Dynamics of neutron-induced fission of ${}^{235}\mathrm{U}$ using four-dimensional Langevin equations

Background: Langevin equations have been suggested as a key approach to the dynamical analysis of energy dissipation in excited nuclei, formed during heavy-ion fusion-fission reactions. Recently, a few researchers theoretically reported investigations of fission for light nuclei in a low excitation energy using the Langevin approach, without considering the contribution of pre- and post-scission particles and $\gamma$-ray emission.

Purpose: We study the dynamical evolution of mass distribution of fission fragments, and neutron and $\gamma$-ray multiplicity for ${}^{236}\mathrm{U}$ as compound nuclei that are constructed after fusion of a neutron and ${}^{235}\mathrm{U}$.

Method: Energy dissipation of the compound nucleus through fission is calculated using the Langevin dynamical approach combined with a Monte Carlo method. Also the shape of the fissioning nucleus is restricted to “funny hills” parametrization.

Results: Fission fragment mass distribution, neutron and $\gamma$-ray multiplicity, and the average kinetic energy of emitted neutrons and $\gamma$ rays at a low excitation energy are calculated using a dynamical model, based on the four-dimensional Langevin equations.

Conclusions: The theoretical results show reasonable agreement with experimental data and the proposed dynamical model can well explain the energy dissipation in low energy induced fission.

Figure 1

Time evolution of mass distribution of fission fragments of ${}^{236}\mathrm{U}$ at $E^{*}=20$ MeV. Experimental data [23] are indicated by solid squares.

Figure 2

Average initial fission fragment spin ($\hslash$) of ${}^{236}\mathrm{U}$ at $E^{*}=20$ MeV as a function of the fragment mass. Experimental data of Durell [24], Aumann et al. [25], and Naik et al. [26], are denoted by solid squares, triangles, and circles, respectively.

Figure 3

Time scale of fission of ${}^{236}\mathrm{U}$ nucleus as a function of the viscosity coefficient ($\hslash /{\text{fm}}^3$).

Figure 4

The energy carried away by emitted neutrons in the fission of ${}^{236}\mathrm{U}$ as a function of fission fragment mass. The theoretical result of the present approach and experimental data of Nishio et al. [28] are denoted by the solid line and open squares, respectively.

Figure 5

The energy carried away by emitted $\gamma$ rays in the fission of ${}^{236}\mathrm{U}$ as a function of fission fragment mass distribution. The theoretical result of the present approach and experimental data of Pleasonton et al. [27] are denoted by the solid line and open squares, respectively.

Figure 6

Average prompt fission $\gamma$-ray multiplicity for ${}^{236}\mathrm{U}$ at $E^{*}=20$ MeV as a function of the fragment mass. Experimental data of Pleasonton et al. [27] and Albinsson et al. [29] are denoted by open squares and circles, respectively.

Figure 7

Average prompt fission neutron multiplicity for ${}^{236}\mathrm{U}$ at $E^{*}=20$ MeV as a function of the fragment mass. Experimental data of Vorobyev et al. [30] are denoted by open squares.