Molecular Collective Vibrations in the Ternary Neutronless Fission of $^{252}$Cf

Based on a recent experimental finding which may suggest the existence of a tri-nuclear molecular structure before the cold ternary fragmentation of $^{252}$Cf takes place, we solved the eigenvalue problem of a certain class of vibrations which are very likely to occur in these molecules. These oscillations are the result of the joined action of rotations of the heavier fragments and the transversal vibrations of the lighter spherical cluster with respect to the fission axis. In the calculation of the interaction between the heavier fragments we took into account higher multipole deformations, including the hexadecupole one, and introduced a repulsive nuclear part to insure the creation of a potential pocket in which a few molecular states can be accommodated. The possibility to observe the de-excitation of such states is discussed in connection with the molecular life-time.