Examples of the failure of proximity approach when the nuclear surface is irregular or has concave regions

We study the results of the proximity approach in calculating the fusion barrier parameters (the height of Coulomb barrier VBVB and its radius RBRB) compared with the results of double folding model (DFM). We considered five interaction systems as examples and made our study at several relative orientations for the interacting deformed nuclei. We found that VBVB and RBRB, evaluated by using the proximity approach, have nonphysical Φ  -dependence when the value of hexadecapole deformation parameter β4<0β4<0 or at least one nucleus has octupole deformation order, β3β3. The results almost agree with those of DFM when β4=0β4=0. For positive β4β4 values the results of the two models almost agree in behavior but differ in values. The reason for failure when β4β4 has negative value is due to the existence of concave region in the nuclear surface, which does not satisfy the requirement of proximity approach based on gently-curved surface. Since the existence of β6β6 and β8β8 induce irregularity and concave regions in the surface, we expect failure of proximity approach in this case, for an example, β6β6 was given.