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

Abstract

We present here a robust analytical model based on nuclear reaction theory for non-resonant fusion cross sections near Coulomb barrier. The astrophysical S-factors involving stable and neutron rich isotopes of C, O, Ne, Mg and Si for fusion reactions have been calculated in the centre of mass energy range of 2-30 MeV. The model is based on the tunneling through barrier arising out of nuclear, Coulomb and centrifugal potentials. Our formalism predicts precisely the suppression of S-factor at sub-barrier energies which are of astrophysical interest by using only five parameters for asymmetric systems and just four parameters for symmetric systems and thus providing an accurate and very compact description of S-factor. The cross sections can be convoluted with Maxwell-Boltzmann distribution of energies to obtain thermo- or pycno-nuclear reaction rates relevant to nucleosynthesis at high density environments and stellar burning at high temperatures as well as for 34Ne + 34Ne fusion occurring in the inner crust of accreting neutron stars.