![]() Brosa 17 introduced several fission modes associating TKE with the shapes (or length) of the nuclei at scission. Total Kinetic Energy is calculated from the sum of Coulomb repulsion and pre-scission kinetic energy. Fission mass yield is calculated from the statistics of fragment mass given by the value of α at scission. The main observables from Langevin calculation are the fission fragment mass yield and TKE. Our aim is to look for the explanation of the transition from the double peak fragment yield of 256Fm to single peak fragment of 258Fm and at the same time, to explain the anomalous increase of 〈TKE〉 in the said transition. In the present work, we use the 4-D Langevin approach with macroscopic transport coefficients for studying the fragment mass and TKE distributions of various fissioning system from Uranium to Rutherfordium. We believe that the more commonly seen transition of fragment mass yield that occurred from 256Fm to 258Fm and its recovery at larger compound mass (or charge) are correlated to the anomalous transition of the TKE seen from the same nuclei. Unfortunately, so far we are stuck with macroscopic transport coefficients when we are using 4-D Langevin equations. Thus for 4-D Langevin approach, the dynamical coordinates are ( z 0/ R 0, δ 1, δ 2, α) to represent the elongation, right fragment tip shape, left fragment tip shape and mass asymmetry. At present we are able to introduce an additional degree of freedom. We assume in 3-D Langevin approach the shape of the fission fragment tips of the left and right fragments to be the same ( δ = δ 1 = δ 2). In 3-D Langevin approach, the dynamical variables are ( z 0/ R 0, δ, α) representing the elongation, fragment tip deformation and mass asymmetry respectively. It seems that the improvements of TKE( A) is due to the strong relationship between the elongation of the fissioning system at the scission point and the TKE 19. Thus within the two-center shell model shape parameterization we 18 took into account an additional degree of freedom by allowing the independent deformation of fission fragment tips, and this allowed us to improve TKE( A) even though we were only able to use it in conjunction with macroscopic transport coefficients. However, there was no clear explanation why the super-short fission modes are preferred at all instead of the super-long fission modes as was common for all the neighboring actinides. 15 even proposed that these transition occur as the fissioning nucleus splits into double magic fragments and the high TKE seen for 258Fm are due to the preference for super-short fission modes 17. 14 for 258Fm and were further corroborated by later experiments 15, 16. It was first observed experimentally by Hoffman et al. These two transitions, in terms of the anomalous changes in the fragment mass yield and TKE, are what we wish to explain. There are some deficiencies with the 3-D Langevin model because we were unable to observe the expected transition from double peak fission yield of 256Fm to the single peak fission yield 258Fm, and the TKE as a function fragment mass TKE( A) are rather poor. ![]() With it, we see the average total kinetic energy 〈TKE〉 decreasing with larger excitation energy E x and the influence of pairing at smaller E x 3. Recently, we have introduced the microscopic mass and friction tensors to improve the calculations of 3-D Langevin equation 7 instead of the usual macroscopic mass and friction tensors 11– 13. The study of fission by Langevin equation in recent years has had some considerable success 1– 10, especially in unraveling the physics involved in the fission process. More specifically, since we kept the shape model parameters unchanged over the entire mass region, we conclude that the correlated twin transition emerge naturally from the dynamics in 4-D potential energy surface. These correlated “twin transitions” have been known empirically by Darleane Hoffman and her group back in 1989, but for the first time we have given a clear explanation in terms of a dynamical model of nuclear fission. The dominant fission modes on the other hand, are persistently asymmetric except for 258Fm, 259Fm and 260Md when the dominant fission mode suddenly becomes symmetric although it returns to the asymmetric mode around 256No. ![]() ![]() As a result, we found that the symmetric mode makes a sudden transition from super-long to super short fission mode around 254Es. We have decomposed to symmetric and asymmetric modes the mass-TKE fission fragment distributions calculated by 4-dimensional Langevin approach and observed how the dominant fission mode and symmetric mode change as functions of Z 2 / A 3 of the fissioning system in the actinides and trans-actinide region. ![]()
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