English

How to derive and compute 1,648 diagrams

Atomic Physics 2007-05-23 v1 Computational Physics

Abstract

We present the first calculation for many-electron atoms complete through fourth order of many-body perturbation theory. Owing to an overwhelmingly large number of underlying diagrams, we developed a suite of symbolic algebra tools to automate derivation and coding. We augment all-order single-double excitation method with 1,648 omitted fourth-order diagrams and compute amplitudes of principal transitions in Na. The resulting ab initio relativistic electric-dipole amplitudes are in an excellent agreement with 0.05%-accurate experimental values. Analysis of previously unmanageable classes of diagrams provides a useful guide to a design of even more accurate, yet practical many-body methods.

Keywords

Cite

@article{arxiv.physics/0306099,
  title  = {How to derive and compute 1,648 diagrams},
  author = {Caleb C. Cannon and Andrei Derevianko},
  journal= {arXiv preprint arXiv:physics/0306099},
  year   = {2007}
}

Comments

5 pages, 2 figures, submitted

R2 v1 2026-07-22T18:56:27.486Z