Theory of hyperfine anomalies in muonic atoms

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 muon g-factor), vary from near zero for μ^-O/N to -5% for μ^-Pd/Rh; this latter is much larger than the calculated muonic or nuclear Bohr-Weisskopf anomalies and much smaller than the 36% measured value. For μ^}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 in μ^}Ni/Co provides strong support for the earlier suggestions that the discrepancy in the case of μ^-Pd/Rh is due to experimental factors.