(e,2e) simple ionization of CO₂by fast electron impact: use of three-center parameterized continuum wave function and Dyson orbitals

Abstract

The variation of the triple differential cross section of the (e,2e) simple ionization of CO 2 with the direction of the ejected electron is studied. The calculations are performed in the frame of a perturbative first Born procedure, using a three-center Dyson type description for the 1π g bound electron and an approximate three-center continuum solution of the corresponding Schrödinger equation for a specific wave vector k e for the free ejected electron, which satisfies the correct asymptotic boundary condition up to the order O kr (()) 2 −. Empirical values for the screening of the three nuclei of the target and for the Sommerfeld parameters of the three-center Coulomb continuum function are introduced. The results are compared to existing experimental results and a theoretical result obtained by the same approach, using a Hartree-Fock Slater type orbital.

Comparison of experimental and theoretical triple differential cross sections for the single ionization ofCO2 (1πg)by electron impact

“…Coulomb continuum (TCC) model, which applies two center Coulomb continuum functions obtained from the solution of the Schrödinger equation for a free electron in the Coulomb field of two fixed charged nuclei, was extended to three-center targets (ThCC), and has been applied to the ionization of CO 2 [17] for higher incident ( 500 eV) energy asymmetric cases. In [18], it was slightly modified by the introduction of a supplementary parameter, which adds some flexibility to the function and adapts it to more general situations. Five types of calculations were done, with different model potential parameters for the interaction of the incident electron with the target.…”

“…The details concerning the different terms of this expression are given in [17], [18]. r is the Dyson orbital [37], [38] for the initially bound electron obtained from the coupled cluster results [39], [40] by calculating the overlap between the N state of the target and the (N-1) state of the ionized ion.…”

“…We will label this approach as the three center continuum (ThCC) approximation. The theory was further modified to use Dyson Gaussian orbitals and the results gave better agreement with the experimental data [18].…”

Theoretical study of $(\gamma ,2e)$ photo-double ionization of CO2in the equal energy sharing regime using Dyson orbitals and the parameterized three center continuum wave function

“…After eliminating the spin part in these expressions, we obtain the following expression Here the 1 g p orbitals in the initial state will be given by the corresponding Dyson orbitals of CO 2 [29]. We think that this is a good compromise between the use of simple Hartree-Fock orbitals and an all electron treatment of CO 2 taking into account all the inactive electrons, which would result in very cumbersome calculations.…”

Natural ionization orbitals for interpreting electron detachment processes

“…Most closely related in scope to this work are the developments of EOM-coupled cluster (CC) by Krylov et al to the study of ionization processes [26][27][28][29][30][31] and the electron propagator theory (EPT) work of Ortiz et al [32][33][34][35][36][37][38] Experimentally, (e,2e) or electron momentum spectroscopy (EMS) provides the ability to probe the electron density of individual orbitals during ionization events. [39][40][41][42][43][44][45][46][47] Although EMS can access the complete valence shell, it does this with lower resolution than more widely used photoelectron spectroscopy (PES). However, the EMS cross-section is proportional to the square of the Dyson orbital associated with the transition and in this regard has the potential to image the electron/hole density of individual orbitals.…”