Fusion by Diffusion Model Revisited

Abstract

A complete set of 27 excitation functions for synthesis of superheavy nuclei produced in cold fusion reactions was analyzed in terms of the "Fusion by Diffusion Model" of Światecki et al., modified to account for the angular momentum dependence of the fusion hindrance factor. The data on cold fusion reactions originate from experiments carried out at GSI Darmstadt, RIKEN Tokyo and LBNL Berkeley in which 208 Pb and 209 Bi targets were bombarded with the variety of projectiles ranging from 48,50 Ti to 70 Zn .

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

“…To this end, I closely follow Ref. [35], in which the angular momentum dependence of the diffusion and the survival probabilities has been introduced to the original version of the model [33,34]. In this ldependent version of the fusion-by-diffusion model, evaporation residue cross sections σ ER are evaluated as,…”

“…where s is the coordinate for diffusion, that is, the surface separation between the two spheres [35], V fiss (s) is the inner (fission) barrier, and J (s) is the moment of inertia for the mono-nuclear system. The last term in Eq.…”

“…In order to describe such a complicated process, Swiatecki et al have proposed a simple one-dimensional model, that is, the fusion-by-diffusion model [33][34][35]. In this model, classical fusion cross sections with a Gaussian barrier distribution are employed for the first stage, while the second stage is modeled as a diffusion of a one dimensional parabolic barrier.…”

“…In this model, classical fusion cross sections with a Gaussian barrier distribution are employed for the first stage, while the second stage is modeled as a diffusion of a one dimensional parabolic barrier. Despite that the model is simple, it accounts for experimental cross sections reasonably well for Pb-and Bi-based cold fusion reactions by introducing one adjustable parameter, that is, the injection point for the second stage, or equivalently the height of the fission barrier relative to the touching configuration [33][34][35][36].…”

Generator coordinate method for transition-state dynamics in nuclear fission

“…Transition-state theory 1 has been at the foundation of the theory of induced fission since the original paper by Bohr and Wheeler in 1939 [1] and continuing up to the present era [2][3][4][5][6][7][8]. It is encapsulated in the formula for the decay rate Γ…”