Compound nucleus formation probabilityPCNdetermined within the dynamical cluster-decay model for various “hot” fusion reactions

Abstract

The compound nucleus (CN) fusion/formation probability ${P}_{CN}$ is defined and its detailed variations with the CN excitation energy ${E}^{*}$, center-of-mass energy ${E}_{\mathrm{c}.\mathrm{m}.}$, fissility parameter $\ensuremath{\chi}$, CN mass number ${A}_{CN}$, and Coulomb interaction parameter ${Z}_{1}{Z}_{2}$ are studied for the first time within the dynamical cluster-decay model (DCM). The model is a nonstatistical description of the decay of a CN to all possible processes. The (total) fusion cross section ${\ensuremath{\sigma}}_{\mathrm{fusion}}$ is the sum of the CN and noncompound nucleus (nCN) decay cross sections, each calculated as the dynamical fragmentation process. The CN cross section ${\ensuremath{\sigma}}_{CN}$ is constituted of evaporation residues and fusion-fission, including intermediate-mass fragments, each calculated for all contributing decay fragments (${A}_{1}$, ${A}_{2}$) in terms of their formation and barrier penetration probabilities ${P}_{0}$ and $P$. The nCN cross section ${\ensuremath{\sigma}}_{\mathit{nCN}}$ is determined as the quasi-fission (qf) process, where ${P}_{0}=1$ and P is calculated for the entrance-channel nuclei. The DCM, with effects of deformations and orientations of nuclei included in it, is used to study the ${P}_{CN}$ for about a dozen ``hot'' fusion reactions forming a CN of mass number $A\ensuremath{\sim}100$ to superheavy nuclei and for various different nuclear interaction potentials. Interesting results are that ${P}_{CN}=1$ for complete fusion, but ${P}_{CN}<1$ or ${P}_{CN}\ensuremath{\ll}1$ due to the nCN contribution, depending strongly on different parameters of the entrance-channel reaction but found to be independent of the nuclear interaction potentials used.