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Recent developments of high-reputation-rate X-ray free electron lasers(XFELs) such as European XFEL and LSCS-II, combined with coincidencemeasurements at the COLTRIMS-Reaction Microscope, is now opening a door torealize a long-standing dream to create molecular movies of photo-inducedchemical reactions of gas-phase molecules. In this paper, we theoreticallypropose a new method to experimentally visualize dissociation of diatomicmolecules via time-resolved polarization-averaged molecular-frame photoelectronangular distributions (PA-MFPADs) measurements using the COLTRIMs--ReactionMicroscope and two-color XFEL pump-probe set-up. The first and second orderscattering theories with the Muffin-tin approximation give us simple EXAFS typeformula for the forward and backward scattering peaks in the PA-MFPADsstructure. This formula acts as an experimentally applicable "bond lengthruler" by adjusting only three semi-empirical parameters from the time-resolvedmeasurements. The accuracy and applicability of a new ruler equation arenumerically examined against the PA-MFPADs of CO<sup>2+</sup> calculated byFull-potential multiple scattering theory as a function of the C-O bond lengthreported in the preceding work. The bond lengths retrieved from the PA-MFPADsvia the EXAFS formula well reproduce the original C-O bond lengths used in thereference <i>ab-initio</i> PA-MFPADs with accuracy of 0.1 {\AA}. We expect thattime-resolved PA-MFPADs will be a new attractive tool to make molecular moviesvisualizing intramolecular reactions.

journal of physics. b, atomic molecular and optical physics/journal of physics. b, atomic, molecular and optical physics

Theory on 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