Isobaric Yield Ratio Difference Research Articles

Improved thermometer for 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.

Probing Temperature from Intermediate Mass Fragment by Isobaric Yield Ratio in Heavy-Ion Collisions**Supported by Program for Science & Technology Innovation Talents in Universities of Henan Province under Grant No. 13HASTIT046

A probe to extract the temperature (TIYR) from intermediate-mass fragment has been proposed using the isobaric yield ratio (IYR) difference based on the modified Fisher model. By analyzing the isobaric cross section in the measured 140A MeV 40,48Ca+9Be reactions, the TIYR can well fit the IYR difference for the large mass fragments. Because of the fragments are produced in different colliding regions, it is also suggested to select the fragments according to different mechanisms when using TIYR.

Isobaric yield ratio difference between the140AMeVNi58+Be9andNi64+Be9reactions studied by the antisymmetric molecular dynamics model

Background: The isobaric yield ratio difference (IBD) method is found to be sensitive to the density difference of neutron-rich nucleus induced reaction around the Fermi energy.Purpose: An investigation is performed to study the IBD results in the transport model.Methods: The antisymmetric molecular dynamics (AMD) model plus the sequential decay model gemini are adopted to simulate the $140A$ MeV ${}^{58,64}\mathrm{Ni}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}^{9}\mathrm{Be}$ reactions. A relative small coalescence radius ${R}_{c}=$ 2.5 fm is used for the phase space at $t=$ 500 fm/c to form the hot fragment. Two limitations on the impact parameter ($b1=0--2$ fm and $b2=0--9$ fm) are used to study the effect of central collisions in IBD.Results: The isobaric yield ratios (IYRs) for the large-$A$ fragments are found to be suppressed in the symmetric reaction. The IBD results for fragments with neutron excess $I=$ 0 and 1 are obtained. A small difference is found in the IBDs with the $b1$ and $b2$ limitations in the AMD simulated reactions. The IBD with $b1$ and $b2$ are quite similar in the AMD + GEMINI simulated reactions.Conclusions: The IBDs for the $I=0$ and 1 chains are mainly determined by the central collisions, which reflects the nuclear density in the core region of the reaction system. The increasing part of the IBD distribution is found due to the difference between the densities in the peripheral collisions of the reactions. The sequential decay process influences the IBD results. The AMD + GEMINI simulation can better reproduce the experimental IBDs than the AMD simulation.

Target effects in isobaric yield ratio differences between projectile fragmentation reactions

Background: The isobaric yield ratio difference (IBD) between reactions is know to be sensitive to the density difference between projectiles in heavy-ion collisions around the Fermi energy.Purpose: The target effects in the isobaric yield ratio (IYR) and the IBD results have been studied.Methods: The amount of isotopes in the $140A$ MeV ${}^{48,40}\mathrm{Ca}+{}^{181}\mathrm{Ta}{/}^{9}\mathrm{Be}$ and ${}^{58,64}\mathrm{Ni}+{}^{181}\mathrm{Ta}{/}^{9}\mathrm{Be}$ reactions have been previously measured with high accuracy. The IYR and IBD results have been obtained from these reactions to study the effects of the light $^{9}\mathrm{Be}$ and heavy $^{181}\mathrm{Ta}$ targets. A ratio (${r}_{\ensuremath{\Delta}\ensuremath{\mu}}$) between the IBD results for the reactions with Ta and Be targets is defined to quantitatively show the target dependence of the IBD results. Results The IYRs for reactions with symmetric projectiles are more easily affected than those for reactions with neutron-rich projectiles. The IBD results are suppressed by using the $^{181}\mathrm{Ta}$ target to different degrees.Conclusions: The IYR and IBD results are influenced by the target used. The IBD for the $I=1$ isobaric chain is suggested as a probe to study the difference between the neutron and proton densities of the reaction systems.

Isobaric yield ratio difference and Shannon information entropy

The Shannon information entropy theory is used to explain the recently proposed isobaric yield ratio difference (IBD) probe which aims to determine the nuclear symmetry energy. Theoretically, the difference between the Shannon uncertainties carried by isobars in two different reactions (ΔIn21), is found to be equivalent to the difference between the chemical potentials of protons and neutrons of the reactions [the IBD probe, IB-Δ(βμ)21, with β the reverse temperature]. From the viewpoints of Shannon information entropy, the physical meaning of the above chemical potential difference is interpreted by ΔIn21 as denoting the nuclear symmetry energy or density difference between neutrons and protons in reactions more concisely than from the statistical ablation–abrasion model.

