Parameterization of fusion barriers for light-projectiles-induced reactions using the proximity approach

Abstract

In this article we propose a pocket formula for fusion barriers calculated by three versions of the proximity formalism, namely AW 95, Bass 80 and Prox. 2010 potentials, for fusion reactions involving the collisions of the proton and helium projectiles with different targets in mass ranges $ 51\leq A_{T} \leq 130$ and $ 40\leq A_{T} \leq 233$ , respectively. For the first type of the colliding systems, it is shown that the proposed pocket formulas are able to predict the actual values of $ R_{B}$ and $ V_{B}$ within accuracies of ±0.4% and ±0.45% , respectively. Moreover, for the second type of the selected reactions, these accuracies are obtained ±0.24% and ±0.36% , respectively. In this study, the ability of the present pocket formulas is also demonstrated to predict the exact values of the fusion cross sections for our selected mass ranges. A comparison with the results of the previous pocket formulas reveals that our parameterized forms are more successful to reproduce the empirical data of the barrier height and position in the proton- and helium-induced reactions.