A novel method for determining the single particle potential directly from the measured single particle density: Application to the charge density difference between the isotones 206Pb–205Tl

Abstract

We present a novel method, based on the single particle Schroedinger equation, to determine the central potential (mean-field) directly from the single particle matter density and its first and second derivatives. As an example, we consider the experimental data for the charge density difference between the isotones 206Pb–205Tl, deduced by phase shift analysis of elastic electron scattering cross-section measurements and corresponds to the shell model 3s1/2 proton orbit, and determine the corresponding single particle potential. We also present results of least-square fits to parametrized single particle potentials. The 3s1/2 wave functions of the determined potentials reproduce fairly well the experimental data within the quoted errors. 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 3s1/2 wave function.