Two-particle atomic coalescences: Boundary conditions for the Fock coefficient components

TL;DR

This paper derives and verifies boundary conditions for Fock coefficient components at two-particle coalescences in two-electron systems, using Green function methods and Mathematica to simplify complex calculations.

Contribution

It introduces new boundary conditions for Fock coefficients based on Kato cusp conditions and applies Green function techniques for their derivation.

Findings

Exact values of Fock coefficient components at coalescences were obtained.

Boundary conditions consistent with Kato cusp conditions were derived and verified.

Additional boundary conditions not from Kato cusp conditions were identified.

Abstract

The exact values of the presently determined components 26of the angular Fock coefficients at the two-particle coalescences were obtained and systematized. The Green Function approach was successfully applied to simplify the most complicated calculations. The boundary conditions for the Fock coefficient components in the hyperspherical angular coordinates, which follows from the Kato cusp conditions for the two-electron wave function in the natural interparticle coordinates, were derived. The validity of the obtained boundary conditions was verified on examples of all the presently determined components. The additional boundary conditions are not arising from the Kato cusp conditions were obtained as well. The Wolfram Mathematica was used intensively.