Role of entrance channel parameters on optimal incident energies in the formation of heavy nuclei using Ca-induced fusion reactions

Abstract

We examined fusion cross-sections and fusion barrier distributions of 80 fusion reactions with ${}^{40,48}$Ca projectiles and targets in the atomic number range 76$\le Z_T\le 93$. The Wong formula was utilized to analyze the fusion cross-sections in which boundary conditions for the total potential were used to estimate the height and position of the fusion barrier. Five different proximity potentials such as Proximity 1977 [Annals of Physics 105, 427 (1977)], modified proximity 1977 [Nuclear Physics A 361, 117 (1981)], Bass 1977 [Physical Review Letters 39, 265 (1977)], Denisov proximity potential [Physics Letters B 526, 315 (2002)], and Ngo et al. [Nuclear Physics A 348, 140 (1980)] were taken into account while calculating the total potential. We found that Bass77 exhibits good agreement with that of the available experiments. To estimate the fusion barrier distributions, the Bass77 proximity potential-evaluated fusion cross-sections were employed. We determined the optimal fusion barrier distribution, $E^{opt}$, for each fusion reaction. We also explored the influence of entrance channel parameters on $E^{opt}$ and discovered that $E^{opt}$ is more systematic for the Coulomb interaction parameter. We also proposed an empirical equation for $E^{opt}$ for ${}^{40,48}$Ca-induced fusion reactions leading to form compound nuclei 96$\le Z_c\le$ 103.