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We present here a robust analytical model based on nuclear reaction theoryfor non-resonant fusion cross sections near Coulomb barrier. The astrophysical$S$-factors involving stable and neutron rich isotopes of C, O, Ne, Mg and Sifor fusion reactions have been calculated in the centre of mass energy range of2-30 MeV. The model is based on the tunneling through barrier arising out ofnuclear, Coulomb and centrifugal potentials. Our formalism predicts preciselythe suppression of $S$-factor at sub-barrier energies which are ofastrophysical interest. The cross sections can be convoluted withMaxwell-Boltzmann distribution of energies to obtain thermo- or pycno- nuclearreaction rates relevant to nucleosynthesis at high density environments andstellar burning at high temperatures as well as for $^{34}$Ne $+$ $^{34}$Nefusion occurring in the inner crust of accreting neutron stars.

Theoretical exploration of $S$-factors for nuclear reactions of astrophysical importance