Optimum orientation versus orientation averaging description of cluster radioactivity

Abstract

While the optimum-orientation concept is frequently used in studies on cluster decays involving deformed nuclei, the orientation-averaging concept is used in most alpha decay studies. We investigate the different decay stages in both the optimum-orientation and the orientation-averaging pictures of the cluster decay process. For decays of 232,233,234U and 236,238Pu isotopes, the quantum knocking frequency and penetration probability based on the Wentzel–Kramers–Brillouin approximation are used to find the decay width. The obtained decay width and the experimental half-life are employed to estimate the clusters preformation probability. We found that the orientation-averaged decay width is one or two orders of magnitude less than its value along the non-compact optimum orientation. Correspondingly, the extracted preformation probability based on the averaged decay width increases with the same orders of magnitude compared to its value obtained considering the optimum orientation. The cluster preformation probabilities estimated by the two considered schemes are in more or less comparable agreement with the Blendowske–Walliser (BW) formula based on the preformation probability of α ( obtained from the orientation-averaging scheme. All the results, including the optimum-orientation ones, deviate substantially from the BW law based on that was estimated from the optimum-orientation scheme. To account for the nuclear deformations, it is more relevant to calculate the decay width by averaging over the different possible orientations of the participating deformed nuclei, rather than considering the corresponding non-compact optimum orientation.