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

TL;DR

This study systematically examines how individual rotational energy levels and hexadecapole deformation influence fusion cross-sections in $^{16}$O-induced reactions near the Coulomb barrier, providing a new algebraic fitting method for potential parameters.

Contribution

It introduces a systematic analysis of rotational levels and deformation effects on fusion cross-sections, along with an algebraic fitting approach for Woods-Saxon potential parameters.

Findings

Hexadecapole deformation significantly affects fusion cross-sections.

Positive $eta_4$ values reduce the contribution of higher rotational levels.

An algebraic method for determining potential parameters across a range of $Z_PZ_T$.

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 $Z_PZ_T$, 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 $480 \le {Z_PZ_T} \le 592$.