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 (eta), mass number of the emitted cluster A(2) 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 Ra-226 is calculated and the obtained results are compared with the preformed cluster model calculation (P-0(PCM)) and another calculation in which the overlapping penetration probability is treated as the preformation probability (P-0(mu)). Our empirical results for the use of Q-value compare well with P-0(mu). Results due to the use of Q and its powers along with the combination of mass number A(2) of the cluster emitted, and mass asymmetry eta, reveal that preformation factor depends strongly on Q-value rather than A(2) and eta. Calculated half-lives of different cluster decays for the use of empirical P-0 values are found to be in good agreement with the experimental values.