Two-photon exchange correction to $2S$-$2P$ splitting in muonic helium-3 ions

TL;DR

This paper calculates the two-photon exchange correction to the Lamb shift in muonic helium-3 ions using dispersion relations, providing a precise energy shift estimate that aligns with previous models.

Contribution

It introduces a dispersion relations approach with analytic fits to scattering data to accurately compute the two-photon exchange correction in muonic helium-3.

Findings

Energy shift of 15.14(49) meV for the 2S state

Good agreement with potential model and EFT calculations

Enhanced understanding of two-photon effects in muonic atoms

Abstract

We calculate the two-photon exchange correction to the Lamb shift in muonic helium-3 ions within the dispersion relations framework. Part of the effort entailed making analytic fits to the electron-$^3$He quasielastic scattering data set, for purposes of doing the dispersion integrals. Our result is that the energy of the 2$S$ state is shifted downwards by two-photon exchange effects by 15.14(49) meV, in good accord with the result obtained from a potential model and effective field theory calculation.