Theoretical study of projectile fragmentation in the ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ reactions at 1 GeV/nucleon

We analyze the production cross sections and isotopic distributions of projectilelike residues in the reactions ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ at an incident beam energy of 1 GeV/nucleon measured with the fragment separator at the GSI laboratory. Calculations within the statistical multifragmentation model for an ensemble of excited sources were performed with ensemble parameters determined previously for similar reactions at 600 MeV/nucleon. The obtained good agreement with the experiment establishes the universal properties of the excited spectator systems produced during the dynamical stage of the reaction. It is furthermore confirmed that a significant reduction of the symmetry-energy term at the freeze-out stage of reduced density and high temperature is necessary to reproduce the experimental isotope distributions. A trend of decreasing symmetry energy for large neutron-rich fragments of low excitation energy is interpreted as a nuclear-structure effect.

Figure 1

(Top panel) Production cross sections of the measured projectile fragments as a function of the fragment atomic number $Z$ for the two reactions (from Ref. [7]). (Bottom panel) The corresponding distributions as obtained from ensemble calculations with standard parameters (for details see text in Sec. 2).

Figure 2

Predicted (lines) and measured (symbols, from Ref. [7]) isotope distributions for final fragments of the projectiles ${}^{124}\mathrm{Sn}$ and ${}^{112}\mathrm{Sn}$ with atomic numbers $Z=12$, 18, 35, and 44. Calculations are shown for three different choices of the symmetry-term coefficient $\gamma =8$ (dotted), 14 (dashed), and 25 MeV (solid lines).

Figure 3

Predicted isotopic cross sections for final fragments with atomic numbers $34\le Z\le 45$ from the fragmentation of ${}^{124}\mathrm{Sn}$ projectiles for two ensemble parameters $a_2=0.015$ ${\mathrm{MeV}}^{-2}$ (solid line) and $a_2=0.009$ ${\mathrm{MeV}}^{-2}$ (dashed) in comparison with the experimental data from Ref. [7] (open squares). The symmetry-term coefficient $\gamma =19$ MeV was used.

Figure 4

Predicted (lines) and measured (symbols, from Ref. [7]) isotopic cross sections for final fragments with atomic numbers $10\le Z\le 21$ from the fragmentation of ${}^{124}\mathrm{Sn}$ (open squares and solid lines) and ${}^{112}\mathrm{Sn}$ projectiles (solid circles and dashed lines). The symmetry-term coefficients $\gamma$ used in the calculations are given in Table 1.

Figure 5

The same as Fig. 4 but for the final fragments with atomic numbers $22\le Z\le 33$.

Figure 6

As Fig. 4 but for the final fragments with atomic numbers $34\le Z\le 45$.