First observation of spontaneous fission and search for cluster decay of ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$

We present results of a long-term search for cluster (neon) decay and spontaneous fission of ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ performed at Gran Sasso Underground Laboratory with nuclear track detectors. We found a lower limit for the partial half-life for ${}_{}{}^{24\mathrm{-}26}{}_{}{}^{}\mathrm{Ne}$ decay, ${\mathit{T}}_{1/2}$>1.57×${10}^{29}$ s and a partial half-life for spontaneous fission ${\mathit{T}}_{1/2}$=3.84×${10}^{28}$ s=1.22×${10}^{21}$ yr. These results are compared with the available theoretical predictions and the experimental systematics for cluster decay and spontaneous fission.