Collinear versus triangular geometry: A ternary fission study

We study in this work the preference of the arrangements of fragments leading to ternary fission. Earlier experimental investigations on this subject have established the fact that the emission of a third particle happens in a direction perpendicular to the direction of the fission axis. Recently, within the missing mass approach, it has been reported that for fragments of comparable masses, the so-called collinear cluster tripartition (CCT), collinear emission of the fragments occurs. The ternary potential energy surface (PES) of three-body fragmentation of $^{252}\mathrm{Cf}$ is studied. The PESs are calculated for the fragment arrangements starting from a collinear configuration to a triangular configuration by varying the angle between the end fragments with respect to the fragment positioned in the middle. Furthermore, the role of the positioning of the three fragments is analyzed. Our results indicate that there is a clear preference for an arrangement in which the lightest fragment is positioned in the middle. Furthermore, for all possible third fragments, collinear geometry is found to be favored over orthogonal geometry.