To test bound-state quantum electrodynamics (BSQED) in the strong-field regime, we have performed high precision x-ray spectroscopy of the $5g–4f$ and $5f–4d$ transitions (BSQED contribution of 2.4 and 5.2 eV, respectively) of muonic neon atoms in the low-pressure gas phase without bound electrons. Muonic atoms have been recently proposed as an alternative to few-electron high-$Z$ ions for BSQED tests by focusing on circular Rydberg states where nuclear contributions are negligibly small. We determined the $5g_{9/2}–4f_{7/2}$ transition energy to be $6297.08\pm 0.04(\mathrm{stat})\pm 0.13(\mathrm{syst})\mathrm{eV}$ using superconducting transition-edge sensor microcalorimeters (5.2–5.5 eV FWHM resolution), which agrees well with the most advanced BSQED theoretical prediction of 6297.26 eV.

• Received 8 December 2021
• Revised 10 February 2023
• Accepted 10 March 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.173001