Fluctuation-dissipation model for synthesis of superheavy elements

Fusion-fission dynamics in superheavy elements is investigated by an approximate fluctuation-dissipation model, i.e., a diffusion model in the deformation space, assuming that the kinetic energy of the incident ion dissipates immediately after the contact. The probability accumulated inside the fission barrier is calculated by the one-dimensional Smoluchowski equation taking account of the temperature dependence of the shell correction energy. A new mechanism for an optimum condition is found as a compromise of two conflicting requirements: higher incident energy for larger fusion probability and lower excitation energy of compound nuclei for larger survival probability. Enhancements of the residue cross sections at the optimum condition are obtained for the cases in which the cooling is quick to restore the shell correction energy, combined with slow fissioning motion due to the strong friction. With symmetric combinations of incident ions, the (HI, $3-4n)$ channels show the enhancement.