Symmetric Euler-Angle Decomposition of the Two-Electron Fixed-Nucleus Problem

Bhatia, A. K.; Temkin, A.

doi:10.1103/revmodphys.36.1050

Cited by 175 publications

(62 citation statements)

References 22 publications

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“…These six coordinates can be taken as the sides of the triangle r 1 , r 2 , r 12 formed by the three particles, i.e., two electrons and the fixed nucleus and the Eulerian angles (θ, φ, ψ) defining the orientation of this triangle in space. The wave function obeying symmetry properties under particle exchange may be written as [44] …”

Section: Methodsmentioning

confidence: 99%

Nonrelativistic structure calculations of two-electron ions in a strongly coupled plasma environment

Bhattacharyya¹,

Saha

Mukherjee³

2015

Phys. Rev. A

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In this work, the controversy between the interpretations of recent measurements on dense aluminum plasma created with Linac coherent light sources (LCLS) X-ray free electron laser (FEL) and Orion laser has been addressed. In both kind of experiments, helium-like and hydrogen-like spectral lines are used for plasma diagnostics . However, there exist no precise theoretical calculations for He-like ions within dense plasma environment. The strong need for an accurate theoretical estimates for spectral properties of He-like ions in strongly coupled plasma environment leads us to perform ab initio calculations in the framework of Rayleigh-Ritz variation principle in Hylleraas coordinates where ion-sphere potential is used. An approach to resolve the long-drawn problem of numerical instability for evaluating two-electron integrals with extended basis inside a finite domain is presented here. The present values of electron densities corresponding to disappearance of different spectral lines obtained within the framework of ion-sphere potential show excellent agreement with Orion laser experiments in Al plasma and with recent theories. Moreover, this method is extended to predict the critical plasma densities at which the spectral lines of H-like and He-like carbon and argon ions disappear. Incidental degeneracy and level-crossing phenomena are being reported for the first time for two-electron ions embedded in strongly coupled plasma. Thermodynamic pressure experienced by the ions in their respective ground states inside the ion-spheres are also reported.

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Section: Methodsmentioning

confidence: 99%

Nonrelativistic structure calculations of two-electron ions in a strongly coupled plasma environment

Bhattacharyya¹,

Saha

Mukherjee³

2015

Phys. Rev. A

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“…The correctness of the sign in Equation (2) can be ascertained from the paper of Temkin and Lamkin (1961) [16]. In Equation (1), L is the angular momentum, u L is the scattering function, and the function Φ L is the correlation function which can be written in terms of generalized "radial" functions, which depend on the radial coordinates and the Euler angles introduced by Bhatia and Temkin (1964) [17]:…”

Section: Introductionmentioning

confidence: 99%

Positron-Hydrogen Scattering, Annihilation, and Positronium Formation

Bhatia

2016

Atoms

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Abstract:In previous papers (Bhatia A.K. 2007, 2012) a hybrid theory for the scattering of electrons from a hydrogenic system was developed and applied to calculate scattering phase shifts, Feshbach resonances, and photoabsorption processes. This approach is now being applied to the scattering of positrons from hydrogen atoms. Very accurate phase shifts, using the Feshbach projection operator formalism, were calculated previously (Bhatia A.K. et al. 1971 and Bhatia et al. 1974a). The present results, obtained using shorter expansions in the correlation function, along with long-range correlations in the Schrödinger equation, agree very well with the results obtained earlier. The scattering length is also calculated and the present results are compared with the previous results. Annihilation cross-sections, and positronium formation cross-sections, calculated in the distorted-wave approximation, are also presented.

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“…The angle θ 12 is the angle between → r 1 and → r 2 . In Equation (1), L is the angular momentum; u L is the scattering function; and the function Φ L is the correlation function which can be written in terms of the generalized "radial" functions, which depend upon the radial coordinates and the Euler angles introduced by Bhatia and Temkin (1964) [5]:…”

Section: Introductionmentioning

confidence: 99%

P-Wave Positron-Hydrogen Scattering, Annihilation, and Positronium Formation

Bhatia

2017

Atoms

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Abstract:In a previous paper (Bhatia A.K. 2016), a hybrid theory for the scattering of positrons from hydrogen atoms was applied to calculate S-wave phase shifts, annihilation, and positronium formation cross sections. This approach is now being applied to calculate P-wave positron-hydrogen scattering. The present results, obtained using short-range correlation functions along with long-range correlations in the Schrödinger equation at the same time, agree very well with the results obtained in an earlier calculation by , using the Feshbach projection operator formalism. In these earlier calculations, the correction due to the long-range correlations was applied to the variational results. In spite of the fact that this ad hoc correction destroyed the variational bound, the final results have been considered accurate. Annihilation cross-sections, positronium formation cross-sections, calculated in the distorted-wave approximation, are also presented.

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Symmetric Euler-Angle Decomposition of the Two-Electron Fixed-Nucleus Problem

Cited by 175 publications

References 22 publications

Nonrelativistic structure calculations of two-electron ions in a strongly coupled plasma environment

Nonrelativistic structure calculations of two-electron ions in a strongly coupled plasma environment

Positron-Hydrogen Scattering, Annihilation, and Positronium Formation

P-Wave Positron-Hydrogen Scattering, Annihilation, and Positronium Formation

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