A three-cluster model is proposed to explain the particle-accompanied binary fission of radioactive nuclei. The model is developed as an extension of the preformed cluster model of Gupta and collaborators. The advantage of this model is that, for a fixed third fragment, we can calculate the fragmentation potential minimized in charge coordinate. For our study we chose the various neutron-deficient to neutron-rich californium nuclei, whose analysis reveals that the closed-shell effect of any one of the fragments in ternary fragmentation presents itself as the most favorable configuration to be observed. As one goes from a neutron-deficient to a neutron-rich californium isotope, the role of the neutron closed shell associated with any one of the preferred fragments changes to that of the proton closed shell, and for very neutron rich isotopes of californium the presence of a double closed shell nucleus enhances the decay probability. The quadrupole deformation of the light fragment $(A_2)$ associated with the preferred configuration in the symmetric mass region also has a transition from positive to negative deformation as one goes from neutron-deficient to neutron-rich californium isotopes. The calculated relative yields of different fragmentation channels are compared with the available experimental yields for ${}^{252}\mathrm{Cf}$.

• Received 16 July 2008

DOI:https://doi.org/10.1103/PhysRevC.79.024610