Nuclear size correction to the Lamb shift of one-electron atoms

TL;DR

This paper calculates the nuclear size correction to the Lamb shift in hydrogen-like ions, including all orders of the nuclear strength parameter, and compares with previous methods to improve accuracy.

Contribution

It provides a comprehensive all-order evaluation of nuclear size effects on the Lamb shift, extending previous expansion-based calculations.

Findings

All-order numerical results for nuclear size correction are obtained.

Comparison with previous calculations shows improved accuracy.

Results are extrapolated to hydrogen (Z=1) for the Lamb shift correction.

Abstract

The nuclear size effect on the one-loop self energy and vacuum polarization is evaluated for the 1s, 2s, 3s, 2p_{1/2}, and 2p_{3/2} states of hydrogen-like ions. The calculation is performed to all orders in the binding nuclear strength parameter Z\alpha. Detailed comparison is made with previous all-order calculations and calculations based on the expansion in the parameter Z\alpha. Extrapolation of the all-order numerical results obtained towards Z=1 provides results for the radiative nuclear size effect on the hydrogen Lamb shift.