First results from the INDRA-FAZIA apparatus on isospin diffusion in ${}^{58,64}\mathrm{Ni}+{}^{58,64}\mathrm{Ni}$ systems at Fermi energies

An investigation of the isospin equilibration process in the reactions ${}^{58,64}\mathrm{Ni}+{}^{58,64}\mathrm{Ni}$ at two bombarding energies in the Fermi regime (32 and 52 MeV/nucleon) is presented. Data have been acquired during the first experimental campaign of the coupled INDRA-FAZIA apparatus in GANIL. Selecting from peripheral to semicentral collisions, both the neutron content of the quasiprojectile residue and that of the light ejectiles coming from the quasiprojectile evaporation have been used as probes of the dynamical process of isospin diffusion between projectile and target for the asymmetric systems. The isospin transport ratio technique has been employed. The relaxation of the initial isospin imbalance with increasing centrality has been clearly evidenced. The isospin equilibration appears stronger for the reactions at 32 MeV/nucleon, as expected due to the longer projectile-target interaction time than at 52 MeV/nucleon. Coherent indications of isospin equilibration come from the quasiprojectile residue characteristics and from particles ascribed to the quasiprojectile decay.

Figure 1

Rendering of the INDRA-FAZIA mechanical coupling, with INDRA on the left side and FAZIA on the right side. The target holder, not visible in the picture, is located inside the INDRA apparatus.

Figure 2

Forward view from the target (left) and polar plot (right) of the INDRA-FAZIA apparatus, showing the 12 FAZIA blocks in a wall configuration. The polar plot is obtained by reporting the polar coordinates $(\theta sin\phi ,\theta cos\phi )$ of all the detected particles, where $\theta$ and $\phi$ are the polar and azimuthal angles in the laboratory reference frame, respectively.

Figure 3

Experimental nuclear chart obtained via the Si1-Si2 $\mathrm{\Delta }\mathrm{E}\text{−}\mathrm{E}$ method with a FAZIA telescope during the E789 experiment.

Figure 4

Experimental $Z$ vs $v_z^{c.m.}$ correlations for the fragments in the events selected by the preliminary conditions for the reactions ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ at (a) 32 MeV/nucleon and (b) 52 MeV/nucleon. The plots are normalized to their integral. The black arrows indicate the original projectile velocity for each reaction.

Figure 5

Charge distributions (top) and velocity distributions (bottom) of the QP remnant for all the studied reactions: [(a), (e)] the system ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$, [(b), (f)] ${}^{58}\mathrm{Ni}+{}^{64}\mathrm{Ni}$, [(c), (g)] ${}^{64}\mathrm{Ni}+{}^{58}\mathrm{Ni}$, and [(d), (h)] ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$. The reactions at 32 MeV/nucleon (52 MeV/nucleon) are plotted in black (red). Experimental data are plotted with solid markers, while AMD $+$ gemini$++$ predictions are drawn with a line. The same legend is valid for all the plots. The plots are normalized to their integral. In plots (e)–(h), the black (red) arrows indicate the original projectile velocity $v_{beam}^{c.m.}$ for each reaction at 32 MeV/nucleon (52 MeV/nucleon).

Figure 6

Correlation between $b_{\mathrm{red}}$ and $p_{\mathrm{red}}$ of the QP remnant in the AMD $+$ gemini$++$ simulated events belonging to the QP evaporation channel for the reactions ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ at (a) 32 MeV/nucleon and (b) 52 MeV/nucleon. The plots are normalized to their integral. Black markers indicate the average $b_{\mathrm{red}}$ for each $p_{\mathrm{red}}$ bin. Vertical lines indicate the minimum $p_{\mathrm{red}}$ value (0.4) above which the correlations are considered reliable in the following analysis.

Figure 7

Comparison between the AMD $+$ gemini$++$ predictions of the average $b_{\mathrm{red}}$ as a function of $p_{\mathrm{red}}$ for (a) different energies and for different systems at (b) 32 MeV/nucleon and (c) 52 MeV/nucleon. Statistical errors are smaller than the marker size.

Figure 8

Experimental neutron to proton ratio $\langle N/Z\rangle$ of the QP evaporation residue as a function of $p_{\mathrm{red}}$ for the four reactions at (a) 32 MeV/nucleon and (b) 52 MeV/nucleon. Statistical errors are plotted on the $y$ axis (generally smaller than the marker size), while the horizontal error bars are set equal to the $p_{\mathrm{red}}$ bin width. The black dotted line represents the $N/Z$ value of the EAL calculated according to the parametrization of Ref. [52] assuming the $\langle Z\rangle$ obtained for each $p_{\mathrm{red}}$ bin considering all the four systems.

Figure 9

Isospin transport ratio calculated with the $\langle N/Z\rangle$ of the QP evaporation residue as a function of $p_{\mathrm{red}}$ (experimental data). The results for the asymmetric reactions ${}^{64}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ and ${}^{58}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ at 32 MeV/nucleon (52 MeV/nucleon) are plotted as black (red) symbols. The vertical error bars, often smaller than the marker size, correspond to statistical errors.

Figure 10

Isospin transport ratio calculated with the $\langle N/Z\rangle$ of the QP evaporation residue, reported as a function of $b_{\mathrm{red}}$, obtained from the plot in Fig. 9 by rescaling $p_{\mathrm{red}}$ into $b_{\mathrm{red}}$ by exploiting their correlation obtained within AMD $+$ gemini$++$. The results for the asymmetric reactions ${}^{64}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ and ${}^{58}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ at 32 MeV/nucleon (52 MeV/nucleon) are plotted as black (red) symbols. The vertical error bars, often smaller than the marker size, correspond to statistical errors.

Figure 11

Experimental neutron to proton ratio $\langle N\rangle /{\langle Z\rangle }_{CP}$ of the complex particles (see text) forward emitted with respect to the QP remnant, as a function of $p_{\mathrm{red}}$ for the four reactions at (a) 32 MeV/nucleon and (b) 52 MeV/nucleon. Statistical errors are plotted on the $y$ axis (generally smaller than the marker size), while the horizontal error bars are set equal to the $p_{\mathrm{red}}$ bin width.

Figure 12

Isospin transport ratio calculated with the $\langle N\rangle /{\langle Z\rangle }_{CP}$ of the complex particles (see text) forward emitted with respect to the QP remnant, as a function of $p_{\mathrm{red}}$ (experimental data). The results for the asymmetric reactions ${}^{64}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ and ${}^{58}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ at 32 MeV/nucleon (52 MeV/nucleon) are plotted as black (red) symbols. The vertical error bars, often smaller than the marker size, correspond to statistical errors.

Figure 13

Isospin transport ratio calculated with the $\langle N\rangle /{\langle Z\rangle }_{CP}$ of the complex particles (see text) forward emitted with respect to the QP remnant, as a function of $b_{\mathrm{red}}$, obtained from the plot of Fig. 12 by rescaling $p_{\mathrm{red}}$ into $b_{\mathrm{red}}$ and exploiting their correlation obtained within AMD $+$ gemini$++$. The results for the asymmetric reactions ${}^{64}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ and ${}^{58}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ at 32 MeV/nucleon (52 MeV/nucleon) are plotted as black (red) symbols. The vertical error bars, often smaller than the marker size, correspond to statistical errors.