Wannier-ridge theory of angular distribution

Kazansky, A K; Ostrovsky, V N

doi:10.1103/physreva.51.3712

Cited by 30 publications

(24 citation statements)

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“…Recently, a complementary technique has been applied to helium which determines the momentum of the recoiling ion in coincidence with one of the photoelectrons, providing similar information but in momentum space [7]. To date, TDCS has been investigated only for rare gases, and the progress in this area has benefited greatly from a close relationship between experiment and theory (e.g., [8][9][10][11][12][13][14][15][16]). However, such studies have yet to be applied to molecules.…”

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confidence: 98%

Triple Differential Cross Section Measurements for Double Photoionization ofD2

et al. 1997

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Angular distributions of the two ejected electrons following photodouble ionization of molecular deuterium have been measured using a toroidal photoelectron-photoelectron coincidence spectrometer in conjunction with synchrotron radiation. Six ͑g, 2e͒ triple differential cross sections (TDCS) were measured in the plane orthogonal to the photon beam direction with E 1 E 2 10 eV. The angular distributions are similar to those of helium, but with differences which we highlight by comparing the D 2 TDCS with helium TDCS measured under nearly identical conditions. [S0031-9007(97)04143-4] PACS numbers: 33.80.Eh, 32.80.Fb In photodouble ionization (PDI) a single photon is absorbed by an atom or a molecule, followed by the ejection of two electrons. PDI is simplest for the fundamental two-electron systems, helium and molecular hydrogen, as there is only one possible ion state and there are no intermediate states above it:It is not possible for direct PDI to be described within the familiar independent particle model as the photon cannot interact with more than one electron. Consequently, PDI is a manifestation of electron-electron interactions and so is a sensitive test for electron correlation theories.The angular distribution-or triple differential cross section (TDCS)-of the ejected electrons is a particularly sensitive measure of the electron correlation. These measurements [e.g., 1-6] have only been possible during the last few years due to improvements in synchrotron radiation sources and in the necessary photoelectronphotoelectron coincidence (PEPECO) techniques. Recently, a complementary technique has been applied to helium which determines the momentum of the recoiling ion in coincidence with one of the photoelectrons, providing similar information but in momentum space [7]. To date, TDCS has been investigated only for rare gases, and the progress in this area has benefited greatly from a close relationship between experiment and theory (e.g., [8][9][10][11][12][13][14][15][16]). However, such studies have yet to be applied to molecules. In this Letter we present the first measurements of molecular TDCS, having performed them in the most fundamental system: hydrogen.The photodouble ionization of helium results in the classic three-particle Coulomb continuum problem, whose solution determines the correlation factor in the expression for the TDCS [8]. The situation in hydrogen is not unrelated, but is further complicated by the inevitable dissociation of the molecule during double ionization. Therefore, PDI in hydrogen results in four unbound particles, albeit with two types of particles having different charges, masses, and velocities. However, it is perhaps not unreasonable to expect similarities in the angular distributions with helium (final state electronic symmetry 1 P 0 ) if the experimental conditions are chosen such that the electrons' speeds are much greater than those of the protons. The nuclear motion could then be considered as a perturbation which increases as the electron energies decrease.Previou...

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Triple Differential Cross Section Measurements for Double Photoionization ofD2

et al. 1997

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“…The secondary structure was reproduced in the calculations by the present authors [4,5] within the framework of the extended Wannier ridge model (EWRM) [6,7]. This theory provides the dynamic description of the electron correlations in which the individual characteristics of any atom are taken into account without any adjustable parameter.…”

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Electron correlation in double photoionization: Comparative study of secondary structure for Ne and Xe

Kazansky

Ostrovsky

1995

Phys. Rev. A

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The extended Wannier ridge model is shown to be able to reproduce the observed triple differential cross sections (TDCS) for the double-photoionization process y+Ne(2p ) -+Ne +(2p 'S')+e+e at a rather high excess energy E=40.6 eV. The secondary maximum in TDCS is related to the kinematic electron correlation in the initial state just as in the previously studied photoionization of Xe atoms. Variation of TDCS patterns at varying energies for Ne and Xe atom is described.PACS number(s): 32.80. Fb, 34.80.Dp, 34.80.Kw

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confidence: 99%

“…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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Wannier-ridge theory of angular distribution

Cited by 30 publications

References 20 publications

Triple Differential Cross Section Measurements for Double Photoionization ofD2

Triple Differential Cross Section Measurements for Double Photoionization ofD2

Electron correlation in double photoionization: Comparative study of secondary structure for Ne and Xe

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

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