Influence of Structural Properties on Fusion Cross-Sections Using Proximity Potentials

Abstract

In this study, an optimal nuclear proximity potential is used to get more accurate fusion cross-section predictions. For 111 colliding systems, we evaluate the predictive accuracy of several proximity potential models interfaced with Wong’s formula in reproducing the fusion cross-section experimental data. For the purpose of Chi-square minimization technique, Christensen and Winther 1976 potential is selected. The analysis examines fusion dynamics across a wide range of nuclear configurations (6 ≤ Zp (projectile atomic number)≤28, 6 ≤ Zt (target atomic number) ≤94, and 36 ≤ Zp Zt ≤ 1880). To increase accuracy and match experimental data, a Python code that calculates cross-sections for all proximity potentials is established using the Nelder–Mead algorithm. The extensive range of calculations facilitates a systematic study of the effects of structural factors, including magic numbers, shell structure, neutron excess, and pairing effect. The results reveal that shell effects can sometimes overcome neutron excess and produce unexpected fusion trends, as seen in the ²⁸Si + ⁹⁰Zr and ²⁸Si + ⁹⁴Zr. In other reactions, the shell effect eliminated the effect of the neutron excess, such as in the ¹⁶O + ⁶²Ni versus ¹⁶O + ⁵⁸Ni and 12C + ²⁰⁸Pb versus ¹²C + ²⁰⁴Pb reactions. Our findings also highlighted the important role of the projectile in the process of fusion. The titanium isotopes (⁴⁶Ti, ⁵⁰Ti) in particular fused more effectively with ¹²C than with 16O. Nickel isotopes show similar projectiledependent behavior.