  A lot of problems of atomic and nuclear physics depend on with high accuracy
to the Coulomb potential. 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 literature of the two parameters (Coulomb radius R_c and
diffuseness parameter a_c) which are important for the coulomb potential are
also discussed.
