Title: Helium-like atoms. The Green's function approach to the Fock expansion calculations,
Abstract: The renewed Green's function approach to calculating the angular Fock
coefficients, $\psi_{k,p}(\alpha,\theta)$ 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
$\theta=0,\pi$ (arbitrary $\alpha$) or $\alpha=0,\pi$ (arbitrary $\theta$) are
indicated as corresponding to the angular Fock coefficients possessing physical
meaning. The most interesting case of $\theta=0$ 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 ($\alpha=0$) and electron-electron ($\alpha=\pi/2$)
coalescences. It is shown that the Green's function method for $\theta=0$
enables us to calculate any component/subcomponent of the angular Fock
coefficient in the form of a single series representation with arbitrary angle
$\theta$. Those cases, where the Green's function approach can not be applied,
are thoroughly studied, and the corresponding solutions are found.