Temperature determined by isobaric yield ratios in a grand-canonical ensemble theory

Abstract

Background: The temperature in heavy-ion collisions is an important question because it reflects the violence of the collisions and affects the results of many important parameters in nuclear physics.Purpose: In this work, we focus on the investigation of the temperature of the measured fragments in the 1$A$ GeV ${}^{112,124}$Sn+${}^{112,124}$Sn, and ${}^{124,36}$Xe+Pb reactions.Methods: The isobaric yield ratio method is deduced in a grand-canonical theory. The decay contribution and the pairing energy contribution to the free energy of the fragment are considered in the analysis.Results: For the odd $I$ ($I\ensuremath{\equiv}N\ensuremath{-}Z$) fragment the decay or pairing energy contribution is found unnecessary. For the even $I$ fragments, both the decay contribution and the decay plus pairing energy contribution can weaken the staggering in the isobaric yield ratios. For the odd $I$ fragment, the temperature in this work is consistent with that of the modified Fisher model [Phys. Rev. C 86, 054611 (2012)]. For the even $I$ fragment, the temperature at which the decay plus the pairing energy contribution have been taken in account is consistent with that of the the odd $I$ fragments. The isospin dependence of the temperature determined by the isobaric yield ratio method is also found.Conclusions: In the grand-canonical theory, after the correction of the decay plus pairing energy to the free energy of the fragments, reasonable temperature of the even $I$ fragment can be obtained.