Abstract
A new model is proposed for the mechanism of cluster formation and then penetration of the confining nuclear interaction barrier in radioactive nuclei. The cluster formation is treated as a quantum-mechanical fragmentation process and the WKB penetrability is found analytically. Applications of the model are made to $^{14}\mathrm{C}$ decay of $^{222\mathrm{\ensuremath{-}}224}\mathrm{Ra}$ and $^{24}\mathrm{Ne}$ decay of $^{232}\mathrm{U}$. The branching ratio for $^{14}\mathrm{C}$ decay of $^{232}\mathrm{U}$ is also calculated and is found to be incredibly small as compared to that for its $^{24}\mathrm{Ne}$ decay.
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