An empirical relation for cluster decay preformation probability

Empirical relations for the preformation probability of cluster decay process in terms of the Q-value, mass asymmetry (η), mass number of the emitted cluster A2 is analyzed based on the discrepancy between the calculated and experimental half-lives of the cluster emitters. For the different empirical expressions considered corresponding to different physical quantities the preformation probability for the complete binary breakup of 226Ra is calculated and the obtained results are compared with the preformed cluster model calculation (P0(PCM)) and another calculation in which the overlapping penetration probability is treated as the preformation probability (P0(μ)). Our empirical results for the use of Q-value compare well with P0(μ). Results due to the use of Q and its powers along with the combination of mass number A2 of the cluster emitted, and mass asymmetry η, reveal that preformation factor depends strongly on Q-value rather than A2 and η. Calculated half-lives of different cluster decays for the use of empirical P0 values are found to be in good agreement with the experimental values. (author)