Empirical model for fusion cross sections of Ca-induced reactions

Abstract

A new empirical formula for the astronomical S-factor has been suggested as a function of
the Coulomb interaction parameter, center of mass energy, and barrier height. About 22 fusion
reactions with 40,48Ca as projectiles were considered for different targets leading to compound nuclei
with the atomic and mass numbers varying between 40 ≤ Z ≤112 and 88 ≤ A ≤278 respectively.
The fusion cross-sections have been estimated using the Geometric factor, Gamow-Sommerfield
factor and empirical formula for the S-factor. A better agreement has been obtained for the present
work with that of available experiments when compared to Wong’s formula. The present work leads
to a smaller standard deviation value when compared to Wong’s formula when used to correlate
with the experimental data of Calcium-induced fusion reactions. Wong’s formula provides a good
approximation of fusion cross-sections when center of mass energy is below the fusion barrier when
compared to above the fusion barrier.