# A new analytical expression for calculation of the Coulomb potential in spherical nuclei

## TL;DR

This paper introduces a new analytical formula for calculating the Coulomb potential in spherical nuclei using the Fermi distribution, providing accurate and simple computations validated against existing data.

## Contribution

A novel analytical expression for Coulomb potential calculation in spherical nuclei using Fermi distribution, improving accuracy and simplicity over previous methods.

## Key findings

- The formula provides accurate Coulomb potential calculations for various nuclei.
- Results are consistent with existing literature data for different parameter values.
- Discussion of key parameters R_c and a_c enhances understanding of Coulomb potential modeling.

## Abstract

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.

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Source: https://tomesphere.com/paper/1903.07199