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

TL;DR

This study analyzes isotope yield distributions in heavy ion multifragmentation, revealing power law behaviors near criticality and demonstrating that secondary decay effects can be systematically corrected.

Contribution

It introduces a method to correct isotope yields for secondary decay effects and confirms the system's critical behavior through power law distributions in isotope yields.

Findings

Power law distributions of isotope yields are observed across different reactions.

The power law exponent $ au$ varies systematically with isotope neutron excess I.

The primary isotope distribution exponent is approximately 2.4, indicating near-critical disassembly.

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, $Y(N,Z)/Y(^{12}C) \sim A^{-\tau}$, 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 $\tau$ 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 $\tau^{prim} = 2.4 \pm 0.2$, suggesting that the disassembling system at the time of the fragment formation is indeed at or very near the critical point.