One-loop electron self-energy with accelerated partial-wave expansion in Coulomb gauge

TL;DR

This paper develops accelerated partial-wave expansion methods to accurately compute the electron self-energy for low nuclear charges and excited states, addressing numerical challenges in high-precision atomic physics calculations.

Contribution

It extends accelerated convergence techniques for electron self-energy calculations to low-Z elements and higher excited states, previously difficult to access.

Findings

Enhanced convergence in numerical calculations for Z<5

Accurate self-energy computations for higher excited states

Addresses numerical cancellations in light elements

Abstract

Numerical calculations of the electron self-energy without any expansion in the binding nuclear field are required in order to match the rapidly advancing precision of experimental spectroscopy. For the lightest elements, particularly hydrogen, these computations are complicated by large numerical cancellations and the slow convergence of the partial-wave expansion. Methods with accelerated convergence of the partial-wave expansion have been recently put forward [V. A. Yerokhin, K. Pachucki, V. M. Shabaev, Phys. Rev. A 72, 042502 (2005); J. Sapirstein and K. T. Cheng, Phys. Rev. A 108, 042804 (2023)]. In our work we extend the accelerated-convergence methods to the previously hardly accessible region of nuclear charges $Z < 5$ and higher excited states.