Impact of zeta parameter and quadrupole deformations on fusion barrier characteristics

Fusion barrier height ([Formula: see text]) and position ([Formula: see text]) are important in understanding nuclear fusion dynamics, reaction cross-sections, tunneling probabilities, and sub-barrier processes. Hence, in this work, we proposed a semi-empirical relation to calculate fusion barrier heights ([Formula: see text]) and positions ([Formula: see text]) as functions of [Formula: see text] and the quadrupole deformations of both the projectile and target nuclei. Experimental data for [Formula: see text] and [Formula: see text] were compiled from various fusion reactions forming compound nuclei with atomic numbers [Formula: see text] and mass numbers [Formula: see text]. The [Formula: see text] values and [Formula: see text] values calculated using the semi-empirical formula show a good agreement with experimental values, with deviations constrained within [Formula: see text]. The comparison spans reactions involving isotopes from light projectiles, such as [Formula: see text]Mg to heavy projectiles, like [Formula: see text]Kr. For example, reactions such as [Formula: see text]Kr+[Formula: see text]Pb, [Formula: see text]Ca+[Formula: see text]Zr, [Formula: see text]Ni,[Formula: see text]Ca, [Formula: see text]Ti+[Formula: see text]Ni, [Formula: see text]Pb, [Formula: see text]Ar+[Formula: see text]Sm, [Formula: see text]Sn, [Formula: see text]Cl+[Formula: see text]Sn, [Formula: see text]Pr, [Formula: see text]Cu+[Formula: see text]Au and [Formula: see text]S+[Formula: see text]Y demonstrate excellent consistency between calculated and experimental [Formula: see text]. However, lighter systems like [Formula: see text]Mg+[Formula: see text]Mg, and [Formula: see text]Si+[Formula: see text]Sm tend to have slightly larger discrepancies, suggesting potential refinements for specific isotopic combinations. Similarly, [Formula: see text]-values show remarkable accuracy, with typical deviations of only 0.01–0.3[Formula: see text]fm. These minimal deviations affirm the reliability of the semi-empirical model, highlighting its application in predicting fusion barrier parameters across a wide range of reactions.