The Coulomb Energy of Finite Size Nucleus from the Study of Classical Electrodynamics Theory

Abstract

The Coulomb energy for different nuclear model with small computing
effort and high accuracy is a great challenge in physics as well as in
quantum chemistry research. In this work we applied a classical
electrodynamics theory and derived a simple procedure and
expression for calculating the Coulomb energy for atomic nuclei
taking into consideration the finite size of protons. The corresponding
results are compared with the direct Coulomb energy obtained from
two-parameter Fermi distributions. The formula obtained, which
varies directly to the proton number and varies inversely to the cube
root of mass number, was applied and calculated numerically the
values of Coulomb energy for light, medium and heavy nuclei. To
examine the effect of finite size of proton on Coulomb energy, a graph
of Coulomb energy as a function of proton number was presented. The
results obtained showed that due to the finite size of proton, the values
of the previously calculated values of the Coulomb energy are reduced
by less than 2%. This is because the proton – proton distance increased
due to finite size effect of the proton and thus affects the magnitude of
the Coulomb energy. This showed that calculation of Coulomb energy
by taking into consideration, the finite size of proton leads to
agreement with the experimental values. Thus, in studying the nuclear
structure, it is very natural to assume the protons to be extended rather
than point charges.