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A three parameter scaling relationship between isotopic distributions for elements with Z$leq 8$ has been observed that allows a simple description of the dependence of such distributions on the overall isospin of the system. This scaling law (termed iso-scaling) applies for a variety of reaction mechanisms that are dominated by phase space, including evaporation, multifragmentation and deeply inelastic scattering. The origins of this scaling behavior for the various reaction mechanisms are explained. For multifragmentation processes, the systematics is influenced by the density dependence of the asymmetry term of the equation of state.
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The isotope yields of fragments, produced in the decay of the quasiprojectile in Au+Au peripheral collisions at 35 MeV/nucleon and those coming from the disassembly of the unique source formed in Xe+Cu central reactions at 30 MeV/nucleon, were measured. We show that the relative yields of neutron-rich isotopes increase with the excitation energy in multifragmentation reaction. In the framework of the statistical multifragmentation model which fairly well reproduces the experimental observables, this behaviour can be explained by increasing N/Z ratio of hot primary fragments, that corresponds to the statistical evolution of the decay mechanism with the excitation energy: from a compound-like decay to complete multifragmentation.
Isotopic effects in the fragmentation of excited target residues following collisions of $^{12}$C on $^{112,124}$Sn at incident energies of 300 and 600 MeV per nucleon were studied with the INDRA 4$pi$ detector. The measured yield ratios for light particles and fragments with atomic number $Z leq$ 5 obey the exponential law of isotopic scaling. The deduced scaling parameters decrease strongly with increasing centrality to values smaller than 50% of those obtained for the peripheral event groups. Symmetry term coefficients, deduced from these data within the statistical description of isotopic scaling, are near $gamma =$ 25 MeV for peripheral and $gamma <$ 15 MeV for central collisions.
Within an isospin and momentum dependent transport model, the dynamics of isospin particles (nucleons and light clusters) in Fermi-energy heavy-ion collisions are investigated for constraining the isospin splitting of nucleon effective mass and the symmetry energy at subsaturation densities. The mass splitting of $m^{*}_{n}>m^{*}_{p}$ and $m^{*}_{n}<m^{*}_{p}$ in nuclear matter and the different stiffness of symmetry energy are used in the model. The single and double neutron to proton ratios of free nucleons and light particles are thoroughly investigated in the isotopic nuclear reactions of $^{112}$Sn+$^{112}$Sn and $^{124}$Sn+$^{124}$Sn at the incident energies of 50 and 120 MeV/nucleon, respectively. It is found that the both effective mass splitting and symmetry energy impact the kinetic energy spectra of the single ratios, in particular at the high energy tail (larger than 20 MeV). Specific constraints are obtained from the double ratio spectra, which are evaluated from the ratios of isospin observables produced in $^{124}$Sn+$^{124}$Sn over $^{112}$Sn+$^{112}$Sn collisions. A mass splitting of $m^{*}_{n}<m^{*}_{p}$ is constrained from the available data at the energy of 120 MeV/nucleon. A soft symmetry energy with the stiffness of $gamma_{s}=$0.5 is close to the experimental double ratio spectra at both energies.
The A/Z dependence of projectile fragmentation at relativistic energies has been studied with the ALADIN forward spectrometer at SIS. A stable beam of 124Sn and radioactive beams of 124La and 107Sn at 600 MeV per nucleon have been used in order to explore a wide range of isotopic compositions. Chemical freeze-out temperatures are found to be nearly invariant with respect to the A/Z of the produced spectator sources, consistent with predictions for expanded systems. Small Coulomb effects (Delta T approx 0.6 MeV) appear for residue production near the onset of multifragmentation.
New results for the strength of the symmetry energy are presented which illustrate the complementary aspects encountered in reactions probing nuclear densities below and above saturation. A systematic study of isotopic effects in spectator fragmentation was performed at the ALADIN spectrometer with 124Sn primary and 107Sn and 124La secondary beams of 600 MeV/nucleon incident energy. The analysis within the Statistical Fragmentation Model shows that the symmetry-term coefficient entering the liquid-drop description of the emerging fragments decreases significantly as the multiplicity of fragments and light particles from the disintegration of the produced spectator systems increases. Higher densities were probed in the FOPI/LAND study of nucleon and light-particle flows in central and mid-peripheral collisions of 197Au+197Au nuclei at 400 MeV/nucleon incident energy. From the comparison of the measured neutron and hydrogen squeeze-out ratios with predictions of the UrQMD model a moderately soft symmetry term with a density dependence of the potential term proportional to (rho/rho_0)^{gamma} with gamma = 0.9 +- 0.3 is favored.
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