Power law behavior of the isotope yield distributions in the multifragmentation regime of heavy ion reactions

Abstract

Isotope yield distributions in the multifragmentation regime were studied with high-quality isotope identification, focusing on the intermediate mass fragments (IMFs) produced in semiviolent collisions. The yields were analyzed within the framework of a modified Fisher model. Using the ratio of the mass-dependent symmetry energy coefficient relative to the temperature, ${a}_{\mathrm{sym}}/T$, extracted in previous work and that of the pairing term, ${a}_{\mathrm{p}}/T$, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields were corrected for these effects. For a given $I=N\ensuremath{-}Z$ value, the corrected yields of isotopes relative to the yield of $^{12}\mathrm{C}$ show a power law distribution $Y(N,Z)/Y({}^{12}\mathrm{C})~{A}^{\ensuremath{-}\ensuremath{\tau}}$ in the mass range $1\ensuremath{\leqslant}A\ensuremath{\leqslant}30$, 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 $\ensuremath{\tau}$ value decreases from $3.9$ to $1.0$ as $I$ increases from $\ensuremath{-}1$ to $3$. These observations are well reproduced by a simple deexcitation model, with which the power law distribution of the primary isotopes is determined to be ${\ensuremath{\tau}}^{\mathrm{prim}}=2.4\ifmmode\pm\else\textpm\fi{}0.2$, suggesting that the disassembling system at the time of the fragment formation is indeed at, or very near, the critical point.