DYNAMICS OF THE SUPERHEAVY ELEMENT SYNTHESIS WITH A DIFFUSION-MODEL

A diffusion model is proposed for the dynamical treatment of the synth esis of superheavy elements. Fusion-fission process is analyzed by one -dimensional Smoluchowski equation with liquid drop model potential of no pocket and the temperature dependent shell correction energy which generates the pocket around the spherical shape. Competition between fission and neutron evaporation is taken into account in terms of the continuous cooling by neutron evaporation. The evaporation residue cro ss sections of superheavy elements have been shown to have an optimum value at a certain temperature, due to the balance between the diffusi bility for fusion at high temperature and the restoration of the shell correction energy against fission at low temperature. The isotope dep endence of the evaporation residue cross section is found to be very s trong. Neutron rich compound system with small neutron separation ener gy is favorable for larger cross section because of the quick restorat ion of the shell correction energy.