Assessment of the quality of different pocket formulas in reproducing experimental sub-barrier fusion cross sections

In the frame of a new introduced energy scaling method, the Coulomb barrier heights calculated by using thirteen different forms of the pocket formulas are systematically analyzed for sub-barrier fusion cross sections of 58 heavy-ion fusion reactions, including O, Al, Si, S, Cl, Ca and Ti projectiles. It is found that the barrier heights, which are generated by the parameterized formulas based on the Zhang 2016, Sahu 1999, Puri 2015 and Puri 1992 approaches, seem to be more suitable for description of the experimental fusion cross sections at energies below the Coulomb barrier. The present obtained results show the importance of the projectile mass and surface energy coefficients in heavy-ion fusion at sub-barrier energies. A discussion concerning the fusion Q-value rule below barrier energies is presented for some fusion systems.