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Register a new userA study of the almost sequential mechanism of true ternary fission
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Authors
R. B. Tashkhodjaev
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We consider the collinear ternary fission which is a sequential ternary decay with a very short time between the ruptures of two necks connecting the middle cluster of the ternary nuclear system and outer fragments. In particular, we consider the case where the Coulomb field of the first massive fragment separated during the first step of the fission produces a lower pre-scission barrier in the second step of the residual part of the ternary system. In this case, we obtain a probability of about $10^{-3}$ for the yield of massive clusters such as uclide[70]{Ni}, uclide[80-82]{Ge}, uclide[86]{Se}, and uclide[94]{Kr} in the ternary fission of uclide[252]{Cf}. These products appear together with the clusters having mass numbers of $A = 132$--$140$. The results show that the yield of a heavy cluster such as uclide[68-70]{Ni} would be followed by a product of $A = 138$--$148$ with a large probability as observed in the experimental data obtained with the FOBOS spectrometer at the Joint Institute for Nuclear Research. The third product is not observed. The landscape of the potential energy surface shows that the configuration of the Ni + Ca + Sn decay channel is lower about 12 MeV than that of the Ca + Ni + Sn channel. This leads to the fact, that the yield of Ni and Sn is large. The analysis on the dependence of the velocity of the middle fragment on mass numbers of the outer products leads to the conclusion that, in the collinear tripartition channel of uclide[252]{Cf}, the middle cluster has a very small velocity, which does not allow it to be found in experiments.
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The ternary cluster decay of heavy nuclei has been observed in several experiments with binary coincidences between two fragments using detector telescopes (the FOBOS-detectors, JINR, Dubna) placed on the opposite sides from the source of fissioning nuclei. The binary coincidences at a relative angle of 180$^0$ deg. correspond to binary fission or to the decay into three cluster fragments by registration of two nuclei with different masses (e.g.$^{132}$Sn,$^{52-48}$Ca,$^{68-72}$Ni). This marks a new step in the physics of fission-phenomena of heavy nuclei. These experimental results for the collinear cluster tripartition (CCT), refer to the decay into three clusters of comparable masses. In the present work we discuss the various aspects of this ternary fission (FFF) mode. The question of collinearity is analysed on the basis of recent publications. Further insight into the possible decay modes is obtained by the discussion of the path towards larger deformation, towards hyper-deformation and by inspecting details of the potential energy surfaces (PES). In the path towards the extremely deformed states leading to ternary fission, the concept of deformed shells is most important. At the scission configuration the phase space determined by the PESs leads to the final mass distributions. The possibility of formation of fragments of almost equal size ($Z_i$ = 32, 34, 32, for $Z$=98) and the observation of several other fission modes in the same system can be predicted by the PES. The PESs show pronounced minima and valleys, namely for several mass/charge combinations of ternary fragments, which correspond to a variety of collinear ternary fission (multi-modal) decays. The case of the decay of $^{252}$Cf(sf,fff) turns out to be unique due to the presence of deformed shells in the total system and of closed shells in all three nuclei in the decay.
We developed a three-center phenomenological model,able to explain qualitatively the recently obtained experimental results concerning the quasimolecular stage of a light-particle accompanied fission process. It was derived from the liquid drop model under the assumption that the aligned configuration, with the emitted particle between the light and heavy fragment, is reached by increasing continuously the separation distance, while the radii of the heavy fragment and of the light particle are kept constant. In such a way,a new minimum of a short-lived molecular state appears in the deformation energy at a separation distance very close to the touching point. This minimum allows the existence of a short-lived quasi-molecular state, decaying into the three final fragments.The influence of the shell effects is discussed. The half-lives of some quasimolecular states which could be formed in the $^{10}$Be and $^{12}$C accompanied fission of $^{252}$Cf are roughly estimated to be the order of 1 ns, and 1 ms, respectively.
Ternary fission of actinides probes the state of the nucleus at scission. Light clusters are produced in space and time very close to the scission point. Within the nonequilibrium statistical operator method, a generalized Gibbs distribution is constructed from the information given by the observed yields of isotopes. Using this relevant statistical operator, yields are calculated taking excited states and continuum correlations into account, in accordance with the virial expansion of the equation of state. Clusters with mass number $A le 10$ are well described using the nonequilibrium generalizations of temperature and chemical potentials. Improving the virial expansion, in-medium effects may become of importance in determining the contribution of weakly bound states and continuum correlations to the intrinsic partition function. Yields of larger clusters, which fail to reach this quasi-equilibrium form of the relevant distribution, are described by nucleation kinetics, and a saddle-to-scission relaxation time of about 7000 fm/c is inferred. Light charged particle emission, described by reaction kinetics and virial expansions, may therefore be regarded as a very important tool to probe the nonequilibrium time evolution of actinide nuclei during fission.
For the first time, we apply the temperature dependent relativistic mean field (TRMF) model to study the ternary fission of heavy nucleus using level density approach. The probability of yields of a particular fragment is obtained by evaluating the convolution integrals which employ the excitation energy and the level density parameter for a given temperature calculated within the TRMF formalism. To illustrate, we have considered the ternary fissions in 252Cf, 242Pu and 236U with fixed third fragment A3 = 48Ca, 20O and 16O respectively. The relative yields are studied for the temperatures T = 1, 2 and 3 MeV. For the comparison, the relative yields are also calculated from the single particle energies of the finite range droplet model (FRDM). In general, the larger phase space for the ternary fragmentation is observed indicating that such fragmentations are most probable ones. For T = 2 and 3 MeV, the Sn + Ni + Ca is the most probable combination for the nucleus 252Cf. However, for the nuclei 242Pu and 236U, the maximum fragmentation yields at T = 2 MeV differ from those at T = 3 MeV. For T = 3 MeV, the closed shell (Z = 8) light mass fragments with its corresponding partners has larger yield values. But, at T = 2 MeV Si/P/S are favorable fragments with the corresponding partners. It is noticed that the symmetric binary fragmentation along with the fixed third fragment for 242Pu and 236U are also favored at T = 1 MeV. The temperature dependence of the nuclear shape and the single particle energies are also discussed.
In highly dissipative collisions between heavy ions, the optimal conditions to investigate different de-excitation channels of hot nuclei such as evaporation, fission or multifragmentation are well known. One crucial issue remains the excitation energy region where fission gives way to multifragmentation. In this paper, the onset of multi-fragment exit channels is investigated in terms of sequential fission. For the first time, the dynamical approach based on solving Langevin transport equations in multidimensional collective coordinate space is used to follow the de-excitation of highly excited (up to E* =223-656 MeV) 248Rf compound nuclei. The sequential fission model we propose contains two steps: (1) time evolution of the compound nucleus up to either scission or residue formation, followed by (2) dynamical calculations of each primary fragment separately. This procedure allows to obtain from one to four cold fragments correlated with the light particles emitted during the de-excitation process. Experimental data measured with the INDRA detector for the 129Xe+ natSn reaction at beam energies 8, 12 and 15 MeV/nucleon provide strong constraints for this sequential fission scenario.
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