Nuclear polarization in muonic helium

Nuclear-polarization energy shifts are calculated for the low-lying levels of muonic ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. In ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, the shift of the $2s_{\frac{1}{2}}$ level is found to be - 3.1 meV, in agreement with the result of Bernabeau and Jarlskog. The corresponding shift in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is - 4.9 meV. Other corrections to the energy levels are calculated, with the improved result that the total theoretical $2s_{\frac{1}{2}}-2\mathrm{}{p}_{\frac{3}{2}}$ energy difference in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is $1.8131-0.102r^2\pm 0.001$ eV, where $r$ is the nuclear rms charge radius (in femtometers). Together with the measured value 1.5274 ± 0.0009 eV, this implies $r=1.674\mathrm{}\pm 0.004$ fm, which is consistent with available electron scattering data.