Hyperfine-induced Intercombination Transitions in $^3$He*

It is well known that hyperfine structure can induce transitions that are otherwise forbidden, or strongly suppressed, in heliumlike ions. We have recently found that, even in neutral helium-3, hyperfine structure can induce spin-forbidden intercombination transitions involving the higher-lying Rydberg states. In this paper we present high precision variational calculations of hyperfine-induced transitions $n\;^1$D$\rightarrow$$n'\;^3$P and $n\;^3$D$\rightarrow$$n'\;^1$P ($n=3-10,\,n'=2-9$) for $^3$He. Comparable strengths of hyperfine-induced transitions to normal E1 transitions are predicted. Conversely, normally allowed transitions can be strongly suppressed by hyperfine structure, as previously discussed and observed experimentally [1], such as $n\,^3\rm{D}_1,F=3/2$ $\rightarrow$ $2\,^3\rm{P}_2,F=5/2$.\\[4pt] [1] I.A. Sulai et al. Phys.\ Rev.\ Lett.\ {\bf 101}, 173001 (2008).