Role of higher-multipole deformations in exoticC14cluster radioactivity

Abstract

We have studied nine cases of spontaneous emission of $^{14}\mathrm{C}$ clusters in the ground-state decays of the same number of parent nuclei from the trans-lead region, specifically from $^{221}\mathrm{Fr}$ to $^{226}\mathrm{Th}$, using the preformed cluster model (PCM) of Gupta and collaborators, with choices of spherical, quadrupole deformation (${\ensuremath{\beta}}_{2}$) alone, and higher-multipole deformations (${\ensuremath{\beta}}_{2}$, ${\ensuremath{\beta}}_{3}$, ${\ensuremath{\beta}}_{4}$) with cold ``compact'' orientations ${\ensuremath{\theta}}^{c}$ of decay products. The calculated $^{14}\mathrm{C}$ cluster decay half-life times are found to be in nice agreement with experimental data only for the case of higher-multipole deformations (${\ensuremath{\beta}}_{2}$-${\ensuremath{\beta}}_{4}$) and ${\ensuremath{\theta}}^{c}$ orientations of cold elongated configurations. In other words, compared to our earlier study of clusters heavier than $^{14}\mathrm{C}$, where the inclusion of ${\ensuremath{\beta}}_{2}$ alone, with ``optimum'' orientations, was found to be enough to give the best comparison with data, here for $^{14}\mathrm{C}$ cluster decay the inclusion of higher-multipole deformations (up to hexadecapole), together with ${\ensuremath{\theta}}^{c}$ orientations, is found to be essential on the basis of the PCM. Interestingly, whereas both the penetration probability and assault frequency work simply as scaling factors, the preformation probability is strongly influenced by the order of multipole deformations and orientations of nuclei. The possible role of $Q$ value and angular-momentum effects are also considered in reference to $^{14}\mathrm{C}$ cluster radioactivity.