Short-range correlations and the proton 3s_1/2 wave function in ²⁰⁶Pb

We consider the experimental data for the charge density difference between the isotones ²⁰⁶Pb – ²⁰⁵Tl, deduced by analysis of elastic electron scattering measurements and corresponds to the shell model 3s_1/2 proton orbit, and investigate the effects of two-body short-range correlations. This is done by: (a) Determining the corresponding single particle potential (mean-field), employing a novel method, directly from the single particle matter density and its first and second derivatives and also by least-square fits to parametrized single particle potentials; (b) Determining the short-range effect by employing the Jastrow correlated many-body wave function to derive a density dependent correlation factor for the densities of single particle orbits. The 3s_1/2 wave functions of the determined potentials reproduce fairly well the experimental data within the quoted errors. Moreover, the calculated 3S_1/2 density obtained with the inclusion of the short-range correlation effect does not reproduce the experimental data. More accurate experimental data, with uncertainty smaller by a factor of two or more, may answer the question how well can the data be reproduced by a calculated 3s_1/2 single particle wave function.