The Dependency on the Dissipation Tensor of Multi-modal Nuclear Fission

Abstract

In the study of the fission of actinide nuclei at low excitation energies including the spontaneous fission, it was found that the fragment mass distribution and the total kinetic energy (TKE) distribution consist of more than one component, in contrast to the simple single peak structure that is found in the fission at high excitation energies. 1– 6 This phenomenon is attributed to the existence of more than one fission path and is called the multi-modal fission. The mass and TKE distributions depend sensitively on the excitation energy and the position of the peaks of the mass distribution suggests the influence of the closed shell structure of the fragments. Therefore, it is supposed that the microscopic energy plays an important role for the manifestation of this phenomenon. It is a great challenge for us to understand this phenomenon in terms of nuclear many-body dynamics. Several authors studied the potential energy surface (PES) including the microscopic energy in a multi-dimensional parameter space that describes various nuclear shapes; one can deduce the possible fission paths by studying the location of the saddle points and the fission valleys in multi-dimensional parameter space. 7 With this method, they could explain the general trend of the position of the peaks of the mass distribution. The dynamical point of view is necessary to progress the study of the fission mode. We have applied the Langevin approach to the study of the fission modes in uranium nuclei and in fermium nuclei. 8–10 We studied the mass and TKE distributions and demonstrated that we can decompose the fission events into several components by tracing the Langevin trajectories. We also studied the isotope dependence and the excitation energy dependence of the fission mode. 8–10 In the previous studies, we adopted the wall-and-window type one-body friction as the dissipation mechanism of the nuclear fission dynamics. The validity of this dissipation mechanism has been demonstrated by one of the authors (T.W.) who studied the dissipation tensor dependence of the pre-scission neutron multiplicity and the mean TKE. 11–14 From the comparison of the results of the dynamical calculation with experimental data, they excluded the possibility of the two-body type dissipation to be the dominant mechanism by showing that it cannot reproduce the pre-scission neutron data and the TKE data simultaneously. On the other hand, they showed that the wall-and-window type one-body friction can reproduce both data reasonably well and concluded that it is a reasonable model for the dissipation mechanism of nuclear fission. There are other models that are of one-body nature, e.g. surface-plus-window formula, modified wall-and-window formula and chaos weighted wall formula. 15–17 Though there were no free parameters in the original derivation of the one-body friction, 18, 19 the strength has been modified frequently in order to reproduce some experimental data. For example, in the study of the light particle evaporation and the mass distribution, Schmitt et al. used the strength as a free parameter. 17 The modification itself should be acceptable when we take account of the simplicity of the model; it is a macroscopic model without any microscopic effect and it has no dependence on the temperature. However, when one modifies the strength of the nuclear dissipation just to reproduce only one physical quantity, it might be inappropriate to conclude that the deduced strength has definite physical meanings. It may reflect the other effects completely different from the dissipation, like the insufficiency of the model space. It is very important to compare many (at least more than one) physical quantities at the same time. Among the physical quantities that are measured in nuclear fission, the TKE and mass distributions are well investigated experimentally in many cases. In this study, we use these quantities to discuss the dissipation dependence of the fission modes. It is shown that the TKE distribution is, as was expected, directly connected to the strength of the dissipation and we can put some constraints on the strength of the dissipation. Furthermore, it is shown that the mass distribution changes rather drastically when one uses different models for the dissipation mechanism. These results demonstrate the importance and the usefulness of the dynamical approach to the study of the fission mode. Section 2 gives a concise description of our framework. Results are shown in Sec. 3 concerning the fission of 264 Fm nucleus at Ex = 20 MeV. Summary is given in Sec. 4. 2. Methods