Dynamics of competing α and cluster radioactive decays within the collective clusterization approach

Cluster radioactivity is the phenomena of heavy radioactive parent nuclei emitting clusters (heavier than alpha particle, α), spontaneously. Sandulescu et al. theoretically found it in 1980, and Rose and Jones empirically confirmed it in 1984, for the ²²³Ra nucleus from which ¹⁴C cluster was formed. In other words, it is the process of a cluster forming in the mother nuclei and then passing over the barrier. The daughter nuclei in these decays are always ²⁰⁸Pb or nuclei that are close by. The model that we utilize to explain the decay process theoretically is Gupta and collaborators' Preformation Cluster Decay Models (PCM) based on Quantum Mechanical Fragmentation Theory (QMFT). Previous research have used PCM to study the influence of deformations and orientations in the radioactivity of the ²⁰⁸Pb-daugther cluster. Now, in this study, we explore the competing aspects of alpha radioactivity and ²⁰⁸Pb daughter cluster radioactivity using fragmentation potential, preformation probability, scattering potential, and penetration probability in the decay of radioactive nuclei ²²²Ra, ²²⁶Th, ²²⁸Th, ²³¹Pa, ²³⁰U, and ²³²U systems with always ²⁰⁸Pb as daughter and ¹⁴C, ¹⁸O, ²⁰O, ²³F, ²²Ne, and ²⁴Ne cluster nuclei emitted correspondingly. The PCM calculated data has a fair comparison with the experimental data for both α cluster decay and ²⁰⁸Pb daughter decay are further improved with the inculcation of the deformation and orientation effects of the nuclei, particularly for the α cluster decays. The results for the latter case are available with the inclusion of orientation effects