Nucleus-nucleus cold fusion reactions analyzed with thel-dependent “fusion by diffusion” model

Abstract

We present a modified version of the Fusion by Diffusion (FBD) model aimed at describing the synthesis of superheavy nuclei in cold fusion reactions, in which a low excited compound nucleus emits only one neutron. The modified FBD model accounts for the angular momentum dependence of three basic factors determining the evaporation residue cross section: the capture cross section ${\ensuremath{\sigma}}_{\text{cap}}(l)$, the fusion probability ${P}_{\text{fus}}(l)$, and the survival probability ${P}_{\text{surv}}(l)$. The fusion hindrance factor, the inverse of ${P}_{\text{fus}}(l)$, is treated in terms of thermal fluctuations in the shape degrees of freedom and is expressed as a solution of the Smoluchowski diffusion equation. The $l$ dependence of ${P}_{\text{fus}}(l)$ results from the $l$-dependent potential energy surface of the colliding system. A new parametrization of the distance of starting point of the diffusion process is introduced. An analysis of a complete set of 27 excitation functions for production of superheavy nuclei in cold fusion reactions, studied in experiments at GSI Darmstadt, RIKEN Tokyo, and LBNL Berkeley, is presented. The FBD model satisfactorily reproduces shapes and absolute cross sections of all the cold fusion excitation functions. It is shown that the peak position of the excitation function for a given 1$n$ reaction is determined by the $Q$ value of the reaction and the height of the fission barrier of the final nucleus. This fact could possibly be used in future experiments (with well-defined beam energy) for experimental determination of the fission barrier heights.