Dynamical fission in ${}^{124}\mathrm{Sn}+{}^{64}\mathrm{Ni}$ collision at 35A MeV

Some properties of fast, nonequilibrium splitting of projectiles in the ${}^{124}\mathrm{Sn}+{}^{64}\mathrm{Ni}$ reaction at 35A MeV were determined using the $4\pi$ CHIMERA detector system. In particular the charge distributions, in- and out-of-plane angular distributions, and relative velocities of projectilelike fragments were measured. The time scale of the process was estimated and it turned out that the process is sequential but much faster than the ordinary, equilibrated fission.

Figure 1

(Color online) The sum of charges of the two heaviest fragments ($Z_{2F})$ vs the lighter fragment parallel velocity (in the laboratory reference frame) for different mass asymmetries and different ranges of kinetic energy of these two fragments. The distributions are shown on a logarithmic scale; the red color corresponds to the highest cross section. The beam velocity was equal to 8.2 cm/ns.

Figure 2

(Color online) $V_{\mathrm{per}}^L$ vs $V_{\mathrm{par}}^L$ plots for the lighter fragment (of the two heaviest) for different values of mass asymmetry and kinetic energy of these fragments. The sharp cuts in the region of $V_{\mathrm{par}}^L<$ 5 cm/ns are due to the angular range of the forward part of CHIMERA being limited to 30${}^{°}$. The distributions are shown on a logarithmic scale; the red color corresponds to the highest cross section.

Figure 3

(Color online) Atomic number distributions of the lighter (of two heaviest) fragments of the PLF splitting, arbitrarily normalized at $Z_L=$ 6. The theoretical distribution is calculated for $E_{2F}=$ 2500–3200 MeV. Because of low statistics the distribution is limited to $Z_L\hspace{1em}\le \hspace{1em}12$; results for higher Z${}_L$ are extrapolated (dotted line). The inset shows comparison of slopes of the “equilibrated” and “dynamical” processes (see Sec. 3c1).

Figure 4

(Color online) Diagram indicating the definition of the in-plane (${\Phi }_{\mathrm{plane}})$ and out-of-plane (${\Psi }_{\mathrm{out}})$ angles.

Figure 5

(Color online) Normalized to unity in-plane angular distributions of the heavier fragment from the PLF splitting. Zero degrees corresponds to forward emission; positive angles correspond to deflection of the fragment toward the beam. Note the presence of a second maximum (at $\pm {180}^{°}$), corresponding to the forward emission of the lighter fragment. The straight line, corresponding to the equilibrated component, was used for calculation of results presented in Table 1.

Figure 6

(Color online) Normalized to unity out-of-plane angular distributions of fission fragments (for $A_H/A_L=$ 1.0–4.6 and for given $E_{2F}$ intervals), corresponding to the “dynamical” (−30${}^{°}<\hspace{1em}{\Phi }_{\mathrm{plane}}<{45}^{°})$ and “equilibrium” (−130${}^{°}<{\Phi }_{\mathrm{plane}}<-{90}^{°}$ and 90${}^{°}<{\Phi }_{\mathrm{plane}}<$ 130${}^{°})$ angular ranges. Dashed lines show results of the statistical model calculation after it is passed through the experimental filter.

Figure 7

(Color online) Relative velocity of the PLF normalized by Viola systematics ($V_{\mathrm{ratio}})$. (a), (b), (c) Mean values of the relative velocity as a function of the in-plane angle for different centralities of collision and asymmetries of the PLF splits; (d) example of velocity spectra at the “dynamical” and “equilibrium” angular regions and the resulting net “dynamical” spectrum after subtraction of the background of the “equilibrated” one.

Figure 8

(Color online) Simulation of the response of the CHIMERA system for the ${\Phi }_{\mathrm{plane}}-{\Psi }_{\mathrm{out}}$ distributions. The left figures show distributions generated for equilibrated (upper figures) and dynamical (lower figure) components of PLF fission (the ${\Phi }_{\mathrm{plane}}$ distributions are assumed flat in both cases). The right figures show modifications of these distribution by imperfections and the angular resolution of the detection system.

Figure 9

(Color online) CHIMERA detection efficiency as a function of the in-plane angle for equilibrated and dynamical fissions, calculated for three mass asymmetry intervals.

Figure 10

(Color online) The $Z_L$ dependence of detection efficiency calculated for equilibrated and dynamical fission.

Figure 11

(a) Comparison of the relative velocity spectrum at the input and output of the detection system. (b) Resolution of $V_{\mathrm{rel}}$ caused by the position resolution of the CHIMERA system.