Probing a Fifth Force in Muonic Atoms through Lamb Shifts and Hyperfine Structure

Abstract

Motivated by the ATOMKI anomalies in 8Be and 4He transitions, we study X17-induced Lamb shifts and hyperfine splittings in muonic atoms with stable nuclei up to Z <= 15. The bound-state problem is solved within the Gaussian Expansion Method using a unified Hamiltonian that includes the standard electromagnetic baseline together with vector and pseudoscalar X17 exchange. The spin-independent Lamb shift is described by a coherent vector muon-nucleus interaction, while the spin-dependent hyperfine sector is built isotope by isotope from shell-model spin fractions. We find a clear complementarity between mediator hypotheses: the vector Lamb-shift signal grows toward heavier nuclei, the vector hyperfine scenario favors odd-N nuclei, and the pseudoscalar scenario favors odd-Z nuclei. Using a signal-to-precision ratio, we identify muonic deuterium, muonic helium-3 ion, and muonic helium-4 ion as the most promising near-term Lamb-shift probes among systems with existing precision benchmarks. For future spectroscopy, the largest vector Lamb-shift signal is predicted in muonic silicon-29, while the leading 1S hyperfine targets are silicon-29 for the vector scenario and phosphorus-31 for the pseudoscalar scenario. The main theoretical uncertainty comes from the Schmidt-model treatment of nuclear spin content.