Three-Dimensional Covariance Mapping

We have seen, in the case of diatomic molecules, that two-dimensional covariance maps allow correlation of the ion pairs. The situation with regard to the multiple ionization of triatomic molecules is more complex. Similar two-dimensional maps serve to indicate correlations between pairs of ions but at high laser intensities it is probable that three ions will be produced. Although one might infer that three ions have been created simultaneously, the only sure way of confirming the creation and subsequent fragmentation of a triple ion is to use three-dimensional covariance mapping. 

A two-dimensional map of N2O taken at 600 nm is shown in Fig. 6, where one sees a weak feature of 45° in the top right hand corner of the map this is associated with the two-body fragmentation [N20 ] NO -I- N . The fea- 

In order to remove this uncertainty, a three-dimensional map is required. In this case one is looking for correlations between three points (ti, tz, ts) in the TOF spectrum. The covariance is given by 

This expression must be evaluated at all times ti, t2 and t3 in the TOF spectrum to produce a three-dimensional (cubic) map where one can imagine the TOF spectrum lying along the x, y and z axes [29]. Apart from the autocorrelation planes, and any statistical noise, only true triple fragment correlations will give real counts on the map. Six three-dimensional features should appear for each triple correlation these occur at (ti, t2, ( 3. fi, (iz 3, i), ( 3, i), 

What is surprising is the lack of peaks in the TOF spectrum (and structure on the covariance map) associated with single ions. The total energy release (about 40 eV) suggests that, as the three atoms move apart and as the laser E field increases, there comes a point when the molecule is suddenly six-times ionized. One can speculate on the mechanism involved, but this interesting phenomenon deserves further study both experimentally and theoretically. 

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Since the covariance map is constructed based on one-dimensional TOF mass spectra, the angular distribution of fragment ions with respect to the laser polarization direction is only indirectly incorporated into the map through the momentum distribution along the TOF axis (see [19] for the extension to two-dimensional measurements). In order to derive three-dimensional momentum vector distributions of the fragment ions together... 

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