Hyperfine-quenched {\boldmath $2s2p\,{^3\!P_2} - 2s^2\,{^1\!S_0}$} M2 transition in Be-like ions*

For isotopes with non-zero nuclear spins, the $2s2p\,{^3\!P_2} - 2s^2\,{^1\!S_0}$ M2 transition in Be-like ions is affected by hyperfine mixing with the much stronger $2s2p\,{^{1,3}\!P_1} - 2s^2\,{^1\!S_0}$ E1 transitions. In this work, these hyperfine-quenched M2 rates are calculated with a large-scale relativistic configuration-interaction method in a perturbative approach that includes coherent hyperfine mixing between the $^3\!P_1$ and $^1\!P_1$ states. It is found that the effect of hyperfine quenching is significant and that for some low-$Z$ Be-like ions with $I=1/2$, the ${^3\!P_2} - {^1\!S_0}$ transition will show up in measurements as a two-component decay comprising of a slower, unperturbed decay from the $F=J+I=5/2$ level and a much faster, hyperfine-quenched decay from the $F=J-I=3/2$ level.