Hyperfine-induced radiative decay rates of heliumlike $^8$B and $^{11}$B

Hyperfine mixing of $LS$-coupled atomic states can open new radiative decay channels for processes that would normally be strongly suppressed. For example, spin-forbidden processes may become enhanced. We study the lifetimes of the hyperfine levels of the two-electron isotopes $^8$B $(I=2)$ and $^{11}$B $(I=3/2)$ in connection with nuclear charge radius measurements by the isotope shift method [1]. We find that the effects of hyperfine structure are relatively small for both $^8$B and $^{11}$B. For the $1s2p\;^1P$ hyperfine states, the decay rates are dominated by transitions to the $1s^2\;^1S$ ground state with $A = 3.72\times10^{11}$ s$^{-1}$. For the $1s2p\;^3P$ states, hyperfine structure alters the decay rates by less than 1\%. The dominant decay channel is the spin-allowed transition to the $1s2s\;^3S$ manifold of states. The decay rate for $^8$B summed over final state hyperfine structure is in the range $A = 4.535\times10^7$ to $4.555\times10^7$ s$^{-1}$. The decay rate to the ground state for the $1s2p\;^3P_1$ state is $4.169\times10^6$ to $4.283\times10^6$ s${-1}$. The effects of hyperfine structure are smaller still for $^{11}$B.\newline [1] W. Noertershaeuser {\it et al.} Phys.\ Rev.\ A {\bf 83}, 012516 (2011); Phys.\ Rev.\ Lett.\ {\bf 102}, 062503 (2009).