Ternary fission through compact and creviced shapes

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Abstract
Using a family of compact and creviced shapes, the authors have calculated the deformation energy of the liquid-drop model and included the nuclear proximity energy. This family of shapes covers the whole deformation range from the sphere to three equal tangential spherical fragments. Simple analytical formulae are given. Double-humped ternary fission barriers are predicted for heavy nuclei: the inner barrier has essentially a microscopic origin while the outer one is a scission barrier governed mostly by the balance between Coulomb and nuclear forces. For Z>or approximately=102, the ternary scission barrier is lower than the binary scission barrier but it is positioned further out. For Z>or approximately=110-115, ternary fission seems as likely as binary fission. Therefore, there appears to be another exit channel for superheavy nuclei, which further reduces the probability of existence of such superheavy elements. The ternary and binary fission barriers become almost identical for the heaviest nuclear systems, as for example in the reaction 238U+238U. The translational kinetic energy of the three fragments agrees well with the experimental data for the U+Ne and U+Ar reactions.