Mu-Mesonic Atoms and the Electromagnetic Radius of the Nucleus

An attempt is made to interpret recent experiments on the x-ray spectrum of ${\mu }^{-}$-mesonic atoms. In particular, an analysis is made of the $2p-1s$ transition energies, which are sensitive to the nuclear charge distribution. Agreement with experiment is obtained for a uniform sphere of nuclear charge of radius $R\approx 1.2\times {10}^{-13\mathrm{}}{A}^{\frac{1}{3}}$ cm. Various effects such as nuclear polarization, electric quadrupole moment, screening by atomic electrons, and a meson-nucleon interaction of the order indicated by the charge exchange capture reaction are considered and do not alter this radius appreciably. However, an anomalous meson-nucleus interaction, though doubtful, could alter the estimated radius. It is shown that the small nuclear radius is not in disagreement with that determined by other electromagnetic measurements, including mirror nuclei experiments.