Simplified partial wave expansion of the Lamb shift

TL;DR

This paper introduces an improved partial wave expansion method for calculating the Lamb shift's self-energy component, achieving accurate results with fewer partial waves, thus enhancing computational efficiency for hydrogenlike and lithiumlike ions.

Contribution

An improved partial wave expansion technique that converges faster, reducing the number of partial waves needed for precise Lamb shift calculations.

Findings

Accurate Lamb shift calculations with fewer partial waves.

Effective for hydrogenlike and lithiumlike boron.

Potential for high-precision calculations on low Z ions.

Abstract

A method for calculating the self energy part of the Lamb shift is revisited. When the electron propagator in an external field is represented as an expansion in partial waves, the original method converges relatively slowly, requiring the calculation of dozens of partial waves. Here we show an improved method in which accurate results can be obtained using a much smaller number of partial waves. The method is illustrated for the ground states of hydrogenlike and lithiumlike boron, and the possibility of high accuracy calculations on lower Z hydrogenic ions is discussed.