Isospin diffusion observables in heavy-ion reactions

Collisions of ${}^{112}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}$ nuclei, which differ in their isospin asymmetry, provide information about the rate of isospin diffusion and equilibration. Although several different probes can provide accurate diffusion measurements, the ratios of the mirror nuclei may be the simplest and most promising one. Ratios of the mass seven mirror nuclei yields are analyzed to show the rapidity, transverse momentum, and impact parameter dependence of isospin diffusion.

Figure 1

(Upper panel) The circles, squares and diamonds show the experimental data for $\alpha ,\beta$, and $\alpha -\beta$, respectively, that have been measured for central Sn+Sn collisions. The x axis corresponds to the isospin asymmetry of the combined system. (Lower panel) The solid circles, and solid squares show the experimental data for $X_7$ and $X_{11}$, respectively, that has been measured for the same reactions shown in the upper panel.

Figure 2

Correlation between the charge of the projectile-like fragment ($Z_{\mathrm{plf}}$) and observed total charge particle multiplicity, $N_C$. The corresponding values of $b/b_{\max }$ are given in the upper axis of the figure. The numbers indicating the contour levels are in arbitrary units.

Figure 3

The solid circles, solid stars, open stars, and open circles show the experimental isotopic distributions at $y/y_{\mathrm{beam}}>0.7$ and $b/b_{\max }>0.8$ that has been measured for ${}^{124}\mathrm{Sn}$+${}^{124}\mathrm{Sn}$, ${}^{124}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$, ${}^{112}\mathrm{Sn}$+${}^{124}\mathrm{Sn}$, and ${}^{112}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$ collisions, respectively. The solid lines are drawn to guide the eyes and the dashed lines are extrapolated from isoscaling parameters as discussed in the text.

Figure 4

The shaded rectangles at $y/y_{\mathrm{beam}}<0.3$ and $y/y_{\mathrm{beam}}>0.7$ show the values of $R_i(\alpha )$ measured for the ${}^{124}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$ and ${}^{112}\mathrm{Sn}$+${}^{124}\mathrm{Sn}$ systems, respectively [6]. The data points show the values of $R_i(X_7)$ measured for $A=7$ mirror nuclei in peripheral ${}^{124}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$ collisions as a function of rapidity.

Figure 5

$d^{2}M/\mathit{dyd}(p_{\perp }/A)$ distribution as function of rapidity, $y/y_{\mathrm{beam}}$, measured in ${}^{124}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$ collisions at $E/A=50$ MeV. From the top (first panel) ${}^7\mathrm{Li}$ fragment distributions. (Second panel) ${}^7\mathrm{Be}$ fragment distributions. (Third panel) Ratio of the ${}^7\mathrm{Li}$ fragment distributions divided by the ${}^7\mathrm{Be}$ distributions. (Fourth panel) $R_7$ distribution.

Figure 6

The solid diamonds, open circles, and solid circles show the rapidity dependencies of $R_7$ for central, midcentral, and peripheral collisions, respectively.

Figure 7

$d^{2}M/\mathit{dyd}(p_{\perp }/A)$ distribution for ${}^{12}\mathrm{C}$ fragments produced in central ${}^{112}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$ collisions at $E/A=50$ MeV. The dashed lines show the boundaries at ${\theta }_{c.m.}={70}^{°}$ and ${110}^{°}$ for the mid-rapidity gate that was used to create the data shown in Fig. 1 [13]. The circle corresponds to the contour of constant velocity in the center of mass.