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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 protonproton 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.
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 protonproton 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.
A new term was added to the well-known semi-empirical mass formula to account for the changes due to gravitational attraction between nucleons in the liquid drop, as well as, accommodates for the necessary corrections in the binding energy of a nucleus. The results of our calculations show a straight forward evidence that the gravitational attraction bears a reasonable contribution to the binding energy. On the other hand, employing the gravitational term in the semi empirical mass formula was led to the calculation of gravitational constant at subnuclear level.
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