High-statistics study of cluster radioactivity fromU233

Using a track-recording phosphate glass detector with a standard deviation ${\mathrm{\sigma }}_{\mathit{Z}}$=0.24 charge unit, we have collected ∼${10}^3$ tracks of energetic Ne clusters emitted from ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$ and have obtained a branching ratio B(Ne/α)=(7.2±0.5±0.7)×${10}^{\mathrm{-}13}$. This is consistent with the previous value of (7.5±2.5)×${10}^{\mathrm{-}13}$ which was based on 16 events. The larger of our two errors is that estimated to be due to uncertainty in absorption in our source. No candidate for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Mg}$ emission survived our energy and angle cuts, from which we infer a branching ratio B(Mg/Ne)<0.0018 (90% C.L.). The smallness of the Mg branch is inconsistent with predictions of the quantitatively most successful models of cluster emission heretofore used. The inconsistency is removed if the cluster emission models are modified by taking into account the Nilsson states of the parent and daughter nuclei for the two decay modes.