Isobaric yield ratios and the symmetry energy in heavy-ion reactions near the Fermi energy

Abstract

The relative isobaric yields of fragments produced in a series of heavy-ion-induced multifragmentation reactions have been analyzed in the framework of a modified Fisher model, primarily to determine the ratio of the symmetry energy coefficient to the temperature, ${a}_{\mathrm{sym}}/T$, as a function of fragment mass $A$. The extracted values increase from 5 to $~$16 as $A$ increases from 9 to 37. These values have been compared to the results of calculations using the antisymmetrized molecular dynamics (AMD) model together with the statistical decay code gemini. The calculated ratios are in good agreement with those extracted from the experiment. In contrast, the values extracted from the ratios of the primary isobars from the AMD model calculation are $~$4 to 5 and show little variation with $A$. This observation indicates that the value of the symmetry energy coefficient derived from final fragment observables may be significantly different than the actual value at the time of fragment formation. The experimentally observed pairing effect is also studied within the same simulations. The Coulomb coefficient is also discussed.