Corrections to Muonic X Rays and a Possible Proton Halo

With the aim of extracting maximum information on nuclear charge structure .209 at large distances, we improve the theory of muonic X-rays in Bl by taking into account all known effects which could change the binding energy by as much as 0.1%. We give improved estimates of vacuum polarization and Lamb shift effects and incorporate Cole’s recent estimate of nuclear polarization effects. Using these corrections to analyze recent experiments on muonicX-rays, we obtain parameters for the charge distribution in Bi 209 which when compared with parameters from electron scattering indicate a small discrepancy. We suggest that this can be explained by a proton “halo” by which we mean a small fraction of the charge (1%) spread over large distances (-8 F. ); we show that such a “halo!’ is not inconsistent with electronproton scattering and brings the theory of the Lamb shift in atomic I3 and D into good agreement with experiments. We find no experiment with which such a model is inconsistent.