Determination of differential cross sections and kinetic energy release of co-products from central sliced images in photo-initiated dynamic processes

For photo-initiated inelastic and reactive collisions, dynamic information can be extracted from central sliced images of state-selected Newton spheres of product species. An analysis framework has been established to determine differential cross sections and the kinetic energy release of co-products from experimental images. When one of the reactants exhibits a high recoil speed in a photo-initiated dynamic process, the present theory can be employed to analyze central sliced images from ion imaging or three-dimensional sliced fluorescence imaging experiments. It is demonstrated that the differential cross section of a scattering process can be determined from the central sliced image by a double Legendre moment analysis, for either a fixed or continuously distributed recoil speeds in the center-of-mass reference frame. Simultaneous equations which lead to the determination of the kinetic energy release of co-products can be established from the second-order Legendre moment of the experimental image, as soon as the differential cross section is extracted. The intensity distribution of the central sliced image, along with its outer and inner ring sizes, provide all the clues to decipher the differential cross section and the kinetic energy release of co-products.