The interaction potentials, cross sections, and $S$-factors for fusion reactions involving stable and neutron-rich isotopes of C, O, Ne, Mg, and Si, for the neutron star crust, are calculated at subbarrier energies, using a microscopic relativistic energy density functional based on the Dirac-Brueckner-Hartree-Fock (DBHF) approach for asymmetric nuclear matter, employing the Bonn potential A for the nucleon-nucleon interaction. This volume energy density of nuclear matter is supplemented by Coulomb energy and by conventional phenomenological surface energy terms. Calculations using Skyrme, M3Y, and São Paulo (SP) potentials are presented for comparison. Self-consistent proton and neutron densities are used in the calculations of the interaction potentials. Coupled-channels (CC) calculations are considered through the ccfull code. The fusion cross sections and $S$-factors calculated with DBHF potentials are found to be in excellent agreement with experimental data for the systems ${}^{16}\mathrm{O}+{}^{16,18}\mathrm{O}$, ${}^{12}\mathrm{C}+{}^{16,18}\mathrm{O}$, and ${}^{28}\mathrm{Si}+{}^{28,30}\mathrm{Si}$. Hindrance is naturally predicted by the DBHF potentials for medium-heavy systems, such as $\mathrm{Ne}+\mathrm{Ne},\mathrm{Ne}+\mathrm{Mg}$, and $\mathrm{Si}+\mathrm{Si}$. CC calculations, in addition to significantly enhancing the cross section at subbarrier energies, predict measurable shifts in the onset energy of hindrance. The M3Y and SP potentials were unable to describe hindrance, as they produce extremely deep potentials in the overlap region, with no pocket in the surface region. The influence of neutron excess on fusion hindrance is investigated for the neutron-rich systems, ${}^{28}\mathrm{Si}+{}^{30-40}\mathrm{Si}$ and ${}^{40}\mathrm{Si}+{}^{40}\mathrm{Si}$, and an interesting correlation between them has been found. The impact of the equation of state on fusion reactions is investigated, finding significant sensitivity to the symmetry energy and incompressibility of nuclear matter. These results in addition to enhancing our understanding for fusion reactions of stable and neutron-rich isotopes, demonstrate the relativistic DBHF approach as a powerful model for a unified description of nuclear matter, nuclear reactions, and astrophysical environments.

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• Hydrostatic stellar nucleosynthesis
• Nuclear astrophysics
• Nuclear fusion
• Nuclear matter in neutron stars
• Nuclear reactions