Accurate Exponential Representations for the Ground State Wave Functions of the Collinear Two-Electron Atomic Systems

Evgeny Z. Liverts*, Nir Barnea

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In the framework of the study of helium-like atomic systems possessing the collinear configuration, we propose a simple method for computing compact but very accurate wave functions describing the relevant S-state. It is worth noting that the considered states include the well-known states of the electron–nucleus and electron–electron coalescences as a particular case. The simplicity and compactness imply that the considered wave functions represent linear combinations of a few single exponentials. We have calculated such model wave functions for the ground state of helium and the two-electron ions with nucleus charge 1 ≤ Z ≤ 5. The parameters and the accompanying characteristics of these functions are presented in tables for number of exponential from 3 to 6. The accuracy of the resulting wave functions are confirmed graphically. The specific properties of the relevant codes by Wolfram Mathematica are discussed. An example of application of the compact wave functions under consideration is reported.

Original languageAmerican English
Article number4
JournalAtoms
Volume10
Issue number1
DOIs
StatePublished - Mar 2022

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

  • Collinear configuration
  • Fock expansion
  • Two-electron atoms
  • Wave functions
  • Wolfram mathematica

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