TY - JOUR

T1 - The Green's function approach to the Fock expansion calculations of two-electron atoms

AU - Liverts, Evgeny Z.

AU - Barnea, Nir

N1 - Publisher Copyright:
© 2018 IOP Publishing Ltd.

PY - 2018/1/25

Y1 - 2018/1/25

N2 - The renewed Green's function approach to calculating the angular Fock coefficients, φk,p(α,⊖) is presented. The final formulas are simplified and specified to be applicable for analytical, as well as numerical calculations. The Green's function formulas with the hyperspherical angles ⊖ = 0, π (arbitrary α) or α = 0,π (arbitrary α) are indicated as corresponding to the angular Fock coefficients possessing physical meaning. The most interesting case of ⊖ = 0 corresponding to a collinear arrangement of the particles is studied in detail. It is emphasized that this case represents the generalization of the specific cases of the electron-nucleus (α = 0) and electron-electron (α = π/2) coalescences. It is shown that the Green's function method for ⊖ = 0 enables us to calculate any component/subcomponent of the angular Fock coefficient in the form of a single series representation with arbitrary angle ⊖. Those cases where the Green's function approach cannot be applied, are thoroughly studied, and the corresponding solutions are found.

AB - The renewed Green's function approach to calculating the angular Fock coefficients, φk,p(α,⊖) is presented. The final formulas are simplified and specified to be applicable for analytical, as well as numerical calculations. The Green's function formulas with the hyperspherical angles ⊖ = 0, π (arbitrary α) or α = 0,π (arbitrary α) are indicated as corresponding to the angular Fock coefficients possessing physical meaning. The most interesting case of ⊖ = 0 corresponding to a collinear arrangement of the particles is studied in detail. It is emphasized that this case represents the generalization of the specific cases of the electron-nucleus (α = 0) and electron-electron (α = π/2) coalescences. It is shown that the Green's function method for ⊖ = 0 enables us to calculate any component/subcomponent of the angular Fock coefficient in the form of a single series representation with arbitrary angle ⊖. Those cases where the Green's function approach cannot be applied, are thoroughly studied, and the corresponding solutions are found.

KW - Fock expansion

KW - Green's function

KW - helium-like atoms

KW - two-particle coalescences

UR - http://www.scopus.com/inward/record.url?scp=85041997290&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/aaa2ce

DO - 10.1088/1751-8121/aaa2ce

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AN - SCOPUS:85041997290

SN - 1751-8113

VL - 51

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 8

M1 - 085204

ER -