Scaling Laws for the Photoionization Cross Section of Two-Electron Atoms

Byun, Chang Woo; Choi, Nark Nyul; Tanner, Gregor

doi:10.1103/physrevlett.98.113001

Cited by 16 publications

(46 citation statements)

References 37 publications

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“…It was also the starting point of the semiclassical analysis in Ref. [33], which uncovered the scaling laws in the photoionization cross section of two-electron atoms discussed in more detail in sec. IV.…”

Section: E the Photoionization Cross Sectionmentioning

confidence: 87%

“…A similar approach was adopted in Refs. [33,45] differing, however, in the treatment of closed channels.…”

Section: The Half-space Scattering Problemsmentioning

confidence: 99%

“…[33]. The technique of quantum maps is introduced starting from first principles and the semiclassical treatment is presented in all detail including a derivation of the modified exponent.…”

Section: Introductionmentioning

confidence: 99%

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Photoionization of two-electron atoms via highly doubly excited states: Numerical and semiclassical results

2010

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The quantum regime of highly doubly excited states in two-electron atoms has, so far, been largely inaccessible both to numerical methods as well as to experiments. Recent advances in semiclassical closed orbit theory in combination with a quantum mapping approach have shown a new way into this region of high dynamical complexity. In particular, new scaling laws near the double-ionization threshold as well as the dominant semiclassical contributions to the total photoionization cross section can be identified. We will present this new approach here in all its detail. It is based on representing the photoionization cross section in terms of quantum maps. These quantum maps or quantum propagators are used as a starting point for developing an efficient numerical method for calculating cross sections. Furthermore, by writing the quantum operators in semiclassical approximations, it is possible to interpret the quantum results in terms of classical triple collision orbits and to derive threshold laws near the three-particle breakup point. Semiclassical and numerical quantum results show excellent agreement for a model system, namely collinear helium.

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Section: E the Photoionization Cross Sectionmentioning

confidence: 87%

“…A similar approach was adopted in Refs. [33,45] differing, however, in the treatment of closed channels.…”

Section: The Half-space Scattering Problemsmentioning

confidence: 99%

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Photoionization of two-electron atoms via highly doubly excited states: Numerical and semiclassical results

2010

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“…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].…”

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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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“…Thanks to these tools, the dynamics near triple collision and the structure of stable and unstable manifolds were elucidated to some extent. In fact, a quantum manifestation of triple collision was demonstrated [15,16]. But we still know less about periodic orbits in two-dimensional dynamics, which are needed for semiclassical analysis.…”

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confidence: 98%