Effects of mutual excitations in the fusion of carbon isotopes

TL;DR

This study uses coupled-channels calculations with a specific potential to analyze fusion data of carbon isotopes, highlighting the crucial role of mutual excitations in accurately modeling fusion cross sections.

Contribution

It introduces a comprehensive coupled-channels approach including mutual excitations to better describe carbon isotope fusion data.

Findings

Mutual excitations to high-lying states are essential for accurate fusion modeling.

Calculated cross sections align well with experimental data for certain isotope combinations.

Fusion cross sections for $^{12}$C+$^{12}$C serve as upper limits for astrophysical extrapolations.

Abstract

Fusion data for $^{13}$C+$^{13}$C, $^{12}$C+$^{13}$C and $^{12}$C+$^{12}$C are analyzed by coupled-channels calculations that are based on the M3Y+repulsion, double-folding potential. The fusion is determined by ingoing-wave-boundary conditions (IWBC) that are imposed at the minimum of the pocket in the entrance channel potential. Quadrupole and octupole transitions to low-lying states in projectile and target are included in the calculations, as well as mutual excitations of these states. The effect of one-neutron transfer is also considered but the effect is small in the measured energy regime. It is shown that mutual excitations to high-lying states play a very important role in developing a comprehensive and consistent description of the measurements. Thus the shapes of the calculated cross sections for $^{12}$C+$^{13}$C and $^{13}$C+$^{13}$C are in good agreement with the data. The fusion cross sections for $^{12}$C+$^{12}$C determined by the IWBC are generally larger than the measured cross sections but they are consistent with the maxima of some of the observed peak cross sections. They are therefore expected to provide an upper limit for the extrapolation into the low-energy regime of interest to astrophysics.