The Coulomb four-body problem in a classical framework: triple photoionization of lithium

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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“…The method used to obtain the results in Figs. 1-3 is the classical trajectory Monte Carlo method detailed in [19].…”

Section: H Y S I C a L R E V I E W L E T T E R S Week Ending 15 Februmentioning

confidence: 99%

Initial State Dependence in Multielectron Threshold Ionization of Atoms

2008

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“…The most relevant selection rule discussed for Li photofragmentation was that the pentuple differential cross section must be zero if all electrons are emitted in a plane perpendicular to the polarization axis, for states with M ¼ 0 and odd parity. More recent studies used a quasiclassical approach to study Li triple photoionization near the triple ionization threshold [22,23]. The latter study predicted that the ionized electrons resulting from triple ionization of ground-state Li should escape via a T-shaped break-up pattern, due to the stability properties of the classical fixed point for multiple threshold fragmentation.…”

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Angular Distributions for the Complete Photofragmentation of the Li Atom

Colgan

Pindzola

2012

Phys. Rev. Lett.

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We explore the complete breakup of the Li atom after absorption of a single photon, the purest example of the so-called four-body Coulomb problem. The resulting strongly correlated three-electron continuum is investigated by calculating the angular distributions of the ionized electrons using advanced close-coupling techniques. We find that the distributions are dominated by the Coulomb interactions between the electrons, that multiple break-up processes can be identified, and that the complex dynamics of the fragmentation process are evident for most scattering geometries.

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“…Emmanouilidou and Rost [9] performed semiclassical calculations for triple-photoionization of lithium. Surprisingly, in contradiction to the above-mentioned theories, they predict that the three electrons emerge in a T-shape pattern very close to threshold for excess energies down to at least E exc 0:5 eV.…”

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Coulomb Four-Body Problem: Electron-Impact Double Ionization of Helium in the Threshold Regime

2008

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Double ionization of helium by electron impact is studied in a kinematical complete experiment in the threshold regime at 5 eV excess energy. As expected the recoil ion carries the full initial projectile momentum and the emitted electrons' sum momentum in average is zero. The electron emission is revealed to be completely dominated by the symmetric 120 degrees configuration predicted by many threshold theories but never observed experimentally before. Fully differential cross sections show a more complex structure than expected for a pure threshold collision dynamics.

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The Coulomb four-body problem in a classical framework: triple photoionization of lithium

Cited by 38 publications

References 31 publications

Initial State Dependence in Multielectron Threshold Ionization of Atoms

Initial State Dependence in Multielectron Threshold Ionization of Atoms

Angular Distributions for the Complete Photofragmentation of the Li Atom

Coulomb Four-Body Problem: Electron-Impact Double Ionization of Helium in the Threshold Regime

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