Theoretical seminar | 02 February 2022

Methods used for quantum electrodynamics (QED) calculations of energy levels in the helium atom and light helium-like ions are reviewed. Calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine structure constant α . The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, r1 , r2 and r12 . The choice of the exponential basis functions of the form exp (− αr 1 − βr 2 − γ r12 ) allows one to construct an accurate and compact representation of the nonrelativistic wave function and to efficiently compute matrix elements of numerous singular operators representing relativistic and QED effects. Calculations of the leading
QED effects of order α 5 m (where m is the electron mass) are complemented with the systematic treatment of higher-order α 6 m and α 7 m QED effects.

Main paper/arXiv, related to the seminar, and other references

V. A. Yerokhin, V. Patkóš, and K. Pachucki, Atomic Structure Calculations of Helium with Correlated Exponential Functions, Symmetry 13, 1246 (2021); https://doi.org/10.3390/sym13071246.
V. Patkóš, V. A. Yerokhin, and K. Pachucki, Complete α7m Lamb shift of helium triplet states, Phys. Rev. A 103, 042809 (2021); https://doi.org/10.1103/PhysRevA.103.042809.
V. A. Yerokhin, V. Patkóš, and K. Pachucki, Relativistic corrections to the Bethe logarithm for the 23S and 23P states of He, Phys. Rev. A 98, 032503 (2018); https://doi.org/10.1103/PhysRevA.98.032503