Background: The formation and decay of the ${}^{220}\mathrm{Th}^{*}$ compound nucleus (CN) formed via some entrance channels $\left({}^{16}\mathrm{O}+{}^{204}\mathrm{Pb},{}^{40}\mathrm{Ar}+{}^{180}\mathrm{Hf},{}^{48}\mathrm{Ca}+{}^{172}\mathrm{Yb},{}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}\right)$ 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 $\left({\beta }_{2i}\right)$ and “optimum” orientations $\left({\theta }^{\mathrm{opt}}\right)$ of the two nuclei or decay fragments lying in the same plane (coplanar nuclei, $\mathrm{\Phi }=0^{\circ })$.

Purpose: We aim to investigate the role of higher-multipole deformations, the octupole $\left({\beta }_{3i}\right)$ and hexadecupole $\left({\beta }_{4i}\right)$, and “compact” orientations $\left({\theta }_{ci}\right)$ together with the noncoplanarity degree of freedom $\left({\mathrm{\Phi }}_c\right)$ in the noncompound nucleus (nCN) cross section, already observed in the above mentioned study with quadrupole deformations $\left({\beta }_{2i}\right)$ alone, the $\mathrm{\Phi }=0^{\circ }$ 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 ${\sigma }_{xn}$ for various experimentally studied entrance channels. The parameter $R_a$ (equivalently, the neck length $\mathrm{\Delta }R$ in $R_a=R_1+R_2+\mathrm{\Delta }R)$, which fixes both the preformation and penetration paths, is used to best fit both unobserved $\left(1n,2n\right)$ 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 $\left({\beta }_{3i},{\beta }_{4i}\right)$, and irrespective of large changes (by 36° and 34°), respectively, in “compact” orientations ${\theta }_{ci}$ and noncoplanarity ${\mathrm{\Phi }}_c$, 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 $\left(\sim 95\%\right)$ nCN content whose magnitude in every case remains the same within $<1\%$ and hence does not get modified, in contrast to our earlier studies of other CN. Also, the near constancy of best fitted $R_a\left(\equiv \mathrm{\Delta }R\right)$ 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 ${\sigma }_{xn},x=3–5$ for ${}^{16}\mathrm{O}+{}^{204}\mathrm{Pb}$ reaction, whose sum $\left(={\sum }_3^5{\sigma }_{xn}\right)$ fits the observed ${\sigma }_{\mathrm{ER}}$ 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 $\left({\mathrm{\Phi }}_c\ne 0\right)$, the results of our above-mentioned earlier study, using quadrupole deformation $\left({\beta }_{2i}\right)$ alone for coplanar $({\mathrm{\Phi }}_c=0)$ 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 ${\sigma }_{n\mathrm{CN}}$, whose magnitude also remains constant (within $<1\%)$ 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 ${\sigma }_{xn}$ for reactions like ${}^{16}\mathrm{O}+{}^{204}\mathrm{Pb}$ using magic nuclei, whose experimental determination will be a good test of our model.

• Received 8 March 2018
• Revised 4 April 2018

DOI:https://doi.org/10.1103/PhysRevC.97.044623