Magnetic Hyperfine Structure of Muonic Atoms

Magnetic hyperfine structure in muonic x rays is calculated for several models of the nuclear magnetism and compared to experimental values for ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$, ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$, ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$, ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$, ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$, ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$, ${}_{}{}^{203}{}_{}{}^{}\mathrm{Tl}$, ${}_{}{}^{205}{}_{}{}^{}\mathrm{Tl}$, and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$. The results are excellent for the realistic models in most cases, and all but one of the nine cases agree within better than two standard deviations with the experiments. For the realistic models, the hyperfine energy is substantially reduced (by about 30% in most cases) from its point-nucleus value. In these models, the single-particle magnetism distribution is modified by the addition of configurations resulting from various residual nuclear interactions, the interaction strength being adjusted in each case to produce the experimental value for the magnetic moment.