Calculation of penetration probability across an arbitrary potential barrier in fusion reactions

The penetration probability across an arbitrary nucleus-nucleus potential barrier is studied by using transfer matrix approach, including continuous variations of effective mass. The calculated penetration probabilities for reaction ${}^{16}$O+${}^{208}$Pb are closed to those of WKB and modified Numerov calculations based on the Bass potential. With the transfer matrix approach, the influence of the effective mass on the penetration probability are simultaneously investigated. The calculations imply that the effective mass is an important quantity for studying the hindrance of fusion cross sections of some reactions at deep sub-barrier energies. The fusion cross sections of heavy-ion fusion reactions and the resonance phenomena due to double-hump barriers are also studied with this approach.