting in ${}^3$He${}^{+}$, we obtain the theoretical prediction for ${}^3$He of ${\nu }_{\mathrm{h}\mathrm{f}\mathrm{s}}=-6739701181(41)$ Hz, which is in perfect agreement with the experimental value $-6739701177(16)$ Hz [S. D. Rosner and F. M. Pipkin, Phys. Rev. A $\mathbf{1}$, 571 (1970)]. This result constitutes a 40-fold improvement in precision as compared to the previous value and is the most accurate theoretical prediction ever obtained for a non-hydrogenic system.