Isotopic Ratio, Isotonic Ratio, Isobaric Ratio and Shannon Information Uncertainty

The isoscaling and the isobaric yield ratio difference (IBD) probes, both of which are constructed by yield ratio of fragment, provide cancelation of parameters. The information entropy theory is introduced to explain the physical meaning of the isoscaling and IBD probes. The similarity between the isoscaling and IBD results is found, i.e., the information uncertainty determined by the IBD method equals to β – α determined by the isoscaling (α (β) is the parameter fitted from the isotopic (isotonic) yield ratio).

Neutron density distributions of neutron-rich nuclei studied with the isobaric yield ratio difference

The isobaric yield ratio difference (IBD) between two reactions of similar experimental setups is found to be sensitive to nuclear density differences between projectiles. In this article, the IBD probe is used to study the density variation in neutron-rich 48Ca . By adjusting diffuseness in the neutron density distribution, three different neutron density distributions of 48Ca are obtained. The yields of fragments in the 80A MeV 40, 48Ca + 12C reactions are calculated by using a modified statistical abrasion-ablation model. It is found that the IBD results obtained from the prefragments are sensitive to the density distribution of the projectile, while the IBD results from the final fragments are less sensitive to the density distribution of the projectile.

Isobaric yield ratio difference and neutron density difference in calcium isotopes

`The isobaric yield ratio difference between two reactions is found to equal Delta mu(21)/ T, which denotes the ratio of the difference between the neutron and proton chemical potentials to the temperature. A series of projectile fragmentation reactions induced by calcium isotopes are calculated using a modified statistical abrasion-ablation model, assuming the neutron density distribution to be the Fermi type. The Delta mu(21)/ T from the prefragments are found to be sensitive to the difference between the neutron density distributions of projectiles, while Delta mu(21)/ T from the final fragments are very similar for the reactions and insensitive to the difference between the neutron density distributions of projectiles. The Delta mu(21)/ T from the prefragments and final fragments verify that the deexcitation modifies the results largely.

Chemical properties of colliding sources in 124, 136Xe and 112, 124Sn induced collisions in isobaric yield ratio difference and isoscaling methods

Isoscaling and isobaric yield ratio difference (IBD) methods are used to study Δμ/T (Δμ being the difference between the chemical potentials of the neutron and proton, and T being the temperature) in the measured 1 A GeV 124Sn + 124Sn, 112Sn + 112Sn, 136Xe + Pb and 124Xe + Pb reactions. The isoscaling phenomena in the 124Sn/112Sn and 136Xe/124Xe reaction pairs are investigated, and the isoscaling parameters α and β are obtained. The Δμ/T determined by the isoscaling method (IS-Δμ/T) and the IBD method (IB-Δμ/T) in the measured Sn and Xe reactions are compared. It is shown that in most fragments, the IS- and IB-Δμ/T are consistent in the Xe reactions, while the IS- and IB-Δμ/T ones are only similar in the less neutron-rich fragments in the Sn reactions. The shell effects in IB-Δμ/T are also discussed.

Isobaric yield ratio difference in heavy-ion collisions, and comparison to isoscaling

An isobaric yield ratio difference (IBD) method is proposed to study the ratio of the difference between the chemical potential of neutron and proton to temperature ($\Delta\mu/T$) in heavy-ion collisions. The $\Delta\mu/T$ determined by the IBD method (IB-$\Delta\mu/T$) is compared to the results of the isoscaling method (IS-$\Delta\mu/T$), which uses the isotopic or the isotonic yield ratio. Similar distributions of the IB- and IS-$\Delta\mu/T$ are found in the measured 140$A$ MeV $^{40,48}$Ca + $^{9}$Be and the $^{58,64}$Ni + $^{9}$Be reactions. The IB- and IS-$\Delta\mu/T$ both have a distribution with a plateau in the small mass fragments plus an increasing part in the fragments of relatively larger mass. The IB- and IS-$\Delta\mu/T$ plateaus show dependence on the $n/p$ ratio of the projectile. It is suggested that the height of the plateau is decided by the difference between the neutron density ($\rho_n$) and the proton density ($\rho_p$) distributions of the projectiles, and the width shows the overlapping volume of the projectiles in which $\rho_n$ and $\rho_p$ change very little. The difference between the IB- and IS-$\Delta\mu/T$ is explained by the isoscaling parameters being constrained by the many isotopes and isotones, while the IBD method only uses the yields of two isobars. It is suggested that the IB-$\Delta\mu/T$ is more reasonable than the IS-$\Delta\mu/T$, especially when the isotopic or isotonic ratio disobeys the isoscaling. As to the question whether the $\Delta\mu/T$ depends on the density or the temperature, the density dependence is preferred since the low density can result in low temperature in the peripheral reactions.