Sao Paulo potential as a tool for calculating S factors of fusion reactions in dense stellar matter

The goal of this paper is to test and justify the use of the Sao Paulo potential model for calculating astrophysical S factors for reactions involving stable and neutron-rich nuclei. In particular, we focus on the theoretical description of S factors at low energies. This is important for evaluating the reaction rates in dense stellar matter. We calculate the S factors for a number of reactions (O-16+O-16, O-20+O-20, O-20+Ne-26, O-20+Mg-32, Ne-26+Ne-26, Ne-26+Mg-32, Mg-32+Mg-32, O-22+O-22, O-24+O-24) with the Sao Paulo potential in the framework of a one-dimensional barrier penetration model. This approach can be easily applied for many other reactions involving different isotopes. To test the consistency of the model predictions, we compare our calculations with those performed within the coupled-channels and fermionic molecular dynamics models. Calculated S factors are parametrized by a simple analytic formula. The main properties and uncertainties of reaction rates (appropriate to dense matter in cores of massive white dwarfs and crusts of accreting neutron stars) are outlined.