In view of the fact that $\alpha$ decay and cluster radioactivity are physically analogical processes, we propose a general formula of half-lives and decay energies for $\alpha$ decay and cluster radioactivity. This new formula is directly deduced from the WKB barrier penetration probability with some approximations. It is not only simple in form and easy to see the physical meanings but also shows excellent agreement with the experimental values. Moreover, the difference between two sets of parameters to separately describe $\alpha$ decay and cluster radioactivity is small. Therefore, we use only one set of adjustable parameters to simultaneously describe the $\alpha$ decay and cluster radioactivity data for even-even nuclei. The results are also satisfactory. This indicates that this formula successfully combines the phenomenological laws of $\alpha$ decay and cluster radioactivity. We expect it to be a significant step toward a unified phenomenological law of $\alpha$ decay and cluster radioactivity.

• Received 1 August 2008

DOI:https://doi.org/10.1103/PhysRevC.78.044310