Role of asymmetry parameter and dissipation coefficient of $K$ coordinate in angular distribution of fission fragments

Using multidimensional Langevin equations, we have calculated the angular distribution of fission fragments with nonconstant values for the dissipation coefficient of the $K$ coordinate (the projection of the total angular momentum $I$ onto the symmetry axis of the fissioning nuclear system) for symmetry and asymmetry fission. We investigated the relaxation time of the $K$ coordinate, ${\tau }_K$, as a function of scission criteria and the asymmetry parameter. Calculations are done for ${}^{16}\mathrm{O}+{}^{232}\mathrm{Th}\to {}^{248}\mathrm{Cf}$, ${}^{16}\mathrm{O}+{}^{238}\mathrm{U}\to {}^{254}\mathrm{Fm}$, and ${}^{16}\mathrm{O}+{}^{248}\mathrm{Cm}\to {}^{264}\mathrm{Rf}$ reactions and obtained results are compared with available experimental data. Our calculations with nonconstant values of the $K$ coordinate show that the agreement between theoretical calculations and experimental data for asymmetry fission is better than that for symmetry fission.

Figure 1

The relaxation time of the $K$ coordinate, ${\tau }_K$, as a function of the asymmetry parameter for $I=80$ at the scission point. Solid, dashed, and dotted lines are the results for ${}^{16}\mathrm{O}+{}^{248}\mathrm{Cm}\to {}^{264}\mathrm{Rf}$, ${}^{16}\mathrm{O}+{}^{238}\mathrm{U}\to {}^{254}\mathrm{Fm}$, and ${}^{16}\mathrm{O}+{}^{232}\mathrm{Th}\to {}^{248}\mathrm{Cf}$ reactions, respectively.

Figure 2

The relaxation time of the $K$ coordinate, ${\tau }_K$, as a function of scission criteria for $I=80$ at the scission point. Solid, dashed, and dotted lines are the results for ${}^{16}\mathrm{O}+{}^{248}\mathrm{Cm}\to {}^{264}\mathrm{Rf}$, ${}^{16}\mathrm{O}+{}^{238}\mathrm{U}\to {}^{254}\mathrm{Fm}$, and ${}^{16}\mathrm{O}+{}^{232}\mathrm{Th}\to {}^{248}\mathrm{Cf}$ reactions, respectively.

Figure 3

The dissipation coefficient for $K$ as a function of the asymmetry parameter at the scission point for the ${}^{16}\mathrm{O}+{}^{248}\mathrm{Cm}\to {}^{264}\mathrm{Rf}$ (a), ${}^{16}\mathrm{O}+{}^{238}\mathrm{U}\to {}^{254}\mathrm{Fm}$ (b), and ${}^{16}\mathrm{O}+{}^{232}\mathrm{Th}\to {}^{248}\mathrm{Cf}$ (c) reactions, respectively.

Figure 4

The anisotropy of the angular distribution of fission fragments as a function of energy for the ${}^{16}\mathrm{O}+{}^{248}\mathrm{Cm}\to {}^{264}\mathrm{Rf}$ (a), ${}^{16}\mathrm{O}+{}^{238}\mathrm{U}\to {}^{254}\mathrm{Fm}$ (b), and ${}^{16}\mathrm{O}+{}^{232}\mathrm{Th}\to {}^{248}\mathrm{Cf}$ (c) reactions, respectively. The open squares are the experimental data [32]. Open and solid circles represent the results based on a nonconstant dissipation coefficient for asymmetry ($\alpha \ne 0)$ and symmetry ($\alpha =0)$ fission, respectively.

Figure 5

The angular distribution of fission fragments for the ${}^{16}\mathrm{O}+{}^{248}\mathrm{Cm}\to {}^{264}\mathrm{Rf}$ reaction at $E_{\mathrm{lab}}=110$ MeV (a), $E_{\mathrm{lab}}=130$ MeV (b), and $E_{\mathrm{lab}}=148$ MeV (c), respectively. The open squares are the experimental data [32]. Open and solid circles represent results with a nonconstant dissipation coefficient for asymmetry ($\alpha \ne 0)$ and symmetry ($\alpha =0)$ fission, respectively.

Figure 6

The angular distribution of fission fragments for ${}^{16}\mathrm{O}+{}^{232}\mathrm{Th}\to {}^{248}\mathrm{Cf}$ reaction at $E_{\mathrm{lab}}=120$ MeV (a), $E_{\mathrm{lab}}=140$ MeV (b), and $E_{\mathrm{lab}}=160$ MeV (c), respectively. The open squares are the experimental data [32]. Open and solid circles represent results with a nonconstant dissipation coefficient for asymmetry ($\alpha \ne 0)$ and symmetry ($\alpha =0)$ fission, respectively.

Figure 7

The angular distribution of fission fragments for ${}^{16}\mathrm{O}+{}^{238}\mathrm{U}\to {}^{254}\mathrm{Fm}$ reaction at $E_{\mathrm{lab}}=90$ MeV (a), $E_{\mathrm{lab}}=130$ MeV (b), and $E_{\mathrm{lab}}=148$ MeV (c), respectively. The open squares are the experimental data [32]. Open and solid circles represent results with non constant dissipation coefficient based on asymmetry ($\alpha \ne 0)$ and symmetry ($\alpha =0)$ fission, respectively.