Fine and hyperfine structure of the muonic ^3He ion

TL;DR

This paper calculates high-order quantum electrodynamics corrections to the fine and hyperfine structure of the muonic helium-3 ion, providing precise theoretical values to compare with experimental measurements.

Contribution

It introduces detailed calculations of vacuum polarization, relativistic, recoil, and structure corrections of orders α^5 and α^6 for the muonic helium-3 ion's energy levels, advancing theoretical precision.

Findings

Calculated fine structure interval: 144803.15 μeV

Hyperfine splitting for 2P_{1/2}: -58712.90 μeV

Hyperfine splitting for 2P_{3/2}: -24290.69 μeV

Abstract

On the basis of quasipotential approach to the bound state problem in QED we calculate the vacuum polarization, relativistic, recoil, structure corrections of orders $\alpha^5$ and $\alpha^6$ to the fine structure interval $\Delta E^{fs}=E(2P_{3/2})-E(2P_{1/2})$ and to the hyperfine structure of the energy levels $2P_{1/2}$ and $2P_{3/2}$ in muonic $^3_2He$ ion. The resulting values $\Delta E^{fs}= 144803.15 \mu eV$, $\Delta \tilde E^{hfs}(2P_{1/2})=-58712.90 \mu eV$, $\Delta \tilde E^{hfs}(2P_{3/2})=-24290.69 \mu eV$ provide reliable guidelines in performing a comparison with the relevant experimental data.