Isospin fractionation and isoscaling in dynamical simulations of nuclear collisions

Isospin fractionation and isoscaling are found to hold for isotopes from nuclear collisions simulated within the anitsymmetrized molecular dynamics model. The observed linear relation between the isoscaling parameter and the fragment isospin asymmetry ${(Z∕A)}^2$ of the liquid corroborates, in particular, the applicability of statistical considerations to the dynamical fragment emission. Using the derived relation, we are able to extract statistical parameters from the outcome of the dynamic evolution of collisions. The relation allows to access the symmetry energy in the equation of state. This is consistent with the previous findings that the isoscaling parameters can be used to limit the symmetry energy parameter in the nuclear equation of state.

Figure 1

Density dependence of the symmetry energy of nuclear matter for the Gogny force (solid line) and for the Gogny-AS force (dashed line).

Figure 2

${\left(Z∕A\right)}^2$ of the liquid part of the system as a function of time for the three reaction systems. The AMD results are represented by the solid and dashed lines, respectively, for the Gogny and Gogny-AS forces. Late-time BUU results are represented by filled diamonds.

Figure 3

Neutron and proton emission rates described by the left- and right-hand scales, respectively, for the three reaction systems as a function of time. The results of AMD simulations with the Gogny and Gogny-AS forces are, respectively, represented by the solid and dashed lines.

Figure 4

The fragment yield ratio between the AMD simulations of central ${}^{60}\mathrm{Ca}+{}^{60}\mathrm{Ca}$ and ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ collisions at $35\text{MeV}∕\text{nucleon}$, at time $t=300\text{fm}∕c$. The top and bottom panels show, respectively, the results obtained using the Gogny and Gogny-AS forces. The extracted isoscaling parameters are $\alpha =1.83\pm 0.03$ and $\beta =-2.31\pm 0.04$ for the Gogny force, and $\alpha =1.60\pm 0.02$ and $\beta =-2.06\pm 0.03$ for the Gogny-AS force.

Figure 5

The same as Fig. 4 but for the ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ and ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ collisions. The extracted isoscaling parameters are $\alpha =1.03\pm 0.02$ and $\beta =-1.22\pm 0.02$ for the Gogny force, and $\alpha =0.84\pm 0.01$ and $\beta =-0.99\pm 0.02$ for the Gogny-AS force.

Figure 6

Relation between ${\left(Z∕A\right)}_{\text{liq}}^2$ and $\alpha$ for the three systems ${}^{60}\mathrm{Ca}+{}^{60}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$, and ${}^{60}\mathrm{Ca}+{}^{60}\mathrm{Ca}$ (from left to right). Open squares and filled circles show the results of AMD with the Gogny force and Gogny-AS force, respectively. Both ${(Z∕A)}_{\text{liq}}^2$ and $\alpha$ are calculated for fragments recognized at $t=300\text{fm}∕c$. The straight lines are drawn so as to connect the points for ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ and ${}^{60}\mathrm{Ca}+{}^{60}\mathrm{Ca}$. The line slopes are $-26.48$ for the Gogny force and $-21.16$ for the Gogny-AS force, respectively.