How to derive and compute 1,648 diagrams

Details How to derive and compute 1,648 diagrams How to derive and compute 1,648 diagrams

2003-06-12

arxiv.org/abs/physics/0306099v1

Physics

Atomic Physics

5 pages, 2 figures, submitted

Scientific paper

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.

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