Formation and decay of the compound nucleus Th*220 within the dynamical cluster-decay model

Abstract

Background: The radioactive $^{220}\mathrm{Th}^{*}$ compound nucleus (CN) is of interest since the evaporation residue (ER) cross sections are available for various entrance channels $^{16}\mathrm{O}+^{204}\mathrm{Pb}$, $^{40}\mathrm{Ar}+^{180}\mathrm{Hf}$, $^{48}\mathrm{Ca}+^{172}\mathrm{Yb}$, and $^{82}\mathrm{Se}+^{138}\mathrm{Ba}$ at near barrier energies. Within the dynamical cluster-decay model (DCM), the radioactive CNs $^{215}\mathrm{Fr}^{*}$, $^{242}\mathrm{Pu}^{*}$, $^{246}\mathrm{Bk}^{*}$, and $^{254}\mathrm{Fm}^{*}$ are studied where the main decay mode is fission, with very small predicted ER cross section. $^{220}\mathrm{Th}^{*}$ provides a first case with experimentally observed ER cross section instead of fission.Purpose: To look for the optimum ``hot-compact'' target-projectile (t-p) combinations for the synthesis of ``cold'' $^{220}\mathrm{Th}^{*}$ and then its decay. For best fitting of the measured ER cross sections, with quasifission (qf) content, if any, the fusion-fission (ff) component is predicted. The magic-shell structure and entrance channel mass-asymmetry effects are analyzed, and the behavior of CN formation and survival probabilities ${P}_{\mathrm{CN}}$ and ${P}_{\mathrm{surv}}$ is studied.Methods: The quantum-mechanical fragmentation theory (QMFT) is used to predict the possible cold t-p combinations for synthesizing $^{220}\mathrm{Th}^{*}$, and the QMFT-based DCM is used to analyze its decay channels for the experimentally studied entrance channels. The only parameter of the model, the neck length $\mathrm{\ensuremath{\Delta}}R$, varies smoothly with the excitation energy ${E}^{*}$ of CN and is used to best fit the ER data and predict qf and ff cross sections.Results: The hot-compact and ``cold-elongated'' fragmentation paths show dissimilar results, whose comparisons with measured fission yields result in t-p combinations, the cold reaction valleys. For the decay process, the fixed $\mathrm{\ensuremath{\Delta}}R$ fit the measured ER cross section nicely, but not the individual decay-channel cross sections, which require the presence of qf effects, less so for asymmetric t-p combinations, and large (predicted) ff cross section.Conclusions: The calculated yields for hot-compact fragmentation path compared favorably with the observed asymmetric fission-mass distribution, resulting in mostly the same t-p reactions as are used in experiments. The best fitted $\mathrm{\ensuremath{\Delta}}R$ are found to be independent of the entrance channels, despite their very different cross sections, in conformity with our earlier works. The entrance-channel effects lead to the largest decay cross section for the most asymmetric and doubly magic t-p combination, the magicity taking over asymmetry for both the total ER and channel cross section. Furthermore, the variation of both ${P}_{\mathrm{CN}}$ and ${P}_{\mathrm{surv}}$ with ${E}^{*}$ fit in with the known systematic of other radioactive CN studied so far, thereby giving credence to our DCM analysis of $^{220}\mathrm{Th}^{*}$.