Double ionization of the water molecule: Influence of the target orientation on the secondary-electron angular distributions

Abstract

Fivefold differential cross sections for electron-induced double ionization of isolated oriented water molecules are reported. The theoretical investigation is performed within the first Born approximation by describing the initial molecular state by means of single-center wave functions. The contributions of each final state to the double-ionization process, i.e., with target electrons ejected from similar and/or different molecular subshells, are studied and compared in terms of shape and magnitude. Furthermore, for the particular target orientations investigated, we identify clearly the signature of the main scenarios involved in (e,3e) reactions, namely, the shake-off and the two-step 1 mechanisms.

Fivefold differential cross sections for electron-induced double ionization of outer and inner valence (1t2 and 2a1) molecular orbitals of CH4

“…In order to compare our results to those previously reported for the isoelectronic water molecule [34,35], we choose here three particular target orientations successively described by means of the Euler angle triplets (0,0,0), (0, /2,0), and (0, /2, /2) (see Fig. 1).…”

“…The latter may be taken as either equal to the value of the residual asymptotic nuclear charge (Z 1 = Z 2 = 2) or as dependent of the different moments k s , k 1 , and k 2 as reported by Berakdar [55] or Zhang [56] for (e,2e) experiments, and more recently by El Azzouzi et al [24] for (e,3e) collisions. In the current work, we have chosen the constant case as in our previous studies on double ionization of water molecule [34,35].…”

“…Note that the summation over the index j considers only the five final states of the doubly ionized molecule, namely, those corresponding to the ejection of two electrons from the same molecular orbital. Moreover, as underlined in our previous works [34,35], the above-cited wave functions j (r) refer to a particular orientation of the molecular target given by the Euler angles (˛,ˇ, ). Thus, the 5DCSs calculated under these conditions refer to the double ionization of an oriented methane molecule, the transition matrix element T j being obviously dependent of the target, namely,…”

“…In this context, the current work aims at extending our model previously tested on water molecule [34,35] to the methane molecular target. Fivefold differential cross sections (5DCS) are then reported within the first Born approximation.…”

“…Finally, let us mention the first Born approximation (FBA), which is up to now the only theoretical model able to treat heavier molecular targets (for more details we refer the interested reader to Refs. [32][33][34][35] dedicated to the water double ionization). In this approach, each ejected electron is described by a Coulomb wave, the repulsion between the two ejected electrons being taken into account via the inclusion of a Gamow factor.…”