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+ hu+A+X followed by A+BC+AB+C. In the limit that AX is stationary relative to BC, we show that the threedimensional 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.