Temperature determined by isobaric yield ratio in heavy-ion collisions

Abstract

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. Isobaric yield ratio (IYR) is used to determine the temperature of heavy fragments. Cross sections of measured fragment 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. Relatively low $T$ of heavy fragments are obtained in different reactions ($T$ ranges from 1 to 3MeV). $T$ is also found to depend on the neutron-richness of the projectile. The incident energy affects $T$ very little. $\Delta\mu/T$ (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 of $A<50$ isobars, is affected greatly by the temperature-corrected $\Delta B(T)$. But $T$ of reactions using IYRs of heavier fragments are only slightly affected by the temperature-corrected $\Delta B(T)$. The SAA model analysis gives a consistent overview of the results extracted in this work. $T$ from IYR, which is for secondary fragment, is different from that of the hot emitting source. $T$ and $\Delta\mu$ are essentially governed by the sequential decay process.