Dynamical aspects of isoscaling

The origin and dynamical evolution of isoscaling was studied using classical molecular dynamics simulations of ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$, and ${}^{52}\mathrm{Ca}+{}^{52}\mathrm{Ca}$ at beam energies ranging from 20 to 85 MeV/nucleon. The analysis included a study of the time evolution of this effect. Isoscaling was observed to exist at all energies in these reactions from the early primary isotope distributions (produced by systems not yet in thermal equilibrium) all the way to 5000 fm/c.

Figure 1

Long time behavior of isoscaling. Typical fit to $R_{21}(N,Z)$ for the case ${}^{40}\mathrm{Ca}$-${}^{48}\mathrm{Ca}$ at 35 MeV/nucleon at 1250 fm/c.

Figure 2

Energy dependence of fitting parameters α and β for three reactions ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$, and ${}^{52}\mathrm{Ca}+{}^{52}\mathrm{Ca}$, at beam energies ranging from 20 to 85 MeV/nucleon and at $t=5000\mathrm{fm}/c$.

Figure 3

Early behavior of isoscaling. Typical fit to $R_{21}(N,Z)$ for the case ${}^{40}\mathrm{Ca}$-${}^{48}\mathrm{Ca}$ at 35 MeV/nucleon at $125\mathrm{fm}/c$.

Figure 4

Time evolution of α and β for the case ${}^{40}\mathrm{Ca}$-${}^{48}\mathrm{Ca}$ at 35 MeV/nucleon.

Figure 5

Time evolution of the effective temperatures for the reaction ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ at 35 MeV/nucleon. The behavior of $T_{\mathrm{loc}}^{\mathrm{beam}}$ is shown with dots, $T_{\mathrm{loc}}^{\mathrm{perp}}$ with squares, the collective velocities (in units of $c/40$) in the beam axis is shown with the dashed line, and in the reaction plane with a dot-dashed line. Also shown with a continuous line is the average size of the biggest source, scaled by a factor 1/20.

Figure 6

Comparison of temperatures (top panel) and sizes of largest fragments (bottom panel) obtained in the reactions ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ (continuous lines) and ${}^{52}\mathrm{Ca}+{}^{52}\mathrm{Ca}$ (dashed lines) both at 35 MeV/nucleon. The top panel shows the time distribution of the $T_{\mathrm{loc}}^{\mathrm{beam}}$ (higher curves) and of the $T_{\mathrm{loc}}^{\mathrm{perp}}$ (lower curves). The vertical dashed line indicates the time when both reactions are in thermal equilibrium and are under conditions of thermal symmetry.

Figure 7

Population of different mass bins as a function of time for the reaction ${}^{40}\mathrm{Ca}$ on ${}^{40}\mathrm{Ca}$ at 35 MeV/nucleon. Circles (3-4), squares (5-6), etc.