Isoscaling in light-ion induced reactions and its statistical interpretation

Isotopic effects observed in fragmentation reactions induced by protons, deuterons, and $\alpha$ particles of incident energies between 660 MeV and 15.3 GeV on ${}^{112}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}$ targets are discussed. The exponential scaling of the yield ratios with the third component of the fragment isospin $t_3=\left(N-Z\right)/2\mathrm{}$ is observed in all reactions, with scaling parameters that depend on the incident energy. Breakup temperatures for these reactions are deduced from double ratios of isotopic yields and tested for their relation with the isoscaling parameters. The quantum-statistical and the statistical multifragmentation (SMM) models are used for interpreting the results. The observed isoscaling can be understood as a consequence of the statistical origin of the emitted fragments in these reactions. The SMM analysis shows that the exponent describing the isoscaling behavior is proportional to the strength of the symmetry term of the fragment binding energy. Using this result, a symmetry-term coefficient $\gamma \approx 22.5\mathrm{MeV}$ for fragments at breakup is deduced from the experimental data. This is close to the standard value and supports SMM assumptions for the breakup configuration. An alternative method of determining the symmetry-energy coefficient, by using isotope distribution widths, is also discussed.