Bound-electron self-energy calculations in Feynman and Coulomb gauges: detailed analysis

The energy correction associated with the self-energy diagram is the leading (in magnitude) and fundamental (in significance) contribution to the Lamb shift in highly charged ions. Conventional approaches to this correction rely on partial-wave expansions, which is a stumbling block limiting accuracy. To elucidate the issue, we perform a comprehensive comparative analysis of partial-wave-expansion convergence between two gauges: Feynman and Coulomb. Some tricks for improving the convergence are discussed as well.