Improved thermometer for intermediate-mass fragments in heavy-ion collisions with isobaric yield ratio difference

Abstract

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 et al., Phys. Rev. C 86, 054611 (2012) and Ma et al., ibid., Phys. Rev. C 88, 014609 (2013)].Purpose: An improved thermometer (TIB) is proposed based on the difference between IYRs. TIB obtained from isobars in different reactions will be compared.Methods: The yields of three isobars are employed in TIB. 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 TIB. Results:The measured fragment yields in the 140A MeV 40,48 Ca + 9 Be ( 181 Ta) and 58,64 Ni + 9 Be ( 181 Ta), the 1A GeV 124,136 Xe + Pb, and the 112,124 Sn + 112,124 Sn reactions have been analyzed to obtain TIB from IMFs. TIB from most of the fragments in the 40,48 Ca and 58,64 Ni reactions is in the range of 0.6 MeV < TIB < 3.5 MeV. TIB from most of the fragments in the 124 Xe and 112,124 Sn reactions is in the range of 0.5 MeV < TIB < 2.5 MeV, while the range is 0.5 MeV < TIB < 4 MeV from most of the fragments in the 136 Xe reaction. In general, for most of the fragments TIB in the 40,48 Ca and 58,64 Ni reactions are very similar (except in the very neutron-rich fragments), and TIB from IMFs in the 124,136 Xe and 112,124 Sn reactions is also similar. A slightly dependence of TIB on A is found.Conclusions: Using the binding energy of the nucleus, TIB can be obtained without the knowledge of the free energies of fragments. In the investigated reactions, TIB from most of the IMFs is low.

Probing Temperature from Intermediate Mass Fragment by Isobaric Yield Ratio in Heavy-Ion Collisions

“…T ID MeV is much smaller than the previous results using the IYR probe, [41−43] which are all larger than 1 MeV. But T ID in this work is similar to the temperatures from the large-A IMFs obtained using the improved IYR method [47] or the isotopic thermometer. [9] Fig.…”

“…The formula and the similar free energy formula have been used to extract the IYR temperature for IMFs. [41,43,47] Defining the IYR [R(A, I + 2, I)] between the isobaric fragments (A, I + 2) and (A, I), one has,…”

An Isoratio Method and an Isoratio Scaling Phenomenon in Heavy-Ion Collisions

“…The improved thermometer (T IB ) based on the isobaric ratio of IMFs has suggested a low temperature for the measured IMFs, and T IB is found to depend on the mass of IMF. [55] No uniform has been found for the IMFs, which makes it difficult to determine the ∆µ n21 or ∆µ p21 from the isoratio results or the isoscaling parameters.…”

Mass dependence of temperature for intermediate mass fragment in heavy-ion reactions

“…The disagreement between the temperatures extracted from the light particles and IMFs has motivated people to extract the temperature from the IMFs, which is important since temperature will make a large difference in the resultant nuclear symmetry energy of nuclear matter, and significantly influences the nuclear equation of state. Efforts have also been made to separate the temperature from the thermodynamic probes by introducing approximation of free energy of fragments [42][43][44][45], or assuming that the symmetry energy of fragment is known [46][47][48][49].…”

“…At the same time, a T sym of fragment also depends on A [21,[30][31][32][49][50][51]. In addition, the A-dependence of T persists for the measured fragments by an improved IYR thermometer, which is labelled as T IB [44]. In the…”