Singular integrals in QED corrections of three-body systems

Author:

Qi Xiao-Qiu12ORCID,Zhong Zhen-Xiang23,Zhang Pei-Pei2

Affiliation:

1. Key Laboratory of Optical Field Manipulation of Zhejiang Province and Physics Department of Zhejiang Sci-Tech University, Hangzhou 310018, China

2. State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China

3. Center for Theoretical Physics, School of Science, Hainan University, Haikou 570228, China

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.

Funder

National Natural Science Foundation of China

Science Foundation of Zhejiang SciTech University

Publisher

World Scientific Pub Co Pte Ltd

Subject

Condensed Matter Physics,Statistical and Nonlinear Physics

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