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Nuclear fusion reactions, at energies, far below the Coulomb barrier play asignificant role in the synthesis of light elements in the primordialnucleosynthesis as well as in the interior of compact stellar objects. Manydifferent kinds of nuclear reactions are occurring simultaneously inside thestellar core depending upon the density and temperature conditions of thenuclear plasma along with other relevant parameters of these stars. Nuclearfusion reactions in the energy range ($E\sim$ 1 eV to few keV) can be explainedsuccessfully by quantum mechanical tunneling through the mutual Coulomb barrierof interacting nuclei. The measurement of the cross-sections at extremely lowenergy is quite difficult because of the larger width of the Coulomb barrier,which results in a very small value of the reaction cross-section. Hence, anyimprovement in the data on astrophysical S-factors for the light nuclei fusionmay give a better picture of the elemental abundance in nucleosynthesis. Inthis work, we have theoretically investigated the energy dependence of fusioncross-sections and astrophysical S-factors for fusion reaction of light nucleilike D-D and p-$^{11}$B using complex Gaussian nuclear potential withadjustable depth and range parameters plus the mutual Coulomb interaction ofthe interacting nuclei. Numerical computation of the observables is done in theframework of the selective resonant tunneling model approach. The results ofour calculation are compared with those found in the literature.

Study of fusion reactions of light nuclei at low energies using complex nucleon-nucleus potential function