Microscopic description of cluster radioactivity in actinide nuclei

Cluster radioactivity is the emission of a fragment heavier than $\alpha$ particle and lighter than mass 50. The range of clusters observed in experiments goes from $^{14}$C to $^{32}$Si while the heavy mass residue is always a nucleus in the neighborhood of the doubly-magic $^{208}$Pb nucleus. Cluster radioactivity is described in this paper as a very asymmetric nuclear fission. A new fission valley leading to a decay with large fragment mass asymmetry matching the cluster radioactivity products is found. The mass octupole moment is found to be more convenient than the standard quadrupole moment as the parameter driving the system to fission. The mean-field HFB theory with the phenomenological Gogny interaction has been used to compute the cluster emission properties of a wide range of even-even actinide nuclei from $^{222}$Ra to $^{242}$Cm, where emission of the clusters has been experimentally observed. Computed half-lives for cluster emission are compared with experimental results. The noticeable agreement obtained between the predicted properties of cluster emission (namely, clusters masses and emission half-lives) and the measured data confirms the validity of the proposed methodology in the analysis of the phenomenon of cluster radioactivity. A continuous fission path through the scission point has been described using the neck parameter constraint.