Systematic study of the effect of individual rotational energy levels on the fusion cross-section of \texorpdfstring{${}^{16}O$}--based reactions of range $480\le Z_P{Z}_T\le 592$

Abstract

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 $Z_P{Z}_T$, where experimental cross-sections are available. From our calculations, it is observed that the hexadecapole deformation (${\hat{I}}_4^2$) with different magnitudes has a significant influence on the fusion cross sections. For the case of the $+ve$ value of ${\hat{I}}_4^2$, 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 ${\hat{I}}_4^2$, 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 $Z_P{Z}_T$ lie in between $480\le Z_P{Z}_T\le 592$.