Hyperfine splitting of $2^3S_1$ state in He$^3$

Relativistic corrections to the hyperfine splitting are calculated for the triplet $2^3S_1$ state of the helium isotope He$^3$. The electron-electron correlations are fully incorporated. Due to the unknown nuclear structure contribution a comparison with the experimental result is performed via He$^{3+}$ hyperfine splitting. A significant discrepancy with the experiment arises and a possible explanation is proposed.