Vacuum polarization corrections to the $n=2$ and $n=3$ levels in muonic $^4$He

TL;DR

This paper calculates vacuum polarization corrections to specific energy levels in muonic helium, incorporating one-loop and recoil effects, and extends existing methods to improve the precision of these quantum electrodynamics predictions.

Contribution

It provides detailed calculations of vacuum polarization effects on muonic helium energy levels, including an extension of the Kinoshita and Nio method for better accuracy.

Findings

Results agree with recent calculations for n=2 levels.

Provides new tabulated results for n=3 levels.

Achieves high-precision energy difference estimates.

Abstract

The $n=2$ and $n=3$ levels for muonic Helium are calculated using a potential that includes all one-loop and recoil effects. Electronic vacuum polarization corrections are calculated using an extension of Kinoshita and Nio method. For $n=2$, the results are $2p_{1/2}-2s_{1/2}=1375.05\pm 1.4$ meV and $2p_{3/2}-2s_{1/2}=1521.65\pm 1.4$ meV, essentially in agreement with the latest summary of the current calculations. The $n=3$ results are summarized in tabular form and give $3p_{1/2}-3s_{1/2}=394.76\pm 0.43$ meV and $3d_{3/2}-3p_{3/2}=111.40$ meV.