Systematic analysis of fusion barrier heights and positions for proton projectiles using the single folding model

The nuclear potentials between protons and different target nuclei are calculated by using the single folding model with the density-dependent nucleon-nucleon interaction.The fusion barrier heights and positions for proton projectiles fusing with different target nuclei with masses from 51 amu to 139 amu are systematically shown,with charge numbers and root-mean-square radii of the interacting nuclei.The parameterized formulas for the fusion barrier height and position are obtained for proton projectile fusing with the different nuclei.The calculated results of parameterized formulas are compared to empirical values,as well as those of the proximity potential and AkyüzWinther（AW） potential.It is shown that the calculated results agree perfectly with theirs.The parameterized formulas can reproduce the exact barrier heights and positions for proton fusion systems.