Fusion Cross Section of Massive Nuclei by Fluctuation-Dissipation Dynamics

Abstract

Fluctuation-dissipation dynamics is applied to the nearly mass-symmetric fusion reactions forming nuclei of Z> 80. We take into account the angular momentum of the system. The fusion cross section is calculated, and the hindrance of fusion is discussed. We estimate the amount of extra energy above the Coulomb barrier needed for fusion. In a fusion reaction with nearly symmetric projectile-target combination forming a compound nucleus with Z> 80 (or fissility larger than 0.65), additional kinetic energy above the incident Coulomb barrier is needed to realize the formation of a spherical compound nucleus. This supplementary energy was defined as the extraextra push energy EXX by Swiatecki 1) and systematic studies of this phenomenon, the so-called fusion hindrance, have been reported. 2) - 4) The origin of the necessity of the extra-extra push energy lies in the characteristics of the potential energy landscape in nuclear deformation parameter space. 5),6) As the system becomes heavier than Z around 80, the contact configuration comes to be located outside the ridge curve of the potential energy surface. Note that the fission saddle point is located on the ridge curve; it divides the deformation space into the mono-nucleus (fusion) region and di-nucleus (fission) region. This implies that the colliding nuclei must overcome the ridge to attain compact shapes, such as a sphere. Fusion hindrance has been investigated in the framework of the classical trajectory method 7) which describes fusion-fission dynamics in terms of the time evolution of the nuclear shape initially located at the contact configuration in the deformation space with a certain collective kinetic energy. To obtain information on EXX, the classical trajectory in a multi-dimensional deformation space has been calculated by Blocki et al. 7) taking into account the dissipative force stemming from the coupling between the collective and the single particle degrees of freedom. In their framework, the critical energy of the fusion reaction was obtained. There is no fusion event below the critical energy, while the trajectory always reaches the spherical region above the energy. The fluctuation of the trajectory which appears as the counterpart of the dissipative force was taken into account by Aguiar et al. 8) By the inclusion of fluctuations, it becomes possible to calculate the fusion probability; the trajectory becomes that of a Brownian particle and can thus be calculated using the Langevin equation. The aim of the present paper is to confirm the validity of the application of fluctuation-dissipation dynamics to the study of fusion of massive nuclei in the mass