Hyperfine Suppression of a $2\;^3$S$_1$ -- $3\;^3$P$_1$ Radiative Transition in Helium

In $^3$He, we have found both experimentally and theoretically that the electric dipole radiative transition $2\;^{3}$S$_{1} (F=3/2) $ to $3\;^{3}$P$_{1} (F= 3/2)$ between hyperfine states is strongly suppressed. The suppression is caused by strong hyperfine mixing and accidental cancellation between two hyperfine states with different $J$ but the same $F$ in the $3\;^{3}$P state. We present high precision variational calculations in Hylleraas coordinates of the line strength, including hyperfine mixing, and compare the results with experiment. The influence of a weak magnetic field up to 100 gauss on the line strength provides an additional test of this hyperfine suppression phenomenon. Theoretical calculations show that a maximum suppression occurs for the Zeeman component $2\;^{3}$S$_{1} (F= 3/2,\,M_F=-1/2)$ to $3\;^{3}$P$_{1} (F= 3/2,\,M_F=-1/2)$ of the hyperfine transition at approximately 65 gauss. Theoretical and experimental studies of other $n\;^3$P states are in progress to check for other similar suppression effects in $^3$He.