Calculation of the Hyperfine Splittings of theD1Levels ofHe3

The ${\mathrm{He}}^3$ hyperfine splittings of the ${}_{}{}^1{}_{}{}^{}D$ levels are shown to arise from the admixture of ${}_{}{}^3{}_{}{}^{}D$ states through the total spin-orbit interaction and the magnetic interaction between the nucleus and the $1s$ electron (Fermi contact term). The results of the calculation using hydrogen-like functions are in qualitative agreement with the splittings observed recently by B. Decomps et al. for the 4, 5, and 6 ${}_{}{}^1{}_{}{}^{}D$ levels (60-80 Mc/sec). The repulsion between ${}_{}{}^1{}_{}{}^{}D$ and ${}_{}{}^3{}_{}{}^{}D$ levels is also sufficient to explain the "specific" isotope shift observed for ${}_{}{}^1{}_{}{}^{}D$ levels of helium.