Spectroscopic factors of cluster decays in an algebraic cluster model

We propose a new ansatz for the cluster spectroscopic factor in an algebraic cluster model. The parameters of the ansatz are fitted to the experimental and Blendowske-Walliser values of the spectroscopic factor for light emitted clusters and then applied to predict the spectroscopic factors for heavier clusters up to the spontaneous cold fission in two equal fragments. We show that due to the cluster and daughter shell structure, the calculated spectroscopic factors are strongly deviating from the empirical law for increasing cluster number. The observed gap between the alpha-like and cluster-like fission on one side and the spontaneous cold fission on the other side for actinides is explained by the moderate increase of spectroscopic factors, as computed in the present Letter, combined with the simultaneous decrease of the barriers when approaching symmetric mass division. This conclusion is inferred by computing the half-lives of cluster emission and spontaneous cold fission for 234U