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 determine the corresponding single particle potential (mean-field). We present and employ a novel method, using the single particle Schrodinger equation, to determine the central potential directly from the single particle matter density and its first and second derivatives. We also present results of least-square fits to parametrized single particle potentials. The 3s_1/2 wave functions of the determined potentials reproduce fairly well the experimental data within the quoted errors. The fair agreement with fitted potentials may be an indication that effects of short range correlations on charge distributions due to shell model wave functions are not significant. 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 wave function.