Subcomponents $\psi_{4,1}^{(2d)}$ and $\psi_{3,0}^{(2c)}$ of the angular Fock coefficients: Explicit analytic representation

TL;DR

This paper derives explicit analytic expressions for complex subcomponents of the angular Fock coefficients in the two-electron atomic wave function expansion, utilizing an innovative Mathematica-based method.

Contribution

It provides new explicit formulas for specific subcomponents of the angular Fock coefficients, advancing the analytical understanding of the two-electron wave function near coalescence points.

Findings

Explicit formulas for $psi_{4,1}^{(2d)}$ and $psi_{3,0}^{(2c)}$ derived

Use of Mathematica facilitated complex calculations

Enhances analytical tools for two-electron atomic systems

Abstract

The Fock expansion [1] describes the $S$-state wave function of the two-electron atomic system in the vicinity of the triple coalescence point. The present work constitutes the additional appendix to our paper [2] devoted to refinement and further development of calculation of the angular Fock coefficients of the Fock expansion. We derive the explicit analytic expressions for the complicated subcomponents $\psi_{4,1}^{(2d)}$ and $\psi_{3,0}^{(2c)}$ of the angular Fock coefficients. An unusual method of using the Wolfram Mathematica was applied.