Three-body systems with Coulomb interaction. Bound and quasi-bound S-states

Evgeny Z. Liverts*, Nir Barnea

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


A simple Mathematica (versions 7-9) code for computing S-state energies and wave functions of three-particles systems is presented. The relevant systems include two-electron atoms, molecular electronic ions and mesomolecular exotic species. In addition to the bound S-states the code enables one to compute the positions and widths of the lowest resonance, quasi-bound, states. The elegant technique derived from the classical papers of Pekeris is applied. The basis functions are composed of Laguerre functions. The method is based on the perimetric coordinates and specific properties of the Laguerre polynomials. A direct solution of the generalized eigenvalues and eigenvectors problem is used, distinct from Pekeris' works. The complex scaling method is applied for calculating the resonance states. The resultant wave functions have a simple analytical form, that enables calculation of expectation values of arbitrary physical operators without any difficulties. Only one mathematical parameter characterizing the basis size is required in the input. The other input parameters are of the physical nature.

Original languageAmerican English
Pages (from-to)2596-2603
Number of pages8
JournalComputer Physics Communications
Issue number11
StatePublished - Nov 2013

Bibliographical note

Funding Information:
This work was supported by the Israel Science Foundation (grant number 954/09 ).


  • Binding energy
  • Eigenvalues
  • Eigenvectors
  • Matrix
  • Quasi-bound states
  • Resonances
  • Three-body system


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