Coupled-channels calculations of $^{16}$O+$^{16}$O fusion

TL;DR

This paper uses coupled-channels calculations to analyze $^{16}$O+$^{16}$O fusion, highlighting the importance of excitation channels and ion-ion potential choice, especially the M3Y+repulsion potential, in fitting experimental data and understanding fusion hindrance.

Contribution

It demonstrates that a shallow M3Y+repulsion potential best fits the fusion data and reveals the sensitivity of fusion cross sections to excitation channels even at low energies.

Findings

Best fit with M3Y+repulsion potential produces shallow entrance channel.

Fusion cross section steps correlate with angular momentum barriers.

Shallow potentials cause stronger low-energy fusion hindrance.

Abstract

Fusion data for $^{16}$O+$^{16}$O are analyzed by coupled-channels calculations. It is shown that the calculated cross sections are sensitive to the couplings to the $2^+$ and $3^-$ excitation channels even at low energies, where these channels are closed. The sensitivity to the ion-ion potential is investigated by applying a conventional Woods-Saxon potential and the M3Y+repulsion potential, consisting of the M3Y double-folding potential and a repulsive term that simulates the effect of the nuclear incompressibility. The best overall fit to the data is obtained with a M3Y+repulsion potential which produces a shallow potential in the entrance channel. The stepwise increase in measured fusion cross sections at high energies is also consistent with such a shallow potential. The steps are correlated with overcoming the barriers for the angular momenta $L$ = 12, 14, 16, and 18. To improve the fit to the low-energy data requires a shallower potential and this causes a even stronger hindrance of fusion at low energies. It is therefore difficult, based on the existing fusion data, to make an accurate extrapolation to energies that are of interest to astrophysics.