Dynamical fission of the quasiprojectile and isospin equilibration for the system ${}^{80}\mathrm{Kr}+{}^{48}\mathrm{Ca}$ at 35 MeV/nucleon

Experimental results concerning the dynamical fission of quasiprojectiles in semiperipheral collisions for the system ${}^{80}\mathrm{Kr}+{}^{48}\mathrm{Ca}$ at 35 MeV/nucleon are presented. Data have been collected with four blocks of the FAZIA setup in the first physics experiment of the FAZIA Collaboration. The degree of isospin equilibration between the two fission fragments and its dependence on their charge asymmetry is investigated. The data are compared with the results of the AMD model coupled to GEMINI as an afterburner, in order to get hints about the timescale of the process.

Figure 1

Layout of the experimental setup in polar representation.

Figure 2

Top: Charge $Z$ vs. laboratory velocity for all the detected products (with multiplicity $\ge 2$) for the reaction ${}^{80}\mathrm{Kr}+{}^{48}\mathrm{Ca}$ at 35 MeV/nucleon. (a) Experimental data. (b) Filtered simulated data (AMD with asystiff symmetry energy, followed by $\text{GEMINI}++$ as afterburner). Dashed arrow: c.m. velocity. Full arrow: beam velocity. Middle: (c) laboratory velocity distribution for all the ejectiles, experimental and simulated data. (d) Charge distribution for all the ejectiles with $Z\ge 3$, experimental and simulated data. (e) and (f): c.m. velocity and c.m. polar angle, respectively, of the biggest fragment in each event for all the events (T), in central events (C), in semiperipheral events with only one fragment detected (QP), experimental and simulated data. All the plots are scaled in such a way that the total integral is 1, except for the C and QP histograms, in the bottom panels, which are scaled with the same factor as the T curve. Details concerning QP and C selections are explained in the text.

Figure 3

${\vartheta }_{\mathrm{rel}}^{\mathrm{c}.\mathrm{m}.}$ vs. $v_{\mathrm{rel}}$ for (semi)peripheral events with two detected fragments. (a) Experimental data. (b) Simulation. The plots are scaled in order to have a total integral equal to 1. The rectangle on both panels corresponds to the QP fission selection.

Figure 4

Top: $Z_{H+L}$ vs. laboratory velocity of the c.m. of the pair of fission fragments for the reaction ${}^{80}\mathrm{Kr}+{}^{48}\mathrm{Ca}$ at 35 MeV/nucleon. (a) Experimental data. (b) Filtered simulated data (AMD with asystiff symmetry energy, followed by $\text{GEMINI}++$ as afterburner). Dashed arrow: c.m. velocity. Continuous arrow: beam velocity. Bottom: (c) Black symbols and histograms: laboratory velocity of the c.m. of the pair of fission fragments, experimental and simulated data; red symbols and histograms: laboratory velocity of the biggest fragment of the QP selection (d) black symbols and histograms: $Z_{H+L}$ distribution, experimental and simulated data; red symbols and histograms: charge distribution of the biggest fragment of the QP selection. All the plots are scaled in such a way that the total integral is 1, except for the black symbols and curves of panels (c) and (d), where the ratio with respect to the QP curves is kept.

Figure 5

Top: $Z_L$ vs. $Z_H$ correlation for the two QP fission fragments for the reaction ${}^{80}\mathrm{Kr}+{}^{48}\mathrm{Ca}$ at 25 MeV/nucleon. (a) Experimental data. (b) Filtered simulated data (AMD with asystiff symmetry energy, followed by $\text{GEMINI}++$ as afterburner). Bottom: (c) $Z_H$ distribution, experimental and simulated data. (d) $Z_L$ distribution, experimental and simulated data. Simulated data have been obtained with the stiff symmetry energy. All the plots are scaled in such a way that the total integral is 1.

Figure 6

Correlation index r between the neutron number $N$ of the big and small fragment of the fissioning pair as a function of $Z_{H+L}$, experimental (full black circles) and simulated (open red circles, with stiff symmetry energy) data.

Figure 7

(a) Experimental data, $\langle N\rangle /Z$ as a function of $Z$ for the fission fragments and for the fragment obtained adding up the fission pair. (b) Main plot: $\langle N\rangle /Z$ as a function of $Z$ for the fragment obtained adding up the fission pair. Insets: $\langle N\rangle /Z$ as a function of $Z$ for the fission fragments. Black symbols: experimental data. Red symbols: AMD stiff followed by $\text{GEMINI}++$. Blue symbols: AMD soft followed by $\text{GEMINI}++$. Green symbols: AMD stiff followed by GEMINI F90.

Figure 8

(a) $cos\alpha$ distribution for two different windows of $\eta$, experimental data (symbols) and $\text{AMD}+\text{GEMINI}$ simulation (histograms). (b) $Asymm.FB$ vs. $\eta$, experimental (black symbols) and simulated (red symbols) data. (c) $cos\alpha$ distribution for two different windows of $\eta$, simulated data. Full histograms: fissions performed by GEMINI. Dash-dotted histograms: fissions performed by AMD. (d) $Asymm.FC$ vs. $\eta$, simulated data. Open squares: fissions performed by GEMINI. Open triangles: fissions performed by AMD. In (a) and (c) the spectra are scaled in order to have total integral equal to 1.

Figure 9

Average isospin asymmetry $\langle \mathrm{\Delta }\rangle$ as a function of $\alpha$ for some fission pairs. Full symbols correspond to experimental data, while open symbols correspond to the simulation with asystiff symmetry energy (for simulated data, broken or not completely working detectors inside the blocks have not been excluded in the geometrical filter due to the particularly demanding request on the statistics necessary to produce these plots). Red and black symbols correspond to the heavier and the lighter fragment of the pair, respectively. (a) Results obtained averaging $\mathrm{\Delta }$ on the pairs $(Z_L,Z_H)=(5–20),(5–21),(5–22)$. (b) Results obtained averaging $\mathrm{\Delta }$ on the pairs $(Z_L,Z_H)=(10–15)$, (10–16), (10–17), (11–14), (11–15), (11–16).

Figure 10

AMD primary data (stiff parametrization) without applying the geometrical filter. (a) Splitting time referred to the beginning of the binary phase $t_{\mathrm{split}}-t_{\mathrm{DIC}}$ for different systems. (b) Correlation between $\alpha$ (calculated at the splitting time) and the splitting time referred to the beginning of the binary phase $t_{\mathrm{split}}-t_{\mathrm{DIC}}$ for the system ${}^{80}\mathrm{Kr}+{}^{48}\mathrm{Ca}$. (c) The same as in (b) but for the AMD simulation with angular momentum conservation.

Figure 11

AMD primary data without applying the geometrical filter. Out-of-plane component of the intrinsic spin of the QP just before the breakup, simulated data. Continuous histogram: AMD without imposing the total angular momentum conservation. Dashed histogram: AMD with total angular momentum conservation.