Systematic study of the eﬀect of individual rotational energy levels on the fusion cross-section of 16O-based reactions of range 480 < Z_PZ_T< 592


 In heavy-ion fusion reactions, the enhancement in the sub-barrier fusion cross-section has been observed as compared to the 1-Dimensional barrier penetration model due to the coupling of many degrees of freedom to the relative motion. This enhancement can be explained theoretically by including nuclear structure effects like deformation and the coupling of relative motion among two colliding nuclei. The present work aims to investigate the effect of individual rotational energy levels on the fusion cross-sections for $^{16}$O-based reaction systems, namely, $^{16}$O + $^{182,184,186}$W, $^{16}$O + $^{176,180}${Hf}, $^{16}$O + $^{174,176}${Yb}, $^{16}$O + $^{166}${Er}, $^{16}$O + $^{148,152,154}$Sm, $^{16}$O + $^{150}$Nd at energies below the fusion barrier. Using the CCFULL code, the effect of low-lying rotational energy levels on the fusion cross-section for $^{16}$O induced reactions has been investigated at energies below and around the Coulomb barrier. The calculations are performed by assuming the fixed value of diffuseness parameter $a_{0}=0.65$ fm in the Woods-Saxon nuclear potential and the other two parameters are optimised by fitting the experimental data at the above barrier. Here we have determined the $V_0$ and $r_0$ as a function of $Z_PZ_T$, where experimental cross-sections are available. From our calculations, it is observed that the hexadecapole deformation ($\beta_4$) with different magnitudes has a significant influence on the fusion cross sections. For the case of the $+ve$ value of $\beta_4$, beyond $10^+$, the rotational levels cease to contribute significantly and also there is a significant difference between the contribution of sequential channels. On the other hand, in the case of -ve $\beta_4$, up to $6^+$ levels contribute significantly. Furthermore, we have established an algebraic systematic of fitting, which one can use to determine the parameters $V_0$, $r_0$ of Woods-Saxon nuclear potential within the range of $Z_PZ_T$ lie in between $480 \le {Z_PZ_T} \le 592$.