# Molecular Dynamics of XFEL-Induced Photo-Dissociation, Revealed by Ion-Ion Coincidence Measurements
## 3 Results and Discussion
### lodomethane
In short, the momentum sharing between I and C ions can be, based on Figure 3a, approximated by a two-body dissociation if the C momentum is corrected by a dark momentum coefficient \(k\):  
\[p_{I,x}=-(p_{C,x}+3p_{H,x})=-\frac{1}{k}p_{C,x}.\]  
As the next step, the correct value of this coefficient is determined by applying a two-dimensional MF and restricting the momentum sum of acceptable pairs on the detector plane to a small circle around zero. The value of the coefficient k is scanned and the filtered coincident pair count obtained for each value, with the result shown in Figure 4. It shows a clear maximum at \(k=0.78\pm 0.02\). When we now regenerate the momentum sum plot with this coefficient, but without applying the MF (Figure 3b), it has the characteristics of a two-body process: a circular diffuse false coincidence background and the true coincidence spot close to zero. Misleadingly, the spot still appears not exactly centered at zero. This is an artifact of the rotation to point \(\mathbf{p}_{\mathrm{I}}\) always in the \(x\)-direction, and warrants a brief discussion in Appendix A.  
Figure 4: Coincident pair (I\({}^{5+}\)C\({}^{2+}\)) counts as a function of the dark momentum coefficient \(k\). Figure 3: Momentum sum plots on the detector plane of the two ions in the (I\({}^{5+}\), C\({}^{2+}\)) coincident pairs of iodomethane. The pairs were rotated to point the momentum of I\({}^{5+}\) in the \(x\)-direction. (**a**) Applying the correction coefficient \(k=1\), (**b**) \(k=0.78\). The black circle illustrates the strength of the MF, applied later. To verify that we have obtained true coincidences, a PIPICO plot is shown in Figure 5a, obtained with the correction coefficient \(k=0.78\), but not applying MF. Here one can see both the true coincidences as a tilted rectangular pattern and the false coincidence background as the fainter rectangle. The tilted pattern is the result of correlation in the axial momentum component, not used for MF. This pattern can be improved by applying the MF to the detector plane, as shown in Figure 5b, where a much sharper PIPICO pattern with almost no background is seen. The strength of the MF is indicated in Figure 3 by the black circle, although the events were chosen from within this circle in the _unrotated_ image, not in the rotated one (see Appendix A) (there was a technical problem in this experiment that resulted in an increased ion source size along the TOF axis. The strong filtering applied resulted also in ions accepted only from part of the source and created a narrower tilted pattern). We also demonstrate an application of the MF to a difficult case where no PIPICO pattern is initially discernible at all--the (I\({}^{11+}\),C\({}^{3+}\)) coincidences. Here, the I\({}^{11+}\) ions (with m/q of 11.5) are completely buried under the strong and broad C\({}^{+}\) peak in the ion TOF spectrum. The initial creation of the unfiltered and unbiased ion pairs produces a momentum sum plot in Figure 6a that is dominated by false coincidences (mostly between C\({}^{+}\) and C\({}^{3+}\)), but a weak coincident spot of I\({}^{11+}\),C\({}^{3+}\) is also seen as a slight enhancement of the intensity just right of the (0,0) position in the plot. Figure 5: Photoion-photoion coincidence (PIPICO) maps of the (I\({}^{5+}\), C\({}^{2+}\)) coincidences, (**a**) without momentum filtering (MF), and (**b**) with two-dimensional MF applied. Figure 6: Momentum sum plots (**a**) and (**b**) and PIPICO plots (**c**) and (**d**) of (I\({}^{11+}\), C\({}^{3+}\)) coincidences. The PIPICO plot in Figure 6c does not show any typical tilted pattern. Repeating the procedure described before, we first obtain the correlation coefficient, \(k\) = 0.825, and recreate the momentum sum plot (Figure 6b). For this plot, the lowest-strength MF is applied--the momentum sum is not restricted to a certain maximum length, but a set of ion pairs was formed that gave the best momentum correlation, instead of forming pairs randomly.