Modified two-centre continuum wavefunction: application to the dissociative double ionization of H₂by electron impact

Abstract

The fully differential cross section (FDCS) of the double ionization of the hydrogen molecule by electron impact, with the coincidence detection of the two ejected and the scattered electrons, is determined by the application of a product of two modified two-centre Coulomb continuum (MTCC) wavefunctions describing the two ejected electrons. The MTCC, which fulfils the correct boundary conditions asymptotically up to the order O((kr) −2), is obtained in a closed analytical form by solving the Schrödinger equation of an electron with wave vector k and position vector r in the Coulomb field of two fixed nuclei. After the study of the variation of the (FDCS) for some typical geometries the multiply differential cross section of the (e, 3 − 1e) process is determined and compared to the experimental values.

Molecular orientation effect on the differential cross sections for the electron-impact double ionization of oriented water molecules

“…Let us cite the PWBA model developed by Chuluunbaatar et al [22] within the first Born approximation for describing the (e,3e) experiments of Lahmam-Bennani et al [23] on H 2 and that developed by Mansouri et al [24] in the PWBA model within the second Born approximation. However, even in this case, a disagreement has been highlighted in the case of small shifts of the binary and the recoil peaks [24] in contradiction to the experimental observations [23].…”

<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.…”

“…Differential cross-section of (e, 3 -1e) process for aligned molecules One of the possible ways to take the electron-electron correlation into account is to introduce the approximate effective potential in which the electron motion takes place. In the present paper we use two effective potentials: 1) for faster ejected electron the total nuclear charge is taken to be Z + =1, i.e., the slower ejected electron shields partially the nuclear field; 2) for faster ejected electron it is assumed that for MTCC [6] and dashdotdot line for OCC [4]. The squares show the experimental results [2].…”

“…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.…”