 Photolytic branching in the chlorine dimer cycle

For dimer photodissociation frequency $J$ and competing thermal dissociation frequency $k_d[M]$, the successful branch fraction is $f=J/(J+k_d[M])$. With steady dimer abundance and rapid subsequent recycling, ozone destruction is $2f{k}_a[M][\mathrm{ClO}{]}^2$. The factor two counts ozone molecules consumed per productive dimer event.