Double ionization of H₂by electron impact: a second Born treatment

Abstract

A second Born treatment is applied to study the (e, 3e) and (e, 3 − 1e) reactions for H2 targets. The results of this approximation are compared to the (e, 3 − 1e) experimental data obtained at about 600 eV impact energy. Several single-centre wavefunctions are used to describe the initial state and excited states of the molecule. Even if the second Born approximation is able to explain part of the experimental results the agreement is not good, similar to the case of the double ionization of helium (Götz et al 2003 J. Phys. B: At. Mol. Opt. Phys. 36 L77).

<title>Double ionization of hydrogen molecule by fast electron impact: calculation using exact wave functions of two-center continuum</title>

“…As a result the calculation of the cross-section is reduced to the calculation of a set of one-dimensional integrals of the spheroidal functions [7,8]. This is a substantial advantage of our method compared to other methods [3,4,6] that require multidimensional integration.…”

“…under the conditions of the experiment [2], the differential cross-section should be additionally averaged over the directions of the internuclear axis (4) (4) . 1 shows the calculated cross-section of the (e, 3 -1e) process versus two angles, namely, the angle R θ between the internuclear axis and the momentum of the incident electron and the ejection angle a θ .…”

“…The calculations of (e, 3 -1e) are additionally complicated by the necessity to average the differential cross-section over the orientations of the molecular axis and to integrate it over the directions of the momentum of one of the ejected electrons. The final-state wave functions were taken as products of approximate two-center Coulomb wave functions [3] with effective charges, one-center Coulomb (OCC) functions [4], modified two-center Coulomb (MTCC) functions [5,6]. All these function are not exact solutions for an electron in the field of two centers.…”

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

“…However, up to now, only few models have been reported within the secondorder Born approximation, the major part of them being limited to simple atomic targets [39][40][41][42][43][44][45][46]. Considering the double ionization of molecular targets, to the best of our knowledge there are only two available models in the literature that use the 2nd Born approximation for describing the double ionization of H 2 [47,48]. For heavier molecular targets, only first order models have been reported in the literature.…”

H2Odouble ionization induced by electron impact

“…[29,30] for more details). However, up to now, only very few second-order Born models have been developed for describing the electron-induced double ionization process for molecular targets, the only one case available in the literature corresponding to the H2 molecule [31,32]. In this context, we have recently reported a detailed comparison between first-and second-order treatments of the double ionization of isolated water molecules and clearly pointed out particular kinematics where a second-order theory was needed [20].…”