Here, we present a nuclear potential model for heavy- ion reactions consisting of four central, spin, iso-spin and Iτ terms. The potential model presented here, predicts more accurate values for the barrier height of 6Li+24Mg→30P* and 7Li+24Mg→31P* reactions compared to the other potential models such as Proximity potential (Prox.77 and Prox.88) and Age Wither potential model (AW 95). A detailed comparative study of the fusion excitation functions of 6Li+24Mg and 7Li+24Mg reactions has been performed in 1–25 MeV energy interval. For energies below the Coulomb barrier and above the 15 MeV, our proposed potential model exhibits a better agreement with the experimental data than the above-mentioned potential models and leads to about 10 to 20 percent improvement in the previous results. Also, the analysis of S factor and the logarithmic derivatives showed that the coupled channel calculation based on our purposed potential is in good agreement with the corresponding experimental data at these energy ranges.
