Abstract
The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrodinger equation and account for relativistic and QED effects by perturbation expansion in the fine structure constant alpha.
The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, r(1), r(2) and r = vertical bar(r) over right arrow (1) - (r) over right arrow (2)vertical bar. The choice of the exponential basis functions of the form exp(-alpha r(1) - beta r(2) - gamma(r)) allows us 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 alpha(5)m (where m is the electron mass) are complemented with the systematic treatment of higher-order alpha(6)m and alpha(7)m QED effects.