Abstract
It is well known that there is a hindrance to fusion in collisions with heavy nuclei that plays a decisive role in synthesis of the super-heavy elements (SHE). The origin of the fusion hindrance is nowadays qualitatively understood but there are still quantitative ambiguities on the dynamics of the fusion mechanism and the predictions need to be assessed. In this communication, we stress the fact that dynamical effects play a crucial role in the amplitude of the reduction of the fusion probability. We found that the fast evolution of the neck degree of freedom affects the slow radial motion, i.e., the fusioning motion, through a dynamical coupling. We showed that we could do a so-called adiabatic elimination of the fast variable in the coupled equation, resulting in an effective one-dimensional equation for the radial motion with a shift of the starting point. This treatment of the dynamical coupling leads to a larger hindrance.
Highlights
It is well known that there is a hindrance to fusion in collisions with heavy nuclei
It confirms the adiabatic approximation that is usually done in the various models, but it shows that the dynamical coupling between the neck and radial degrees of freedom induces a shift of the effective initial value of the relative distance
We have stressed the importance of the neck parameter that can change the fusion cross sections by orders of magnitude
Summary
It is well known that there is a hindrance to fusion in collisions with heavy nuclei. The origin of the fusion hindrance is nowadays qualitatively understood: after crossing the Coulomb barrier, the fusing system at contact have to overcome a second barrier under strong dissipation. For the Coulomb barrier, one can extrapolate the models validated on the fusion of lighter nuclei Note that for this first step a so-called fusion hindrance at energies far below the barrier exists. One of our goals is to obtain an analytical formula of the fusion probability for an incident channel with an arbitrary combination of projectile and target nuclei
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