# Exploring the accurate nuclear potential

## TL;DR

This paper develops empirical formulas for nuclear fusion and interaction barrier heights, compares various models with experimental data, and identifies the Broglia and Winther model as the most accurate for predicting fusion barriers.

## Contribution

It introduces new empirical formulas for barrier heights and evaluates multiple models, establishing the Broglia and Winther model as the most reliable for fusion predictions.

## Key findings

- Broglia and Winther model best matches experimental fusion barriers.
- Current interaction barrier predictions are lower than Bass potential model.
- The models are useful for planning experiments, especially for super heavy elements.

## Abstract

We have constructed empirical formulae for fusion and interaction barrier heights using experimental values available in the literature. Fusion excitation function measurements are used for the former and back angle quasi-elastic excitation function for the latter case. The fusion barriers so obtained have been compared with various model predictions such as Bass potential, Christenson and Winther, Broglia and Winther, Aage Winther, Siwek-Wilczynska and J.Wilczynski, Skyrme energy density function model, and the Sao Paulo optical potential along with experimental results. The comparison allows us to find the best model, which is found to be the Broglia and Winther model. Further, to examine its predictability, the Broglia and Winther model parameters are used to obtain total fusion cross sections showing good agreement with the experimental values for beam energies above the fusion barriers. Thus, this model can be useful for planning any experiments, especially ones aiming for super heavy elements. Similarly, current interaction barrier heights have also been compared with the Bass potential model predictions. It shows that the present model calculations are much lower than the Bass potential model predictions. We believe the current interaction barrier model prediction will be a good starting point for future quasi-elastic scattering experiments. Whereas both the Broglia and Winther model and our interaction barrier model will have practical implications in carrying out physics research near the Coulomb barrier energies.