Recent theoretical activities of heavy-ion fusion reactions in Sendai

We discuss three topics. The first is the effect of difference of the deformation of the neutron and proton density distributions predicted for some nuclei on their fusion cross section. The second is the results of calculations of the fusion cross section based on the double folding potential. We discuss the sensitivity of the fusion cross section to the surface properties of nuclei, and the necessity of normalization of the potential to reproduce the experimental data at high energies. The third is related to the synthesis of superheavy elements. We show that the quantum effects originating from the finite curvature of the fission barrier play significant roles in describing the synthesis of superheavy elements, i.e. the evolution from the fusion to the fission barriers, in terms of a diffusion process. We especially point out the importance of the memory effect, which increases at lower temperatures. It makes the net quantum effects enhance the probability to cross the fission barrier.