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Neutronless $^{10}$be-Accompanied Ternary Fission of $^{252}$Cf}

A new type of decay corresponding to the neutronless $^{10}$Be-accompanied fragmentation of $^{252}$Cf is studied. We employ a cluster model similar to the model used for the description of cluster radioactivity. No preformation factors were considered. The ternary relative isotopic yields were calculated as the ratio of the penetrability of a given ternary fragmentation over the sum of penetrabilities of all possible ternary neutronless fragmentations. The corresponding barriers between the light and heavy fragment and between the $^{10}$Be cluster and the two heavier fragments were computed with the help of a double folding potential generated by M3Y-$NN$ effective interaction and realistic fragment ground state deformations. Also, we studied the influence of the fragment excitation energies on the yields, by including the level densities and the $β$-stretching of the fragments. The new phenomenon could be experimentally observed by the triple gamma coincidence technique between the fragments and $^{10}$Be.