An accurate treatment of two-electron systems using hyperspherical coordinates

Klar, H.; Klar, Maximilian

doi:10.1088/0022-3700/13/6/014

Cited by 88 publications

(39 citation statements)

References 18 publications

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“…That space is spanned by 3-body configurations rather of single electron positions. The kinetic energy of the electron pair as one was already calculated in [7]. We obtained [7] …”

Section: Geometrical Aspectsmentioning

confidence: 99%

“…That configuration may be easily represented with our coordinates. To this end we write the potential energy of the atom, see [7], in our coordinates. We get with help of (7) ( )…”

Section: Propagation Of Electron-pair Wavesmentioning

confidence: 99%

“…Electron exchange is described in our coordinates by the replacement 2π ϕ ϕ → − , the other coordinates remain unchanged [7]. The Appendix shows the symmetry property…”

Section: Propagation Of Electron-pair Wavesmentioning

confidence: 99%

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Formation of Slow Electron Pairs in an External Coulomb Field

Klar¹

2017

JMP

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The wave equation for two electrons in an external Coulomb field (heliumlike atoms) has been shown to be a problem in a three-dimensional half-space. The wave-equation becomes quasi-separable in inertial coordinates. This allows to work out the electron motion in the frame of principal inertia axes. We find that non-adiabatic coupling terms constitute a fictitious force and lead to a deformation of the static potential surface. Incoming and outgoing modes of electron pairs are studied in detail, and applied to the threshold ionization of hydrogen-like atoms by electrons. Our analysis confirms the classical work by Wannier. However, we go beyond Wannier and present bending and stretch vibrations of electron pairs. The bending vibration has no influence onto the total ionization cross-section. The pair formation below threshold destroys the existence of high double Rydberg resonances. Finally, we describe the propagation of an electron pair through a linear chain of Rydberg atoms.

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“…That space is spanned by 3-body configurations rather of single electron positions. The kinetic energy of the electron pair as one was already calculated in [7]. We obtained [7] …”

Section: Geometrical Aspectsmentioning

confidence: 99%

“…That configuration may be easily represented with our coordinates. To this end we write the potential energy of the atom, see [7], in our coordinates. We get with help of (7) ( )…”

Section: Propagation Of Electron-pair Wavesmentioning

confidence: 99%

See 1 more Smart Citation

Formation of Slow Electron Pairs in an External Coulomb Field

Klar¹

2017

JMP

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“…The position vectors of the positron f+ and the electron f_ with respect to the proton read in terms of hyperspherical coordinates [11][12][13][14][15][16][17] /cosy sin /2+3 )} f~ = rR(c~, p, 7) tsin ~b _ .…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…It is evident that these data depend very sensitively on a correct description of the correlated motion of an electron-positron pair in the field of a nucleus. It is now well known that two-electron systems, on the other hand, can be handled satisfactorily in terms of hyperspherical coordinates [7][8][9][10][11][12]. These treatments solve directly the Schr6dinger equation in the configuration space representation without assuming any particular configuration mixing for doubly excited states.…”

Section: Introductionmentioning

confidence: 99%