The 1958 Pekeris-Accad-WEIZAC Ground-Breaking Collaboration
that computed Ground States of Two-Electron Atoms
(by Christoph Koutschan and Doron Zeilberger)
(and its 2010 Redux)
On this webpage we give supplementary material which accompanies
our article. It is based on the paper
State of Two-Electron Atoms by C. L. Pekeris.
More information about this project, as well as Doron Zeilberger's
Maple programs, can be found on his
We provide a Mathematica notebook that contains all the symbolic computations
(and also some (unfortunately) unsatisfying numerical ones due to the restrictions of Mathematica):
The package HolonomicFunctions that is required for performing
the computations can be downloaded
We have prepared two MATLAB programs for the fast computation
of the energy parameter (in the para and the ortho case).
They mainly consist of automatically
generated code that rephrases the monstrous recurrence (22) in Pekeris'
article. In this sense it may be closer to Yigal Accad's original
code, compared to our Mathematica code which uses the recurrence
as a symbolic object.
Note that in both cases many more values were computed than appear
in the original papers.