Cross-sections for (e, 3e) collisions on helium: the DS6C wavefunction

Götz, J.; Walter, Michael; Briggs, J S

doi:10.1088/0953-4075/39/21/003

Cited by 23 publications

(27 citation statements)

References 25 publications

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“…But no model has yet been able to reproduce all the data. Furthermore, we notice that even the most sophisticated model DS6C of Götz et al (2006) fails to describe the strong violation of the first Born symmetry seen in the experiment. The relative good agreement between our model and the experiment means that the TS2 mechanism (which is implicitly included in the second Born approximation) plays an important role here.…”

Section: D) Double Ionization Of Helium By Electrons and Positronsmentioning

confidence: 80%

The second Born approximation for the single and double ionization of atoms by electrons and positrons

Cappello

Haddadou

Menas

et al. 2010

J. Phys. B: At. Mol. Opt. Phys.

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have shown that the second Born approximation is necessary to describe the experimental results of the double ionization of atoms and molecules. The second Born approximation needs a difficult triple numerical integration and often many authors find some controversial results. We now investigate, in greater detail, the application of the second Born approximation for the easier case: the ionization of atomic hydrogen by electrons. The ionization of atomic hydrogen allows us to check accurately this approximation because the wavefunctions describing the target are known exactly. Moreover, sophisticated models such as convergent close coupling (CCC) and the continuum distorted wave eikonal initial state (CDW-EIS) exist and give closer results leading to easier comparisons. We report accurate second Born results for differential cross sections for the ionization of atomic hydrogen using a basis including 100 discrete states, and another basis including 32 discrete states and pseudo-states. The results of the present method are compared with other calculations and experiment. The single ionization of helium is also investigated in order to answer an old controversy between two different theoretical results. Finally, an application of the second Born approximation to the double ionization of helium has been performed.

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Section: D) Double Ionization Of Helium By Electrons and Positronsmentioning

confidence: 80%

The second Born approximation for the single and double ionization of atoms by electrons and positrons

Cappello

Haddadou

Menas

et al. 2010

J. Phys. B: At. Mol. Opt. Phys.

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show abstract

“…Three-body Coulomb dynamics, in particular, twoelectron atoms, are very well studied in the energy regime of single as well as double ionization [1][2][3][4]. Much less is known about correlated dynamics in four-body Coulomb systems, more precisely on differential observables for fragmentation of a three-electron atom in its nucleus and all electrons [5][6][7][8]. A recent experiment provides for the first time detailed information in terms of differential cross sections on the angular and energetic breakup parameters of three electrons following impact double ionization of Helium [9].…”

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confidence: 99%

Initial State Dependence in Multielectron Threshold Ionization of Atoms

2008

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It is shown that the geometry of multielectron threshold ionization in atoms depends on the initial configuration of bound electrons. The reason for this behavior is found in the stability properties of the classical fixed point of the equations of motion for multiple threshold fragmentation. Specifically for three-electron breakup, apart from the symmetric triangular configuration also a breakup of lower symmetry in the form of a T shape can occur, as we demonstrate by calculating triple photoionization for the lithium ground and first excited states. We predict the electron breakup geometry for threshold fragmentation experiments. DOI: 10.1103/PhysRevLett.100.063002 PACS numbers: 32.80.Fb, 05.45.ÿa, 34.80.Dp Three-body Coulomb dynamics, in particular, twoelectron atoms, are very well studied in the energy regime of single as well as double ionization [1][2][3][4]. Much less is known about correlated dynamics in four-body Coulomb systems, more precisely on differential observables for fragmentation of a three-electron atom in its nucleus and all electrons [5][6][7][8]. A recent experiment provides for the first time detailed information in terms of differential cross sections on the angular and energetic breakup parameters of three electrons following impact double ionization of Helium [9]. For small excess energies E (each continuum electron carries away about 9 eV energy), it was found that the electrons form an equilateral triangle upon breaking away from the nucleus. This is expected in accordance with Wannier's theory [10], quantified for three electrons in [11]. There, it is shown that the fixed point of classical dynamics, through which full fragmentation near threshold E 0 should proceed, is given for a three-electron atom by an equilateral triangle with the nucleus in the center and the electrons at the corners.In two-electron atoms the corresponding fixed point implies a collinear escape of the electrons in opposite directions [10,12]. The normal mode vibration about this collinear configuration is stable. This is in marked contrast to the three-electron case, where the triangular configuration is linked to two unstable, degenerate normal modes [11,13].We will show that the latter property has the consequence that the preferred final geometry of the three escaping electrons becomes initial state dependent and can change between an equilateral triangle and a less symmetric T-shaped escape. While the former is realized, e.g., in electron impact double ionization of helium, the latter should be seen in triple photoionization of lithium. These are only two prominent examples. The general pattern and the reason for it will be detailed below.Because of the scaling of the Coulomb potential, states of finite total angular momentum L will all behave like the L 0 state close to threshold which is therefore sufficient to consider [14]. In hyperspherical coordinates with the radial variable w instead of the hyperradius r w 2 , the Hamiltonian for a three-electron atom with total angular momentum L 0 reads whe...

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“…This limit corresponds to the collinear emission configuration in which both electrons leave the reaction region seeing a nuclear charge equal to Z − 1/4. Studies performed in the (e,3e) context [36] clearly show that the DS3C model is in much better agreement with the available data than the pure 3C model. In any case, from the inspection of these figures one can conclude that the results obtained by means of the GS2-DS3C model cannot be accurately reproduced by any combination based on the simpler models currently under study for the final state.…”

Section: Resultsmentioning

confidence: 64%

“…Although these models have shown partial success in different contexts (electron impact studies, ion-impact studies, photo-double ionization) and for different energy ranges, none of them has arisen in subsequent studies as the ultimate analytical wave function. For two lowenergy electrons in the continuum, the effective charges model of Berakdar and Briggs has shown some success in (e,2e) and (e,3e) studies [32,33,36]. For each pair of particles these effective charges are…”

Section: Theorymentioning

confidence: 99%

“…A simple extension, from the analytical point of view, would be to increase the number of Coulomb waves and distortion factors in order to deal with a 6C model. This model has been used in the (e,3e) context by Götz and Briggs [36] and considers all the twobody interactions between the particles in the final channel and hence goes beyond a second Born series. However, the amount of calculation needed (9-D integrals) only allowed the calculation of a few FDCSs as stated by the authors and their conclusions are still the focus of debate [37].…”

Section: Theorymentioning

confidence: 99%

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Double ionization of helium by bare ions: Theoretical study of the fully differential cross sections

2011

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This work presents a theoretical study of fully differential cross sections (FDCSs) for the double ionization of an He target by ion impact within a distorted wave model. The initial atomic system is described by two approximated wave functions of different accuracy proposed by Bonham and Kohl. For the final channel several models are considered based upon improvements and simplifications of the well-known three-body Coulomb (3C) model. The influence of the receding projectile on the resulting fragments is also studied by implementing a model with effective charges that depend on the momenta of the four particles. The FDCSs resulting for different electron energy sharing are discussed. The sensitivity of the FDCSs to the projectile charge sign and magnitude is explored over the energy range 700 keV/amu through 6 MeV/amu.

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Cross-sections for (e, 3e) collisions on helium: the DS6C wavefunction

Cited by 23 publications

References 25 publications

The second Born approximation for the single and double ionization of atoms by electrons and positrons

The second Born approximation for the single and double ionization of atoms by electrons and positrons

Initial State Dependence in Multielectron Threshold Ionization of Atoms

Double ionization of helium by bare ions: Theoretical study of the fully differential cross sections

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