Influences of isospin-asymmetry and skin thickness on fusion of oxygen isotopes at stellar energies

Fusion reactions with stable and radioactive isotopes of light nuclei are indicated to control the crustal composition, nucleosynthesis, and heating mechanism during nuclear burning in neutron stars. The role of isospin asymmetry and proton-/neutron-skin thickness in the fusion excitation function and its related astrophysical $S$ factor is investigated for the reactions involving ${}_{12,14-20,22,24,25,28}O$ isotopes at sub-barrier energies of astrophysical interest. The calculations are performed in an extended quantum diffusion framework. Among many examined potentials, the only potentials based on the Skyrme-BSk19 and M3Y-Reid nucleon-nucleon interactions successfully reproduce the experimental ${}_{16}O+{}_{16}O$, ${}_{12}C+{}_{16}O$, ${}_{36}S+{}_{48}\mathrm{Ca}$, and ${}_{48}\mathrm{Ca}+{}_{48}\mathrm{Ca}$ fusion data, over the whole considered energy range. The height, radius, and curvature of the Coulomb barrier for the interactions involving proton-rich ${}_{12,15}O$ isotopes are found to impede the near- and above-barrier fusion cross section and the corresponding $S$ factor relative to the ${}_{16}O+{}_{16}O$ reaction. However, the relatively small reduced mass and proton-skin thickness act to enhance fusion at deeply sub-barrier energies. For the interactions involving neutron-rich $O(N>8)$ isotopes, the fusion enhancement due to the produced Coulomb barrier is supported by relatively large $Q$ values and neutron-skin thicknesses, against the increase of reduced masses. The neutron transfer is indicated to hinder the fusion in some ${}_{A_1}O+{}_{A_2}O$ $(A_2\ge A_1+4)$ reactions at sub-barrier energy.