S-states of helium-like ions

Evgeny Z. Liverts*, Nir Barnea

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A simple Mathematica (version 7) code for computing S-state energies and wave functions of two-electron (helium-like) ions is presented. The elegant technique derived from the classical papers of Pekeris is applied. The basis functions are composed of the Laguerre functions. The method is based on the perimetric coordinates and specific properties of the Laguerre polynomials. Direct solution of the generalized eigenvalues and eigenvectors problem is used, distinct from the Pekeris works. No special subroutines were used, only built-in objects supported by Mathematica. The accuracy of the results and computation times depend on the basis size. The ground state and the lowest triplet state energies can be computed with a precision of 12 and 14 significant figures, respectively. The accuracy of the higher excited states calculations is slightly worse. The resultant wave functions have a simple analytical form, that enables calculation of expectation values for arbitrary physical operators without any difficulties. Only three natural parameters are required in the input. The new version of Mathematica code takes into account the fact that the negative hydrogen ion has only one bound state.

Original languageAmerican English
Pages (from-to)844-845
Number of pages2
JournalComputer Physics Communications
Issue number3
StatePublished - Mar 2012


  • Eigenvalues
  • Eigenvectors
  • Excited energies
  • Ground state energy
  • Helium-like ions
  • Wave functions


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