Theory of hyperfine anomalies in muonic atoms

Abstract

Negative muon spin precession experiments by Yamazaki et al. have found giant hyperfine anomalies in muonic atoms ranging from a few percent up to 36%. In order to understand their results, we present Breit interaction calculations based on atomic self-consistent unrestricted Dirac-Fock solutions which explicitly include all electrons and the negative muon. The Breit interaction results (including the relativistic correction for the bound muong-factor), vary from near zero forμ ⁻O/N to −5% forμ ⁻Pd/Rh; this latter is much larger than the calculated muonic or nuclear Bohr-Weisskopf anomalies and much smaller than the 36% measured value. Forμ ^}Ni/Co we find a calculated range of results (depending on assumed electronic configurations) of −2.3 to −2.7% in excellent agreement with recent measurements of the Yamazaki group. This excellent agreement inμ ^}Ni/Co provides strong support for the earlier suggestions that the discrepancy in the case ofμ ⁻Pd/Rh is due to experimental factors.