Theory of cluster radioactive decay and of cluster formation in nuclei

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 ${}_{}{}^{222\mathrm{-}224}{}_{}{}^{}\mathrm{Ra}$ 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.