Expression for the heavy-ion fusion cross section

The expression for calculation of the heavy-ion fusion cross section is obtained in the case of approximation of the total heavy-ion potential around the barrier by the Morse potential. The approximation of the total heavy-ion potential around the barrier by the Morse potential is more realistic than the parabolic one. The asymptotic expressions of the fusion cross section at sub-barrier energies obtained for the Morse and parabolic approximations of the total heavy-ion potential have different dependencies on collision energy. The fusion cross sections calculated for the Morse and parabolic approximations of the total heavy-ion potential are discussed for the reactions 12C + 24Mg and 12C + 30Si in detail.