Unified formula of half-lives for α decay and cluster radioactivity

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.