In low-energy heavy-ion fusion, the term 'Coulomb barrier' commonly refers to the barrier formed by the repulsive 'Coulomb' and the attractive 'nuclear' (nucleus-nucleus) interactions in a central (s-wave) collision. This barrier is frequently called fusion barrier (for light and medium mass heavy-ion systems) or capture barrier (heavy systems). In general, there is a centrifugal component to such a barrier (non central collisions). Experimenters may use the term 'Coulomb barrier' to the nominal value of the 'Coulomb barrier distribution' when either coupled-channel effects operate or (at least) a collision partner is deformed as the barrier features depend on orientation. To my knowledge, the terminology 'transfer barrier' has not been used much. In my view, it could be applied to the transfer of charged particles/clusters.
There is a vast literature on methods for calculating Coulomb barriers. For instance, the double-folding method is broadly used in the low-energy nuclear physics community. Based on this technique, there is a potential called 'Sao-Paulo potential' because it has been developed by theorists in Sao Paulo city in Brazil.
The coulomb barrier is calculated theoretically by adding the nuclear and Coulomb contributions of the interaction potential. For fusion, there are other contributions coming from the different degrees of freedom such as the angular momentum (centrifugal potential), the vibrational and rotational states in both interacting nuclei in addition to the transfere contribution. There are several procedures are used to calculate the nuclear part ( folding based on M3Y forces (PR C 81, 034607 (2010)), Skyrme interaction (PRC72, 064616 (2005), EPJA 38, 85 (2008)), proximity, ...). The Coulomb contribution is calculated by folding (PLB563, 53(2003))or by approximate methods. The coupling to the vibrational and rotational states is taken into account by solving coupled equations or by linear coupling. The fusion barrier is extracted experimentally through the fusion barrier distribution extracted from the fusion cross section.
I agree with Alexis Diaz-Torres , For the calculation of fusion barrier Refer, (Nuclear Physics A231 (1974) 45 - 63), here fusion of heavy nuclei is calculated using classical two body potential.