A novel method for determining the mean-field directly from the single particle matter density

摘要

We present 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. As an example, we consider the experimental data for the charge density difference between the isotones ~(206)Pb - ~(205)Tl that corresponds to the shell model 3s_(1/2) proton orbit, and determine the corresponding single particle potential (mean-field). We also present results of least-square fits to parametrized single particle potentials.