Theory of polarization-averaged core-level molecular-frame photoelectron angular distributions: II. Extracting the x-ray-induced fragmentation dynamics of carbon monoxide dication from forward and backward intensities

Recent developments in high-repetition-rate x-ray free electron lasers (XFELs) such as the European XFEL and the LSCS-II, combined with coincidence measurements using the COLTRIMS-reaction microscope, are now opening a door to realize the long-standing dream of creating molecular movies of photo-induced chemical reactions in gas-phase molecules. In this paper, we propose a new theoretical method to experimentally visualize the dissociation of diatomic molecules via time-resolved polarization-averaged molecular-frame photoelectron angular distribution (PA-MFPAD) measurements using the COLTRIMS-reaction microscope and the two-color XFEL pump-probe set-up. We used first- and second-order scattering theory within the muffin-tin approximation, which is valid for a sufficiently high kinetic energy of photoelectrons, typically above 100 eV, and for long bond lengths. This leads to a simple extended x-ray absorption fine structure (EXAFS)-type formula for the forward and backward scattering peaks in the PA-MFPAD structure. This formula relies only on three semi-empirical parameters obtainable from the time-resolved measurements. It can be used as a 'bond length ruler' on experimental results. The accuracy and applicability of the new ruler equation are numerically examined against the PA-MFPADs of CO2+ calculated with full-potential multiple scattering theory as a function of the C-O bond length reported in the preceding work (Ota et al J. Phys. B: At. Mol. Opt.). The bond lengths retrieved from the PA-MFPADs via our EXAFS-like formula coincide within an accuracy of 0.1 angstrom with the original C-O bond lengths used in the reference ab initio PA-MFPADs. We expect time-resolved PA-MFPADs to become a new attractive tool to make molecular movies visualizing intramolecular reactions.