Cumulant mapping as the basis of multi-dimensional spectrometry

Abstract

Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance...

Molecular photodissociation dynamics revealed by Coulomb explosion imaging

“…Based on the examples featured in this Perspective one might argue that CEI methods have ‘yet to deliver’ penetrating new insights into the photofragmentation dynamics of neutral molecules, but this situation can surely be expected to improve as the technique is applied to a wider range of (larger) molecules, along with greater use of covariance and coincidence analysis methods. 210 The data shown in Fig. 15(a) highlight some of the potential benefits ( e.g.…”

Multiparticle Cumulant Mapping for Coulomb Explosion Imaging

“…All fragment ion pairs contribute to this term, resulting in a roughly Gaussian distributed background. This illustrates the importance of using the correction in calculating the appropriate four particle correlation, which is equivalent to the calculation of a cumulant [41].…”

“…For the data presented here, the typical acquisition time was approximately 20 minutes, with on average 8 ions detected per shot. The detection efficiency of our apparatus is estimated to be η = 60% to 90% per particle resulting in a four-fold channel overall efficiency of around η 4 = 13% to 65% [41]. The full 3D information of correlated particles can be used to reconstruct the recoil frame and determine the kinetic energy release and angular distributions in the same way as coincidence measurements [7,37].…”

“…These can be dealt with using more extended techniques, such as partial and contingent covariance [38][39][40]. However, covariance measurements have not yet been established in four-or-more body relationships because four-body and higher covariance is qualitatively different from two-and three-body [39,41]. This can be seen by evaluating the expressions for collective correlations amongst a few fragments:…”

“…This will lead to a non-zero correlation value even in the absence of collective correlation amongst all N fragments [39]. With a small correction, the covariance formula can be modified to capture only the full four-body correlations, which is equivalent to a four-fold cumulant [41]:…”