Dynamical aspects of isotopic scaling

Investigation of the effect of the dynamical stage of heavy-ion collisions indicates that the increasing width of the initial isospin distributions is reflected by a significant modification of the isoscaling slope for the final isotopic distributions after deexcitation. For narrow initial distributions, the isoscaling slope assumes the limiting value of the two individual initial nuclei while for wide initial isotopic distributions the slope for hot fragments approaches the initial value. The isoscaling slopes for final cold fragments increase due to secondary emissions. The experimentally observed evolution of the isoscaling parameter in multifragmentation of hot quasiprojectiles at E${}_{\mathrm{inc}}=50A\mathrm{MeV}$, fragmentation of ${}^{86}\mathrm{Kr}$ projectiles at E${}_{\mathrm{inc}}=25A\mathrm{MeV}$ and multifragmentation of target spectators at relativistic energies was reproduced by a simulation with the dynamical stage described using the appropriate model (deep inelastic transfer and incomplete fusion at the Fermi energy domain and spectator-participant model at relativistic energies) and the deexcitation stage described with the statistical multifragmentation model. In all cases the isoscaling behavior was reproduced by a proper description of the dynamical stage and no unambiguous signals of the decrease of the symmetry energy coefficient were observed.

Figure 1

Isoscaling plots after deexcitation by the SMM for nuclei with mass $A=50$ and an excitation energy of 125 MeV. Upper and lower rows represent cold and hot partitions, respectively. Squares and thick solid lines—isoscaling plots and exponential fits for $Z⩽6$, scattered dots—all $Z$'s. The dynamical stage (stars connected by thin solid lines) was simulated by shifted Gaussians (N/Z = 1.0, 1.3) with three different values of widths (${\sigma }_Z=0.5$, 2.5, 4.5, see panels from left to right).

Figure 2

Isoscaling plots after deexcitation by the SMM for nuclei with mass $A=50$ and an excitation energy of 250 MeV (${\sigma }_Z=0.5$, 2.5, 4.5). Symbols and lines as in Fig. 1.

Figure 3

Isoscaling plots after deexcitation by the SMM for nuclei with mass $A=25$ and an excitation energy of 63 MeV (${\sigma }_Z=0.5$, 1.5, 3.5). Symbols and lines as in Fig. 1.

Figure 4

Isoscaling plots after deexcitation by the SMM for nuclei with mass $A=25$ and an excitation energy of 125 MeV (${\sigma }_Z=0.5$, 1.5, 3.5). Symbols and lines as in Fig. 1.

Figure 5

Isoscaling plots after deexcitation by the SMM for nuclei with mass $A=100$ and an excitation energy of 250 MeV (${\sigma }_Z=0.5$, 2.5, 4.5). Symbols and lines as in Fig. 1.

Figure 6

Isoscaling plots after deexcitation by the SMM for nuclei with mass $A=100$ and an excitation energy of 500 MeV (${\sigma }_Z=0.5$, 2.5, 4.5). Symbols and lines as in Fig. 1.

Figure 7

Simulated isoscaling plots (symbols) and fits to experimental data (lines) from the statistical decay of hot quasi-projectiles in the reactions ${}^{28}\mathrm{Si}$+${}^{124,112}\mathrm{Sn}$ at incident energies of $50A\mathrm{MeV}$. The upper left panel corresponds to inclusive data while the other panels correspond to the five excitation energy bins.

Figure 8

Isoscaling plots for the reactions of ${}^{86}\mathrm{Kr}$+${}^{124,112}\mathrm{Sn}$ at an incident energy of $25A\mathrm{MeV}$. Left panel-simulated data for final fragments, middle panel-experimental data [15], right panel-simulated data after dynamical stage. The lines represent exponential fits.

Figure 9

Evolution of the isoscaling parameter at the dynamical stage as a function of the centrality for the reactions ${}^{12}\mathrm{C}$+${}^{112,124}\mathrm{Sn}$ at relativistic energies. Solid line-results of simulations. Symbols-experimental data [17].