Measured difference between 206Pb, 205Tl charge distributions and the proton 3s1/2 wave function

Charge density difference between 206Pb and 205Tl, measured by elastic electron scattering, is very similar to the charge density due to a proton in a 3s1/2 orbit. We look for a potential well whose 3s1/2 wave function yields the measured data. We developed a novel method to obtain the potential directly from the density and its first and second derivatives. Fits to parametrized potentials were also carried out. The 3s1/2 wave functions of the potentials determined here, reproduce fairly well the experimental data within the quoted errors. To detect possible effects of short-range two-body correlations on the 3s1/2 shell model wave function, more accurate measurements are required.