Isocaling and the symmetry energy in the multifragmentation regime of heavy-ion collisions

The ratio of the symmetry energy coefficient to temperature, $a_{\mathrm{sym}}/T$, in Fermi energy heavy-ion collisions, was experimentally extracted as a function of the fragment atomic number using isoscaling parameters and the variance of the isotope distributions. The extracted values were compared to the results of calculations made with an antisymmetrized molecular dynamics (AMD) model employing a statistical decay code to account for deexcitation of excited primary fragments. The experimental values are in good agreement with the values calculated from the final ground-state products but are significantly different from those characterizing the yields of the primary AMD fragments.

Figure 1

Typical linearized isotope spectra are shown for $Z$ $=$ 6 (top) and 12 (bottom) cases. The number at the top of each peak is the mass number assigned. Linear background is assumed from valley to valley for a given $Z$. Each Gaussian indicates the yield of the isotope above the background.

Figure 2

(Top) $R$${}_{21}$ as a function of $Z$ for ${}^{64}\mathrm{Ni}+{}^{124}\mathrm{Sn}$ and ${}^{64}\mathrm{Ni}+{}^{58}\mathrm{Ni}$. From left to right, each line corresponds to $Z$ $=$ 1 to $Z$ $=$ 18. (Bottom) The extracted $\alpha (Z)$ values are plotted as a function of $Z$.

Figure 3

$\alpha (Z)$ values as a function of $\Delta (Z/\mathrm{Ā}){}^2$ for $Z$ $=$ 6 (top) and $Z$ $=$ 12 (bottom). The lines are the results of a linear fit.

Figure 4

Experimental $a_{\mathrm{sym}}/T$ values extracted from Eq. (4) are shown by dots as a function of $Z$. Open circles show calculated values, extracted in the same way, from the fragment yields in AMD-Gemini calculations, and open squares indicate results from the primary fragments of the AMD simulation with $R$${}_c=5$. The experimental results from $\zeta (Z)$ in Eq. (7) are shown by the solid squares.

Figure 5

$K$($N$,$Z$) distribution from five reaction systems: ${}^{64}\mathrm{Ni}+{}^{58}\mathrm{Ni}$, ${}^{64}\mathrm{Ni}$,${}^{112}\mathrm{Sn}$, ${}^{197}\mathrm{Au}$, and ${}^{232}\mathrm{Th}$.