%0 Journal Article
%T How to derive and compute 1,648 diagrams
%A Caleb C. Cannon
%A Andrei Derevianko
%J Physics
%D 2003
%I arXiv
%X 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.
%U http://arxiv.org/abs/physics/0306099v1