  Using the Sao Paulo potential and the barrier penetration formalism we have
calculated the astrophysical factor S(E) for 946 fusion reactions involving
stable and neutron-rich isotopes of C, O, Ne, and Mg for center-of-mass
energies E varying from 2 MeV to 18-30 MeV (covering the range below and above
the Coulomb barrier). We have parameterized the energy dependence S(E) by an
accurate universal 9-parameter analytic expression and present tables of fit
parameters for all the reactions. We also discuss the reduced 3-parameter
version of our fit which is highly accurate at energies below the Coulomb
barrier, and outline the procedure for calculating the reaction rates. The
results can be easily converted to thermonuclear or pycnonuclear reaction rates
to simulate various nuclear burning phenomena, in particular, stellar burning
at high temperatures and nucleosynthesis in high density environments.
