Fusion studies in ${}^{16}\mathrm{O}+{}^{142,150}\mathrm{Nd}$ reactions at energies near the Coulomb barrier

Background: Enhancement in fusion cross sections over one-dimensional barrier penetration model (1D-BPM) predictions has been observed at sub-barrier energies owing to the coupling of various internal degrees of freedom to the relative motion. On the other hand, hindrance in fusion is noticed at energies well above the barrier in a few cases.

Purpose: The purpose is to probe the dynamics of heavy ion fusion at energies below and well above the Coulomb barrier.

Methods: Fusion excitation functions for the ${}^{16}\mathrm{O}+{}^{142,150}\mathrm{Nd}$ reactions are measured using the Heavy Ion Reaction Analyzer (HIRA) at IUAC, New Delhi. Measurements have been performed in the range $12\%$ below to $50\%$ above the Coulomb barrier for both systems. The measured fusion cross sections are compared with coupled channels calculations using ccfull code. The cross sections are also compared with reactions using ${}^{16}\mathrm{O}$ beams with other isotopes of Nd to explore the systematic behavior of fusion.

Results: Compared with 1D-BPM predictions, fusion enhancement is observed in both ${}^{16}\mathrm{O}+{}^{142}\mathrm{Nd}$ and ${}^{16}\mathrm{O}+{}^{150}\mathrm{Nd}$ reactions at below-barrier energies, with the latter reaction showing a higher enhancement. Coupled channels calculations incorporating the collective excitations of the target nuclei reproduce the fusion cross sections in both reactions. The collective excitations of the projectile nucleus do not seem to contribute to the observed fusion enhancement. Calculations using Akyüz-Winther potential parameters fail to reproduce the fusion cross sections at energies well above the barrier.

Conclusions: Fusion enhancement is observed in both reactions studied. Degree of enhancement of sub-barrier fusion cross section is larger for the reaction using ${}^{150}\mathrm{Nd}$ target. Fusion hindrance is observed in both reactions at very high energies. The hindrance seems to increase with increasing beam energy. Larger value of diffuseness parameter compared with the value consistent with elastic-scattering measurements is required to reproduce the fusion excitation function at energies well above the barrier. This could be a strong indication of dynamical effects in fusion at very high energies.

Figure 1

Schematic representation of HIRA.

Figure 2

Two-dimensional $\mathrm{\Delta }E$ versus ToF spectra for the ${}^{16}\mathrm{O}+{}^{142}\mathrm{Nd}$ at 88 MeV beam energy. ERs are shown inside the rectangular gate and are clearly separated from other scattered particles reaching the focal plane through multiple scattering.

Figure 3

The experimental ER cross sections of the reactions ${}^{16}\mathrm{O}+{}^{142}\mathrm{Nd}$ and ${}^{16}\mathrm{O}+{}^{150}\mathrm{Nd}$ as a function of energy in c.m. frame.

Figure 4

The experimental fusion cross sections in the energy range $V_b<E<1.2V_b$ is plotted against the inverse of center-of-mass energy ($E$). The $x$ intercept of the linear fit gives the inverse of experimental barrier.

Figure 5

The experimental fusion excitation function for the ${}^{16}\mathrm{O}+{}^{142}\mathrm{Nd}$ reaction along with CC calculations.

Figure 6

The experimental fusion excitation function for the ${}^{16}\mathrm{O}+{}^{150}\mathrm{Nd}$ reaction along with CC calculations.

Figure 7

(a) Plot of ${\sigma }_{\mathrm{ER}}$ (on linear scale) for ${}^{16}\mathrm{O}+{}^{142}\mathrm{Nd}$ reaction against the center-of-mass energy in excess of the barrier. Only cross sections at above-barrier energies are shown here. (b) Similar plot for ${}^{16}\mathrm{O}+{}^{150}\mathrm{Nd}$ reaction is shown.

Figure 8

Experimental fusion cross sections (on linear scale) compared with calculations using different $V_0$ (MeV), $r_0$ (fm), and $a$ (fm) values, for the ${}^{16}\mathrm{O}+{}^{142}\mathrm{Nd}$ reaction. A calculation using AW parametrization is shown with the solid red line.

Figure 9

Comparison of the reduced fusion cross sections forming the same CN (${}^{166}\mathrm{Er}$); the reaction ${}^{18}\mathrm{O}+{}^{148}\mathrm{Nd}$ has a positive $Q$ value for $2n$-stripping channel.

Figure 10

Comparison of experimental fusion cross sections for the ${}^{16}\mathrm{O}+{}^{142,144,148,150}\mathrm{Nd}$ reactions. The cross sections are converted to reduced scale by dividing the absolute cross section by $\pi {ƛ}^2$ to remove the geometrical effects of the targets.