Singular integrals in QED corrections of three-body systems

Abstract

Singular integrals that appear in calculations of quantum electrodynamic (QED) corrections for three-body Coulomb systems are studied using Hylleraas coordinates. A general scheme is developed to separate divergent parts of singular integrals involving Hylleraas basis functions. Subsequently, the obtained singular integrals can be used in the calculations of QED corrections. The numerical results of two typical operators that appear in [Formula: see text] order QED corrections are precisely calculated. The leading radiative corrections are presented as well. These singular integrals would be intensively used in the calculations of high-order QED corrections for three-body systems such as helium, lithium ions, and hydrogen molecular ions.