A generalized version of the fusion by diffusion model is proposed, in which evolution from dinuclear to mononuclear regimes is taken into account in terms of the coupled Langevin equations in the three-dimensional collective space of neck, radial, and asymmetric degrees of freedom. By simulating numerically these dynamic equations, the probability distribution of $s_{\mathrm{inj}}$, the separation between the surfaces of two approaching nuclei at the injection point in the asymmetric fission valley, is obtained. From the injection points, the system starts its climb uphill over the saddle point in the presence of thermal fluctuation; thus for very heavy systems the injection-point distance is a very critical constituent in the calculations of fusion probability. The present model is applied for the study of the mass asymmetric system ${}^{58}\mathrm{Fe}+{}^{208}$Pb. The excitation function for the ${}^{208}$Pb(${}^{58}$Fe,$n$)${}^{265}$Hs reaction is calculated and compared with the experimental data. By comparing the theoretical results with and without taking the asymmetric degree of freedom into account, we have arrived at the conclusion that nucleon flow between the asymmetric reaction partners in the early stage of the fusion process plays an important role in the formation of superheavy nuclei in the cold fusion reactions.

• Received 12 March 2012

DOI:https://doi.org/10.1103/PhysRevC.85.057603