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

\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.