<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo stretchy="false">(</mml:mo><mml:mi>e</mml:mi><mml:mo>,</mml:mo><mml:mn>3</mml:mn><mml:mi>e</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>on Helium at Low Impact Energy: The Strongly Correlated Three-Electron Continuum

Dürr, M.; Dorn, Alexander; Ullrich, J.; Cao, Sheng; Czasch, A.; Kheifets, Anatoli; Götz, J.; Briggs, J S

doi:10.1103/physrevlett.98.193201

Cited by 50 publications

(52 citation statements)

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“…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.…”

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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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confidence: 99%

Initial State Dependence in Multielectron Threshold Ionization of Atoms

2008

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“…Recent advances in measurement techniques have allowed kinematically complete measurements of the electron-impact double ionization of helium to be made [1,2]. Together with fully differential measurements for the electron-impact single ionization with excitation [3] (where the He + ion is left in an excited state), a significant insight has been given into the complex dynamics of the full four-body system.…”

Section: Introductionmentioning

confidence: 99%

“…While theoretical methods have provided accurate ab initio calculations for the three-body channels open to these collisions, such as convergent close coupling (CCC) [4], R matrix with pseudostates (RMPS) [5], and time-dependent close coupling (TDCC) [6], the progress of ab initio methods on the four-body channels has been limited. Hybrid methods that combine CCC or RMPS with distorted-wave techniques, or indeed full distorted-wave methods, have made some progress in this regard [1,3] though large discrepancies remain, especially with low-energy collisions. Presently, TDCC is the only ab initio method that has been applied to electron-impact double ionization of helium, and while it is in reasonable agreement with measurements of the total cross sections [7], angular-differential calculations differ markedly from measurement [8].…”

Section: Introductionmentioning

confidence: 99%

Electron-heliumS-wave model benchmark calculations. II. Double ionization, single ionization with excitation, and double excitation

Bartlett

Stelbovics

2010

Phys. Rev. A

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The propagating exterior complex scaling (PECS) method is extended to all four-body processes in electron impact on helium in an S-wave model. Total and energy-differential cross sections are presented with benchmark accuracy for double ionization, single ionization with excitation, and double excitation (to autoionizing states) for incident-electron energies from threshold to 500 eV. While the PECS three-body cross sections for this model given in the preceding article [Phys. Rev. A 81, 022715 (2010)] are in good agreement with other methods, there are considerable discrepancies for these four-body processes. With this model we demonstrate the suitability of the PECS method for the complete solution of the electron-helium system.

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“…Many four-body processes such as double excitation and ionization with excitation are yet to be explored with this method, so the electron-helium system remains only partially solved. Given the kinematically complete "reaction microscope" measurements [9,10] for helium that have been performed recently, the demand for accurate theoretical modeling of four-body processes is increasing.…”

Section: Introductionmentioning

confidence: 99%

Electron-heliumS-wave model benchmark calculations. I. Single ionization and single excitation

Bartlett

Stelbovics

2010

Phys. Rev. A

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A full four-body implementation of the propagating exterior complex scaling (PECS) method [J. Phys. B 37, L69 (2004)] is developed and applied to the electron-impact of helium in an S-wave model. Time-independent solutions to the Schrödinger equation are found numerically in coordinate space over a wide range of energies and used to evaluate total and differential cross sections for a complete set of three-and four-body processes with benchmark precision. With this model we demonstrate the suitability of the PECS method for the complete solution of the full electron-helium system. Here we detail the theoretical and computational development of the four-body PECS method and present results for three-body channels: single excitation and single ionization. Four-body cross sections are presented in the sequel to this article [Phys. Rev. A 81, 022716 (2010)]. The calculations reveal structure in the total and energy-differential single-ionization cross sections for excited-state targets that is due to interference from autoionization channels and is evident over a wide range of incident electron energies.

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(e,3e)on Helium at Low Impact Energy: The Strongly Correlated Three-Electron Continuum

Cited by 50 publications

References 27 publications

Initial State Dependence in Multielectron Threshold Ionization of Atoms

Initial State Dependence in Multielectron Threshold Ionization of Atoms

Electron-heliumS-wave model benchmark calculations. II. Double ionization, single ionization with excitation, and double excitation

Electron-heliumS-wave model benchmark calculations. I. Single ionization and single excitation

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