Systematic study of the fusion barriers for helium projectile fusing with targets in the mass range 12 ≤ A ≤ 233

Nuclear physics deals with the study of structure of nuclei as well as interactions among these nuclei and their nucleons. This study is quite helpful in the formation of super-heavy elements, which are synthesized either by cold fusion reactions or by hot fusion reactions. Fusion barriers play significant role in deciding the fate of a fusion reaction. These fusion barriers can be derived from the total interaction potential, which is sum of attractive nuclear potential and repulsive Coulomb potential. Our aim is to give pocket formulae, which can be used to directly estimate the barrier parameters. With this aim in our mind, we parameterize the fusion barriers for helium induced reactions using various proximity potentials