Improved Thermometer from Intermediate Mass Fragments in Heavy-Ion Collisions with Isobaric Yield Ratio Difference

Abstract

\item[Background] Temperature is an important parameter in studying many important questions in heavy-ion collisions. A thermometer based on the isobaric yield ratio (IYR) has been proposed [Ma \textit{et al.}, Phys. Rev. C \textbf{86}, 054611 (2012) and Ma \textit{et al.}, \textit{ibid.}, Phys. Rev. C \textbf{88}, 014609 (2013)]. \item[Purpose] An improved thermometer ($T_{IB}$) is proposed based on the difference between IYRs. $T_{IB}$ obtained from isobars in different reactions will be compared. \item[Methods] The yields of three isobars are employed in $T_{IB}$. The residual free energy of the three isobars are replaced by that of the binding energy. No secondary decay modification for odd $A$ fragment is used in $T_{IB}$. \item[Results] The measured fragment yields in the 140$A$ MeV ${}^{40,48}$Ca + ${}^9$Be (${}^{181}$Ta) and ${}^{58,64}$Ni + ${}^9$Be (${}^{181}$Ta), the 1$A$ GeV ${}^{124,136}$Xe + Pb, and the ${}^{112,124}$Sn + ${}^{112,124}$Sn reactions have been analyzed to obtain $T_{IB}$ from IMFs. $T_{IB}$ from most of the fragments in the ${}^{40,48}$Ca and ${}^{58,64}$Ni reactions is in the range of 0.6 MeV $<T_{IB}<$ 3.5 MeV. $T_{IB}$ from most of the fragments in the ${}^{124}$Xe and ${}^{112,124}$Sn reactions is in the range of 0.5 MeV $<T_{IB}<$ 2.5 MeV, while the range is 0.5 MeV $<T_{IB}<$ 4 MeV from most of the fragments in the ${}^{136}$Xe reaction. In general, for most of the fragments $T_{IB}$ in the ${}^{40,48}$Ca and ${}^{58,64}$Ni reactions are very similar (except in the very neutron-rich fragments), and $T_{IB}$ from IMFs in the ${}^{124,136}$Xe and ${}^{112,124}$Sn reactions is also similar. A slightly dependence of $T_{IB}$ on $A$ is found. \item[Conclusions] Using the binding energy of the nucleus, $T_{IB}$ can be obtained without the knowledge of the free energies of fragments. In the investigated reactions, $T_{IB}$ from most of the IMFs is low.

7 pages, 9 figures. To appear on Physical Review C

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