The 1958 Pekeris-Accad-WEIZAC Ground-Breaking Collaboration that Computed Ground States of Two-Electron Atoms (and its 2010 Redux)

TL;DR

This paper revisits the pioneering 1958 calculations of two-electron atom ground states, comparing historical manual methods with modern automated computational techniques to highlight advancements in scientific computing.

Contribution

It provides a comprehensive re-evaluation of Pekeris's original work using current software and hardware, emphasizing the evolution of computational methods in atomic physics.

Findings

Modern software reproduces Pekeris's results accurately

Symbolic computations are now fully automatable

Historical manual efforts are now streamlined with automation

Abstract

In order to appreciate how well off we mathematicians and scientists are today, with extremely fast hardware and lots and lots of memory, as well as with powerful software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and compare how things went then. We have chosen, as a case study, a problem that was considered a huge challenge at the time. Namely, we looked at C.L. Pekeris's seminal 1958 work on the ground state energies of two-electron atoms. We went through all the computations ab initio with today's software and hardware, with a special emphasis on the symbolic computations which in 1958 had to be made by hand, and which nowadays can be automated and generalized.