Role of the higher static deformations of fragments in the cold binary fission of ${}^{252}\mathrm{Cf}$

We study the binary cold fission of ${}^{252}$Cf in the frame of a cluster model where the fragments are born to their respective ground states and interact via a double-folded potential with deformation effects taken into account up to multipolarity $\lambda =4\mathrm{}$. The preformation factors were neglected. In the case when the fragments are assumed to be spherical or with ground-state quadrupole deformation, the $Q$-value principle dictates the occurrence of a narrow region around the double magic ${}^{132}$Sn, like in the case of cluster radioactivity. When the hexadecupole deformation is turned on, an entire mass region of cold fission in the range 138–156 for the heavy fragment arise, in agreement with the experimental observations. This fact suggests that in the above-mentioned mass region, contrary to the usual cluster radioactivity where the daughter nucleus is always a neutron/proton (or both) closed shell or nearly closed shell spherical nucleus, the clusterization mechanism seems to be strongly influenced by the hexadecupole deformations rather than the $Q$ value.