Dynamical simulation of neutron-induced fission of uranium isotopes using four-dimensional Langevin equations

Four-dimensional Langevin equations have been suggested for the dynamical simulation of neutron-induced fission at low and medium excitation energies. The mass distribution of the fission fragments, the neutron multiplicity, and the fission cross section for the thermal and fast neutron-induced fission of ${}^{233}\mathrm{U},{}^{235}\mathrm{U}$, and ${}^{238}\mathrm{U}$ is studied by considering energy dissipation of the compound nucleus through the fission using four-dimensional Langevin equations combined with a Monte Carlo simulation approach. The calculated results using this approach indicate reasonable agreement with available experimental data.

Figure 1

Mass distribution of fragments in the thermal neutron-induced fission of ${}^{233}\mathrm{U}$. Experimental data [46] are denoted by the solid squares.

Figure 2

Mass distribution of fragments in the thermal neutron-induced fission of ${}^{235}\mathrm{U}$. Experimental data [47] are denoted by the solid squares.

Figure 3

Mass distribution of fragments in the fast neutron-induced fission of ${}^{238}\mathrm{U}$. Experimental data [2] are denoted by the solid squares.

Figure 4

Average multiplicity of emitted neutrons for ${}^{233}\mathrm{U}$ as a function of incident neutron energy. Experimental data [48] are denoted by the solid squares.

Figure 5

Average multiplicity of emitted neutrons for ${}^{235}\mathrm{U}$ as a function of the incident neutron energy. Experimental data [49] are denoted by the solid squares.

Figure 6

Average multiplicity of emitted neutrons for ${}^{238}\mathrm{U}$ as a function of the incident neutron energy. Experimental data [50] are denoted by the solid squares.

Figure 7

Fission cross section for the reaction $n_{\text{th}}+{}^{233}\mathrm{U}$ as a function of the incident neutron energy. The theoretical results are denoted by the dashed line and the experimental data [51] are denoted by the open squares.

Figure 8

Fission cross section for the reaction $n_{\text{th}}+{}^{235}\mathrm{U}$ as a function of the incident neutron energy. The theoretical results are denoted by the dashed line and the experimental data [52] are denoted by the open squares.

Figure 9

Fission cross section for the reaction $n+{}^{238}\mathrm{U}$ as a function of the incident neutron energy. The theoretical results are denoted by the dashed line and the experimental data [53] are denoted by the open squares.

Figure 10

Deformation dependence of the average potential energy for the reaction $n_{\text{th}}+{}^{235}\mathrm{U}$ as a function of the distance between two potential centers. The asymmetric and symmetric cases are denoted by the dashed and dotted lines, respectively.