Role of higher-multipole deformations and noncoplanarity in the decay of the compound nucleus Th*220 within the dynamical cluster-decay model

Abstract

Background: The formation and decay of the $^{220}\mathrm{Th}^{*}$ compound nucleus (CN) formed via some entrance channels $(^{16}\mathrm{O}+^{204}\mathrm{Pb},^{40}\mathrm{Ar}+^{180}\mathrm{Hf},^{48}\mathrm{Ca}+^{172}\mathrm{Yb},^{82}\mathrm{Se}+^{138}\mathrm{Ba})$ at near barrier energies has been studied within the dynamical cluster-decay model (DCM) [Hemdeep et al. Phys. Rev. C 95, 014609 (2017)], for quadrupole deformations $({\ensuremath{\beta}}_{2i})$ and ``optimum'' orientations $({\ensuremath{\theta}}^{\mathrm{opt}})$ of the two nuclei or decay fragments lying in the same plane (coplanar nuclei, $\mathrm{\ensuremath{\Phi}}={0}^{\ensuremath{\circ}})$.Purpose: We aim to investigate the role of higher-multipole deformations, the octupole $({\ensuremath{\beta}}_{3i})$ and hexadecupole $({\ensuremath{\beta}}_{4i})$, and ``compact'' orientations $({\ensuremath{\theta}}_{ci})$ together with the noncoplanarity degree of freedom $({\mathrm{\ensuremath{\Phi}}}_{c})$ in the noncompound nucleus (nCN) cross section, already observed in the above mentioned study with quadrupole deformations $({\ensuremath{\beta}}_{2i})$ alone, the $\mathrm{\ensuremath{\Phi}}={0}^{\ensuremath{\circ}}$ case.Methods: The dynamical cluster-decay model (DCM), based on the quantum mechanical fragmentation theory (QMFT), is used to analyze the decay channel cross sections ${\ensuremath{\sigma}}_{xn}$ for various experimentally studied entrance channels. The parameter ${R}_{a}$ (equivalently, the neck length $\mathrm{\ensuremath{\Delta}}R$ in ${R}_{a}={R}_{1}+{R}_{2}+\mathrm{\ensuremath{\Delta}}R)$, which fixes both the preformation and penetration paths, is used to best fit both unobserved $(1n,2n)$ and observed $(3n$--$5n)$ decay channel cross sections, keeping the root-mean-square (r.m.s) deviation to the minimum, which allows us to predict the nCN effects, if any, and fusion-fission (ff) cross sections in various reactions at different CN excitation energies ${E}^{*}$.Results: For the decay of CN $^{220}\mathrm{Th}^{*}$, the mass fragmentation potential $V({A}_{i})$ and preformation yields ${P}_{0}({A}_{i})$ show an asymmetric fission mass distribution, in agreement with one observed in experiments, independent of adding or not adding $({\ensuremath{\beta}}_{3i},{\ensuremath{\beta}}_{4i})$, and irrespective of large changes (by 36\ifmmode^\circ\else\textdegree\fi{} and 34\ifmmode^\circ\else\textdegree\fi{}), respectively, in ``compact'' orientations ${\ensuremath{\theta}}_{ci}$ and noncoplanarity ${\mathrm{\ensuremath{\Phi}}}_{c}$, and also in the potential energy surface $V({A}_{i})$ in light mass $(1n$--$5n)$ decays. Whereas the $3n$- and $5n$-decay channels fit nearly exactly, i.e., they are always the pure CN decays, the $4n$-decay channel shows the presence of large $(\ensuremath{\sim}95%)$ nCN content whose magnitude in every case remains the same within $l1%$ and hence does not get modified, in contrast to our earlier studies of other CN. Also, the near constancy of best fitted ${R}_{a}\phantom{\rule{4pt}{0ex}}(\ensuremath{\equiv}\mathrm{\ensuremath{\Delta}}R)$ with ${E}^{*}$, and with an upper limiting value for reactions with magic nuclei as reaction partner(s), independent of the entrance channel nuclei, allows us to predict the decay channel cross sections ${\ensuremath{\sigma}}_{xn},x=3--5$ for $^{16}\mathrm{O}+^{204}\mathrm{Pb}$ reaction, whose sum $(={\ensuremath{\sum}}_{3}^{5}{\ensuremath{\sigma}}_{xn})$ fits the observed ${\ensuremath{\sigma}}_{\mathrm{ER}}$ data nicely. Also, the variations of CN fusion/formation probability ${P}_{CN}$ and survival probability ${P}_{\mathrm{surv}}$ follow the required systematic behavior, giving credence to our DCM analysis.Conclusions: With the inclusion of higher-multipole deformations and ``compact'' noncoplanarity degree of freedom $({\mathrm{\ensuremath{\Phi}}}_{c}\ensuremath{\ne}0)$, the results of our above-mentioned earlier study, using quadrupole deformation $({\ensuremath{\beta}}_{2i})$ alone for coplanar $({\mathrm{\ensuremath{\Phi}}}_{c}=0)$ nuclei, remain the same; i.e., of the measured $3n$--$5n$ decay channels of CN $^{220}\mathrm{Th}^{*}$, the $3n$ and $5n$ decays are always pure CN decays and the $4n$ decay is mainly of nCN content ${\ensuremath{\sigma}}_{n\mathrm{CN}}$, whose magnitude also remains constant (within $l1%)$ under all approximations. Furthermore, the upper limiting value of the linear dependence of first turning point ${R}_{a}$ on ${E}^{*}$ is shown to be a better choice for predicting the decay channel cross sections ${\ensuremath{\sigma}}_{xn}$ for reactions like $^{16}\mathrm{O}+^{204}\mathrm{Pb}$ using magic nuclei, whose experimental determination will be a good test of our model.