We assume a simple model to describe the ion-ion potential with dynamical change in its surface diffuseness. In particular, this model is used to calculate the heavy-ion fusion cross-section using different values of the surface diffuseness. Both the static and dynamic nuclear Woods-Saxon potentials with diffuseness values ranging between 0.65 fm and 1.3 fm are used to reproduce the fusion cross-sections data of the 19F+208Pb and 16O+154Sm reactions. The results estimate that there are different physical processes which could contribute to the fusion cross-section with different weights at each energy value. Each of these processes has its own nuclear potential. © 2013 World Scientific Publishing Company.

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