Hyperfine-induced Intercombination Transitions $n^3{\rm D}_1$ to $2^1{\rm P}_1$ in $^3$He$^*$

In heliumlike ions with nuclear spin, the electric dipole transition $2\;^3{\rm P}_J\rightarrow1\;^1{\rm S}_0$ is allowed since hyperfine interaction causes mixing between two hyperfine states with different $J$ but the same $F$ (due in part to fine-structure interactions for $J=1$). Since the pioneering works of Garstang and Mohr, the hyperfine-induced intercombination transition has been a subject of experimental and theoretical interest. However, previous works treated only the more highly charged He-like ions ($Z\geq 6$) since the singlet-triplet mixing caused by hyperfine interaction is so small for low-$Z$ ions that the induced intercombination line $2\;^3{\rm P}_J\rightarrow1\;^1{\rm S}_0$ is difficult to observe. In contrast, we have found theoretically that for $^3$He ($Z=2$), the hyperfine-induced intercombination transitions $n\;^3{\rm D}_1(F=3/2) \rightarrow 2\; ^1{\rm P}_1(F=1/2)$ with higher $n$ have comparable intensities to normal E1 transitions between two hyperfine states. The calculated results show that hyperfine-induced intercombination transitions contribute 46 percent $(n=10)$, and 35 percent $(n=9)$ of all E1 transitions $^3{\rm D}_1(F=3/2) \rightarrow 2\;^{1,3}{\rm P}_J(F)$. Similar results of this induced transition have been obtained as well for $^3{\rm D}_1(F=3/2)$ $\rightarrow$ $n\; ^1{\rm P}_J(F)$ with $n=3$ to $10$. High precision variational calculations in Hylleraas coordinates of the line strength will be presented.