New look at Geiger-Nuttall law and α clustering of heavy nuclei

The Geiger-Nuttall (GN) law of alpha decay is commonly explained in terms of the quantum tunneling phenomenon. In this study, we show that such an explanation is actually not enough regarding the alpha particle clustering. Such a conclusion is drawn after exploring the involved coefficients of the GN law based on the conventional description of alpha decay, namely the formation of an a cluster and its subsequent penetration. The specific roles of the two former processes, in the GN law, manifest themselves via the systematical analysis of the calculated and experimental alpha decay half-lives versus the decay energies across the Z = 82 and N = 126 shell closures. The alpha-cluster preformation probability is then found to behave in a GN-like pattern. This previously ignored point is explicitly demonstrated as the product of an interplay between the mean-field and pairing effect, which in turn reveals the structural influence on the formation of the alpha cluster in a simple and clear manner. In addition to providing an effective method to evaluate the amount of surface alpha clustering in heavy nuclei, the present conjecture supports other theoretical treatments of the alpha preformation probability.

Automated summary

The Geiger-Nuttall law of alpha decay is commonly explained by quantum tunneling, but this study shows that this explanation alone is insufficient to explain alpha particle clustering. By analyzing the coefficients involved in the law, it is revealed that the preformation of alpha clusters and their subsequent penetration play specific roles in the Geiger-Nuttall law. This previously overlooked point is attributed to an interplay between mean-field and pairing effects, shedding light on the structural influence on alpha cluster formation.