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Manuscript Title: S - states of helium-like ions
Authors: Evgeny Z. Liverts, Nir Barnea
Program title: TwoElAtomSL(SH)
Catalogue identifier: AEHY_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 182(2011)1790
Programming language: Mathematica 7.0.
Computer: Any PC.
Operating system: Any which supports Mathematica; tested under Microsoft Windows XP and Linux SUSE 11.0.
RAM: ≥ 109 bytes
Keywords: Energies, Wave functions, Helium-like ions, Matrix, Eigenvalues, Eigenvectors.
PACS: 31.15.A-, 31.15.ac, 31.15.ae, 31.15.-p.
Classification: 2.1, 2.2, 2.7, 2.9.

Nature of problem:
The Schrödinger equation for atoms (ions) with more than one electron has not been solved analytically. Approximate methods must be applied in order to obtain the wave functions or another physical attributes from quantum mechanical calculations.

Solution method:
The S-wave function is expanded into a triple set of basis functions which are composed of the exponentials combined with the Laguerre polynomials in the perimetric coordinates. Using specific properties of the Laguerre polynomials, solution of the two-electron Schrödinger equation reduces to solving the generalized eigenvalues and eigenvector problem for the proper Hamiltonian. The unknown exponential parameter is determined by means of minimization of the corresponding eigenvalue (energy).

First, the too large length of expansion (basis size) takes the too large computation time and operative memory giving no perceptible improvement in accuracy. Second, the number of shells Ω in the wave function expansion enables one to calculate the excited nS-states up to n = Ω + 1 inclusive.

Running time:
2 - 60 minutes (depends on basis size and computer speed)