Critical behavior of the isotope yield distributions in the Multifragmentation Regime of Heavy Ion Reactions

Abstract

Isotope yields have been analyzed within the framework of a Modified Fisher Model to study the power law yield distribution of isotopes in the multifragmentation regime. Using the ratio of the mass dependent symmetry energy coefficient relative to the temperature, $a_{sym}/T$, extracted in previous work and that of the pairing term, $a_p/T$, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields have been corrected for these effects. For a given I = N - Z value, the corrected yields of isotopes relative to the yield of ${}^{12}C$ show a power law distribution, $Y(N,Z)/Y{(}^{12}C)\sim A^{-\ddot{I}„}$, in the mass range of $1\le A\le 30$ and the distributions are almost identical for the different reactions studied. The observed power law distributions change systematically when I of the isotopes changes and the extracted $\ddot{I}„$ value decreases from 3.9 to 1.0 as I increases from -1 to 3. These observations are well reproduced by a simple de-excitation model, which the power law distribution of the primary isotopes is determined to $\ddot{I}{„}^{prim}=2.4\pm 0.2$, suggesting that the disassembling system at the time of the fragment formation is indeed at or very near the critical point.

5 pages, 5 figures