Determination of the compound nucleus survival probabilityPsurvfor various “hot” fusion reactions based on the dynamical cluster-decay model

Abstract

After a successful attempt to define and determine recently the compound nucleus (CN) fusion/ formation probability ${P}_{\text{CN}}$ within the dynamical cluster-decay model (DCM), we introduce and estimate here for the first time the survival probability ${P}_{\text{surv}}$ of CN against fission, again within the DCM. Calculated as the dynamical fragmentation process, ${P}_{\text{surv}}$ is defined as the ratio of the evaporation residue (ER) cross section ${\ensuremath{\sigma}}_{\text{ER}}$ and the sum of ${\ensuremath{\sigma}}_{\text{ER}}$ and fusion-fission (ff) cross section ${\ensuremath{\sigma}}_{\text{ff}}$, the CN formation cross section ${\ensuremath{\sigma}}_{\text{CN}}$, where each contributing fragmentation cross section is determined in terms of its formation and barrier penetration probabilities ${P}_{0}$ and $P$. In DCM, the deformations up to hexadecapole and ``compact'' orientations for both in-plane (coplanar) and out-of-plane (noncoplanar) configurations are allowed. Some 16 ``hot'' fusion reactions, forming a CN of mass number ${A}_{\text{CN}}\ensuremath{\sim}100$ to superheavy nuclei, are analyzed for various different nuclear interaction potentials, and the variation of ${P}_{\text{surv}}$ on CN excitation energy ${E}^{*}$, fissility parameter $\ensuremath{\chi}$, CN mass ${A}_{\text{CN}}$, and Coulomb parameter ${Z}_{1}{Z}_{2}$ is investigated. Interesting results are that three groups, namely, weakly fissioning, radioactive, and strongly fissioning superheavy nuclei, are identified with ${P}_{\text{surv}}$, respectively, $\ensuremath{\sim}1,\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}{10}^{\ensuremath{-}6}$, and $\ensuremath{\sim}{10}^{\ensuremath{-}10}$. For the weakly fissioning group ($100l{A}_{\text{CN}}\ensuremath{\lesssim}200$), independent of the interaction potential, different isotopes and for coplanar or noncoplanar collisions, ${P}_{\text{surv}}$ decreases from one to zero as ${E}^{*}$ increases, whereas, independent of entrance channel effects, the same is surprisingly the reverse for the radioactive group (${A}_{\text{CN}}\ensuremath{\sim}200--250$), i.e., ${P}_{\text{surv}}$ increases with the increase of ${E}^{*}$. This is shown to be so due to the different relative magnitudes of ${\ensuremath{\sigma}}_{\text{ER}}$ and ${\ensuremath{\sigma}}_{\text{ff}}$ and their variations with ${E}^{*}$ in the two cases. For the superheavy nuclei also ${P}_{\text{surv}}$ is a decreasing function of ${E}^{*}$. Furthermore, of particular interest are the cases of ${}^{105}{\mathrm{Ag}}^{*}$, isotopes of ${\mathrm{Pt}}^{*}$, and ${}^{213,215,217}{\mathrm{Fr}}^{*}$ nuclei --- for ${}^{105}{\mathrm{Ag}}^{*}$, whereas the ${P}_{\text{CN}}$ belongs to the strongly fissioning superheavy group, ${P}_{\text{surv}}$ belongs to weakly fissioning nuclei; for ${\mathrm{Pt}}^{*}$ isotopes, the inverse of all the compound systems studied, both ${P}_{\text{CN}}$ and ${P}_{\text{surv}}$ decrease with the increase of ${E}^{*}$; for ${}^{213,215,217}{\mathrm{Fr}}^{*}$ nuclei, though fissility $\ensuremath{\chi}$ is nearly the same, ${P}_{\text{surv}}$ for ${}^{213,217}{\mathrm{Fr}}^{*}$ is of the same order as for weakly fissioning nuclei, but that for ${}^{215}{\mathrm{Fr}}^{*}$ is of the order of radioactive nuclei. Apparently, further calculations are called for.