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

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 Zα (where Z is the nuclear charge number and α 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. Published by the American Physical Society 2025