Fission dynamics of intermediate-fissility systems: A study within a stochastic three-dimensional approach

The system of intermediate fissility ${}^{132}\mathrm{Ce}$ has been studied experimentally and theoretically to investigate the dissipation properties of nuclear matter. Cross sections of fusion-fission and evaporation-residue channels together with light charged particle multiplicities in both channels, their spectra, light charged particle-evaporation residue angular correlations, and mass-energy distribution of fission fragments have been measured. Theoretical analysis has been performed using a multidimensional stochastic approach coupled with a Hauser-Feshbach treatment of particle evaporation. The main conclusions are that the full one-body shape-dependent dissipation mechanism allows the reproduction of the full set of experimental data and that after a time ${\tau }_d=5\times {10}^{-21}$ s from the equilibrium configuration of the compound nucleus, fission decay can occur in a time that can span several orders of magnitude.

Figure 1

(a) Schematic layout of the experimental apparatus. The letters from A to G label the seven rings of the BALL section. (b) The geometry used for the angular distribution of LCP detected in a ring around the beam in coincidence with ER detected in a parallel-plate avalanche counter (PPAC) horizontal plane. $\pi$ indicates the reaction plane, which is defined as the plane containing the beam and the PPAC.

Figure 2

The reduced friction coefficient ${\beta }_{q_2{q}_2}$ as a function of elongation for ${}^{132}\mathrm{Ce}$ composite system for the one-body dissipation mechanism with the values of reduction coefficient from the wall formula $k_s=1$, 0.5, and 0.1 and for two-body dissipation mechanism with the the two-body dissipation coefficient ${\nu }_0=0.02\times {10}^{-21}$ MeV s ${\text{fm}}^{-3}$ and ${\nu }_0=0.15\times {10}^{-21}$ MeV s ${\text{fm}}^{-3}$.

Figure 3

Measured proton (a) and $\alpha$-particle (b) energy spectra in the center-of-mass system (${\theta }_{\text{LAB}}={137}^{\circ }$) for the ER channel compared with the prediction of the dynamical model obtained with the basic set of input model parameters.

Figure 4

Same as Fig. 3 for the FF channel.

Figure 5

Measured ER-$\alpha$ (a) and ER-$p$ (b) angular correlations, compared with the predictions of the dynamical model. LCP have been detected by $8\pi LP$-BALL detectors, whose number is reported in the abscissa. Evaporation residues have been detected at ${\theta }_{\text{LAB}}=4.5^{\circ }$.

Figure 6

Experimental (a) and theoretical (b) MED of fission fragments for the ${}^{132}\mathrm{Ce}$ composite system. See text for details.

Figure 7

Experimental and theoretical kinetic-energy distribution of fission fragments.

Figure 8

Experimental and theoretical mass distributions of fission fragments.

Figure 9

(a) Fission time distribution; (b) fission rate obtained in the calculations with the dynamical model. In (b), dashed and dotted lines refer to calculations without particle evaporations. See text for details.

Figure 10

Distribution of the yields of pre-scission particle multiplicities vs time of emission from equilibrium: (a) first- ($Y_{n1}$), second- ($Y_{n2}$), and third- ($Y_{n3}$) chance pre-scission neutrons together with time distribution of fission events ($N_f$); (b) first-chance neutron ($Y_{n1}$), proton ($Y_{p1}$) and $\alpha$ particle ($Y_{\alpha 1}$). See text for details.