Calculations of the anisotropy of the fission fragment angular distribution and neutron emission multiplicities prescission from Langevin dynamics

The anisotropy of the fission fragment angular distribution defined at the saddle point and the neutron multiplicities emitted prior to scission for fissioning nuclei ${}^{224}\mathrm{Th}$, ${}^{229}\mathrm{Np}$, ${}^{248}\mathrm{Cf}$, and ${}^{254}\mathrm{Fm}$ are calculated simultaneously by using a set of realistic coupled two-dimensional Langevin equations, where the $\{c,h,\alpha =0\}$ nuclear parametrization is employed. In comparison with the one-dimensional stochastic model without neck variation, our two-dimensional model produces results that are in better agreement with the experimental data, and the one-dimensional model is available only for low excitation energies. Indeed, to determine the temperature of the nucleus at the saddle point, we investigate the neutron emission during nucleus oscillation around the saddle point for different friction mechanisms. It is shown that the neutrons emitted during the saddle oscillation cause the temperature of a fissioning nuclear system at the saddle point to decrease and influence the fission fragment angular distribution.

Figure 1

Potential energy surface for the compound nucleus ${}^{224}\mathrm{Th}$ at zero angular momentum. The dotted lines from the top to the bottom are, respectively, the saddle line and two kinds of scission lines determined by the balance between the repulsive Coulomb force and attractive nuclear force acting on the neck $F_c=F_n$ and the zero-neck $P_s(z)=0$.

Figure 2

Calculated prescission neutron multiplicities (filled circles) and anisotropy of the fragment angular distribution (filled inverted triangles) as functions of projectile laboratory energy for ${}^{224}\mathrm{Th}$, ${}^{229}\mathrm{Np}$, ${}^{248}\mathrm{Cf}$, and ${}^{254}\mathrm{Fm}$. Available experimental data of the prescission neutron multiplicities (open squares) and angular anisotropy (open triangles) are from Refs. [29, 30, 31, 32].

Figure 3

Comparison of various models for (a) precission neutron multipicities and (b) angular anisotropy of the reaction ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}\to {}^{224}$Th. Results are calculated by the two-dimensional stochastic model (filled squares) and the two one-dimensional stochastic models in which the fissioning system follows the passage with $h=0$ (filled triangles) or the bottom of the fission valley (filled circles). Experimental data are from Ref. [30] (open circles) and Ref. [29] (open squares).

Figure 4

Various coefficients of friction of ${}^{224}\mathrm{Th}$ as functions of the elongation coordinate. Here $q$ is the half of the c.m. distance between two fragments.

Figure 5

(a) Temperatures of two kinds at the saddle point as functions of energy for ${}^{224}\mathrm{Th}$ (triangles) and ${}^{254}\mathrm{Fm}$ (squares), the open symbols are $T_f$ and filled symbols $T_l$; (b) neutron emission multiplicities $N_{\mathrm{sd}}$ during nucleus oscillation around the saddle point for ${}^{224}\mathrm{Th}$ (triangles) and ${}^{254}\mathrm{Fm}$ (squares).