Temperature determined by isobaric yield ratios in heavy-ion collisions

Abstract

Background: Temperature ($T$) in heavy-ion collisions is an important parameter. Previously, many works have focused on the temperature of the hot emitting source. But there are few systematic studies of the temperature among heavy fragments in peripheral collisions with incident energies near the Fermi energy to a few $A$ GeV, though it is very important to study the property of neutron-rich nucleus in heavy-ion collisions.Purpose: This work focuses on the study of temperature associated with the final heavy fragments in reactions induced by both the neutron-proton symmetric and the neutron-rich projectiles, and with incident energy ranges from 60$A$ MeV to 1$A$ GeV.Methods: Isobaric yield ratio (IYR) is used to determine the temperature of heavy fragments. Cross sections of measured fragments in reactions are analyzed, and a modified statistical abrasion-ablation (SAA) model is used to calculate the yield of fragment in 140$A$ MeV ${}^{64}$Ni+${}^{9}$Be and 1$A$ GeV ${}^{136}$Xe+${}^{208}$Pb reactions.Results: Relatively low $T$ of heavy fragments are obtained in different reactions ($T$ ranges from 1 to 3 MeV). $T$ is also found to depend on the neutron richness of the projectile. The incident energy affects $T$ very little. $\ensuremath{\Delta}\ensuremath{\mu}/T$ (the ratio of the difference between the chemical potential of neutron and proton to temperature) is found to increase linearly as $N/Z$ of projectile increases. It is found that $T$ of the ${}^{48}$Ca reaction, for which IYRs are $A<50$ isobars, is affected greatly by the temperature-corrected $\ensuremath{\Delta}B(T)$. But $T$ of reactions using IYRs of heavier fragments are only slightly affected by the temperature-corrected $\ensuremath{\Delta}B(T)$. The SAA model analysis gives a consistent overview of the results extracted in this work.Conclusions: $T$ from IYR, which is for secondary fragments, is different from that of the hot emitting source. $T$ and $\ensuremath{\Delta}\ensuremath{\mu}$ are essentially governed by the sequential decay process.