Eur. Phys. J. D 58, 57-68 (2010)
https://doi.org/10.1140/epjd/e2010-00089-4

The two-loop self-energy: diagrams in the coordinate-momentum representation

Center for Advanced Studies, St. Petersburg State Polytechnical University, Polytekhnicheskaya 29, St. Petersburg, 195251, Russia

Corresponding author: yerokhin@pcqnt1.phys.spbu.ru

Received: 29 January 2010
Revised: 15 March 2010
Published online: 13 April 2010

Abstract

The paper reports a technique of evaluation of Feynman diagrams in the mixed coordinate-momentum representation. The technique is employed for a recalculation of the two-loop self-energy correction for the ground state of hydrogen-like ions with the nuclear charge numbers Z=10-30. The numerical accuracy is considerably improved as compared to the previous calculations. The higher-order (in Zα) remainder function is inferred from the numerical results and extrapolated towards Z=0 and 1. The extrapolated value for hydrogen is consistent (but still not in perfect agreement) with the analytical result obtained within the perturbative approach.