## The 1958 Pekeris-Accad-WEIZAC Ground-Breaking Collaboration that
computed Ground States of Two-Electron Atoms

(and its 2010
Redux)

(by Christoph Koutschan and Doron Zeilberger)

On this webpage we give supplementary material which accompanies our article. It is based on the paper Ground 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 webpage.

### Mathematica material

We provide a Mathematica notebook that contains all the symbolic computations (and also some (unfortunately) unsatisfying numerical ones due to the restrictions of Mathematica):- Pekeris.nb (Mathematica 7.0 notebook)
- Pekeris.nb.pdf (pdf screenshot of the notebook, if you don't have Mathematica)

### MATLAB material

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.-
**Para**: the program PekerisPara.m produces this output (Z = 1...10) in 15 seconds, and this output (Z = 1...50) in 69 seconds! -
**Ortho**: the program PekerisOrtho.m produces this output (Z = 1...10) in 11 seconds, and this output (Z = 1...50) in 55 seconds!