Analytical solution of the Coulomb potential for spherical nuclei

Abstract

A lot of problems of atomic and nuclear physics depend on Coulomb potential with high accuracy. Therefore, it is very important to carefully and accurately calculate the Coulomb potential. In this study, a new analytical expression was obtained for calculating the Coulomb potential by choosing the Fermi distribution function, which is suitable for charge distribution in nuclei. The proposed formula guarantees an accurate and simple calculation of the Coulomb potential of nuclei. Using the analytical expression obtained, the Coulomb potentials for several spherical nuclei were calculated for all values of the parameters. It is shown that the results obtained for arbitrary values of the radius are consistent with the literature data. In this study, the accepted values in the literature of the two parameters (Coulomb radius Rc and diffuseness parameter ac) which are important for the Coulomb potential are also discussed. © 2019 World Scientific Publishing Company.