State-to-state differential cross sections from photoinitiated bulb reactions

We consider a mixture of a diatomic photolytic precursor AX and a reagent BC that undergoes the photoinitiated reaction AX + hν → A + X followed by A + BC → AB + C. In the limit that AX is stationary relative to BC, we show that the three-dimensional velocity distribution of the AB product in a specified quantum state can be related to the differential cross section of the A + BC reaction by a simple, invertable, closed-form expression. With a favorable choice of kinematics, we demonstrate that it is possible to extract the full state-to-state differential cross section from a measurement of the velocity distribution of the AB product in the laboratory frame.