Hot fusion reactions with deformed nuclei for synthesis of superheavy nuclei: an extension of the fusion-by-diffusion model

TL;DR

This paper extends the fusion-by-diffusion model to include target nucleus deformation and orientation effects, improving predictions of evaporation residue cross sections in hot fusion reactions for superheavy element synthesis.

Contribution

The model is enhanced by incorporating target deformation and orientation dependence, providing a more accurate description of hot fusion reactions near the Coulomb barrier.

Findings

Maximum evaporation residue cross section occurs slightly above the capture barrier for side collisions.

Deformation effects significantly influence the energy dependence of the fusion process.

The model explains the energy dependence previously attributed to other factors.

Abstract

The fusion-by-diffusion model proposed by Swiatecki {\it et al.} [Phys. Rev. C71, 014602 (2005)] has provided a simple and convenient tool to estimate evaporation residue cross sections for superheavy nuclei. I extend this model by taking into account deformation of the target nucleus, and discuss the role of orientation of deformed target in hot fusion reactions at energies around the Coulomb barrier. To this end, I introduce an injection point for the diffusion process over an inner barrier which depends on the orientation angle. I apply this model to the $^{48}$Ca+$^{248}$Cm reaction and show that the maximum of evaporation residue cross section appears at an energy slightly above the height of the capture barrier for the side collision, for which the effective inner barrier is considerably lower than that for the tip collision, thus enhancing the diffusion probability. I also discuss the energy dependence of the injection point, and show that a large part of the energy dependence found in the previous analyses can be attributed to the deformation effect of a target nucleus.