Green-function approach to electron angular correlations in the Wannier threshold law

Ak, Kazansky; Vn, Ostrovsky

doi:10.1103/physreva.48.r871

Cited by 26 publications

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“…In addition, the ionic motion maximizes along the polarization axis (β + > 0) while the electron pair breaks up predominantly perpendicular to the polarization (β − < 0). This can be understood by a Wannier type analysis, which predicts, that double ionization near threshold can only be reached if ionic and electron motion are perpendicular, all other cases lead to single ionization [6][7][8][9][10][11][12].The preferential break up of the electron pair can also be understood by studying the helium atom in a molecular picture, where the electronic separation R is interpreted as a molecular axis and the projection m of the total angular momentum on this axis is taken as an approximate quantum number. This analysis was performed in [13] where some misprints appeared, so we repeat it briefly here.…”

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Energy sharing and asymmetry parameters for photo double ionization of helium 100 eV above threshold in single-particle and Jacobi coordinates

Knapp

Walter

Weber

et al. 2002

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

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We present a joint experimental and theoretical study of the double differential cross section for the double ionization of helium by absorption of one 179 eV linear polarized photon (100 eV above threshold). We show the energy sharing and the asymmetry parameters in both single particle coordinates and in Jacobi coordinates. An asymmetric sharing of the electron excess energy and a breakup of the electron pair preferentially parallel to the polarization axis is found. This marks a deviation from the propensity rule favoring perpendicular relative electron motion which has been observed to hold at energies closer to the double ionization threshold. * Electronic address: doerner@hsb.uni-frankfurt.de 1 Double ionization of helium by single photon absorption is a benchmark process for the investigation of electron-electron correlation in few-body systems. The three particles final state is completely kinematically determined by a set of 5 linear independent degrees of freedom (the remaining 4 are fixed by momentum and energy conservation). This fivefold differential cross section can be reduced by one degree of freedom by taking the dipole approximation into account. For examination within the dipole approximation it is helpful to integrate over 2 or 3 of the degrees of freedom to obtain doubly or singly differential cross sections. These cross sections give an overview of which regions of this 4 dimensional phase space are most important. The cross section differential in an arbitrary momentum vector k can be described by only two parameters, the cross section differential in energy dσ/dE and the asymmetry parameter β. It can always be expressed in the simple form. Hereǫ is the linear light polarization axis and P 2 the second legendre polynomial. While such cross sections are extremely valuable for the characterization of the process, there has been only three experiments reported [1][2][3].Two coordinate sets are widely used in the literature to describe the momentum configurations: The first set is the electron momenta k 1,2 relative to the center of mass of all particles with the excess energy given by E excess = E 1 + E 2 and E 1,2 = k 2 1,2 /2. The second set is the Jacobi momenta -the center of mass momentum of the electron pair k + = k 1 + k 2 , where − k + is the momentum of the recoiling nucleus, and k − = ( k 1 − k 2 )/2 is the relative momentum of the electrons. The excess energy shared in the corresponding energies readsAtomic units are used throughout. The two coordinate systems suggest two different perspectives on the double ionization process: single electron coordinates describe the escape of each electron from the nuclear potential. Therefore they would be most appropriate if the coupling between the electrons could be treated as perturbation while their motion is mainly governed by the nuclear field and the photon. This can be expected for example at very high photon energies, where one expects [4,5] that one electron absorbs the majority of the photon energy and angular momentum while ...

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Energy sharing and asymmetry parameters for photo double ionization of helium 100 eV above threshold in single-particle and Jacobi coordinates

Knapp

Walter

Weber

et al. 2002

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

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“…At the same time the relevance of the physically transparent Wannier mechanism became an open question of fundamental importance. The present authors have suggested recently [8,9,17] an approach to the angular distributions which eliminates the ad hoc assumptions of the previous treatments [2,3]. It lies along the lines of the original Wannier mechanism, but also includes an extension which seems to be of principle importance.…”

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“…In a consistent development [8,9], a Gaussian shape could be obtained only under some additional, unnecessary, quite restrictive, and physically unjustified assumptions. The proper treatment incorporates specifics of the doubleionization process, of the initial state, etc.…”

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Wannier-ridge theory of angular distribution

Kazansky

Ostrovsky

1995

Phys. Rev. A

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An extended Wannier-ridge model is put forward that reproduces essentially a11 available experimental data on the relative angular distribution of the electrons emitted in near-threshold double photoionization. Under the condition of equal-energy sharing by the electrons, the model is applicable to unexpectedly high values of the energy excess above the threshold. Depending on the character of the correlations in the initial state, complicated angular distribution patterns appear with the secondary structure.PACS number(s): 32.80. Fb, 34.80.Dp, 34.80.Kw

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2006

Electronic Correlation Mapping

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Green-function approach to electron angular correlations in the Wannier threshold law

Cited by 26 publications

References 20 publications

Energy sharing and asymmetry parameters for photo double ionization of helium 100 eV above threshold in single-particle and Jacobi coordinates

Energy sharing and asymmetry parameters for photo double ionization of helium 100 eV above threshold in single-particle and Jacobi coordinates

Wannier-ridge theory of angular distribution

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