Dipolar degrees of freedom and isospin equilibration processes in heavy ion collisions

The dipolar degrees of freedom on the ${}^{48}\mathrm{Ca}+{}^{27}\mathrm{Al}$ system at 40 MeV/nucleon have been investigated for the first time with the $4\pi$ multidetector CHIMERA. The global variable $\langle Dz\rangle$ was measured for well-reconstructed events in binary dissipative processes. Both the close link with isospin equilibration processes and its insensitivity to later statistical hot source decays have been discussed. This latter feature provides the opportunity to investigate globally and exclusively the dynamics of the equilibration processes. At this first level of investigation the experimental evidence, supported by the study of the reference system ${}^{27}\mathrm{Al}+{}^{40}\mathrm{Ca}$ and the auxiliary one ${}^{27}\mathrm{Ca}+{}^{48}\mathrm{Ca}$, substantially agree with the CoMD-III calculations by describing the isovectorial forces through stiffness parameter values $\gamma \approx 0.8–1.2.$

Figure 1

Charges $Z$ of the detected fragments versus their velocities $Vz$ along the beam axis are shown for the main system (a) and the auxiliary one (b).

Figure 2

In the inset we show $\mathrm{TKEL}<$ 350 MeV. Full dots: Charge distribution of PLF's punching through the Si detectors (direct estimate based on the $\Delta E-E$ method) for the ${}^{27}\mathrm{Al}+{}^{48}\mathrm{Ca}$ system at 40 MeV/nucleon. Open dots: Charge distribution of TLF's stopped in the $\text{Si}$ detectors (indirect estimate based on the TOF method) for the ${}^{48}\mathrm{Ca}+{}^{27}\mathrm{Al}$ system at 40 MeV/nucleon. (a) For the system ${}^{48}\mathrm{Ca}+{}^{27}\mathrm{Al}$ at 40 MeV/nucleon, the measured values of $Dz,c$ are plotted for different $Zb$ associated with the selected events (charged multiplicity $m\ge 2$). The dot-dashed vertical lines indicates the reference limiting values $D_m$ (see the text). Panels (b)–(d): $Dz,c$ distributions obtained as projections of the above 2-D plot, for different $Zb$ intervals. In panel (b) the $Dz,c$ spectra for $Zb=20$ and for quasielastic events (TKEL $<70$ MeV) are plotted with star symbols.

Figure 3

Same as in Fig. 2 but for the reference system ${}^{27}\mathrm{Al}+{}^{40}\mathrm{Ca}$.

Figure 4

For the investigated system ${}^{48}\mathrm{Ca}+{}^{27}\mathrm{Al}$ we plot for different $Zb$ windows (the respective extremes are indicated by the double labeling in the $Zb$ axis), and for TKEL $<$ 350 MeV, the measured average dipolar signal $\langle Dz,c\rangle$ (red [gray] star points). The observed data are compared in the same figure with the results of CoMD-III + gemini calculations (black points), filtered through the simulated response of the experimental apparatus and data-analysis selections. Panels (a), (b), and (c) show the comparisons for different $\gamma$ values characterizing the isovectorial interaction. The “chi-square” values with respect to the experimental data are also shown. (d) The calculated values of $\langle Dz\rangle$ for $\gamma =1$ are compared to the experimental values for $\langle Dz,c\rangle$. The error bars represent statistical uncertainties due to the simulations. The estimated uncertainties related to the experimental values $\langle Dz,c\rangle$ are in many cases smaller than the plotted symbols.