Two-loop electron self-energy with accelerated partial-wave expansion

TL;DR

This paper introduces an improved method for calculating the two-loop electron self-energy in hydrogen-like ions, achieving faster convergence and higher accuracy across a broader range of nuclear charges.

Contribution

It presents an accelerated partial-wave expansion technique enabling more precise and efficient calculations of electron self-energy for various nuclear charges.

Findings

Enhanced convergence of partial-wave expansion

Calculations performed for lower nuclear charges

Higher numerical accuracy achieved

Abstract

Calculations of the two-loop electron self-energy for the $n = 1$ and $n = 2$ states of hydrogen-like ions are reported, performed to all orders in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine structure constant). The presented approach features an accelerated convergence of the partial-wave expansion and allows calculations to be accomplished for nuclear charges lower than previously possible and with a higher numerical accuracy.