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.
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