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 (∆µ/T ) in heavy-ion collisions. The ∆µ/T determined by the IBD method (IB-∆µ/T ) is compared to the results of the isoscaling method (IS-∆µ/T ), which uses the isotopic or the isotonic yield ratio. Similar distributions of the IB-and IS-∆µ/T are found in the measured 140A MeV 40,48 Ca + 9 Be and the 58,64 Ni + 9 Be reactions. The IB-and IS-∆µ/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-∆µ/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 (ρn) and the proton density (ρp) distributions of the projectiles, and the width shows the overlapping volume of the projectiles in which ρn and ρp change very little. The difference between the IB-and IS-∆µ/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-∆µ/T is more reasonable than the IS-∆µ/T , especially when the isotopic or isotonic ratio disobeys the isoscaling. As to the question whether the ∆µ/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.

In the framework of a modified Fisher model, using the isobaric yield ratio method, we investigate the fragments produced in the 140 𝐴 MeV 40,48 Ca+ 9 Be and 58,64 Ni+ 9 Be projectile fragmentation reactions. Using different approximation methods, 𝑎sym/𝑇 (the ratio of symmetry-energy coefficient to temperature) of symmetric and neutron-rich fragments are extracted. It is found that 𝑎sym/𝑇 of fragments depend on the reference nucleus and the neutron excess of fragments. The 𝑎sym/𝑇 of the isobar decreases when the neutron-excess of the isobar increases, while for a fragment with the same neutron-excess, 𝑎sym/𝑇 increases as the mass of the fragment increases but saturate when the mass of the fragment becomes larger.

The general idea of information entropy provided by C.E. Shannon "hangs over everything we do" and can be applied to a great variety of problems once the connection between a distribution and the quantities of interest is found. The Shannon information entropy essentially quantify the information of a quantity with its specific distribution, for which the information entropy based methods have been deeply developed in many scientific areas including physics. The dynamical properties of heavy-ion collisions (HICs) process make it difficult and complex to study the nuclear matter and its evolution, for which Shannon information entropy theory can provide new methods and observables to understand the physical phenomena both theoretically and experimentally. To better understand the processes of HICs, the main characteristics of typical models, including the quantum molecular dynamics models, thermodynamics models, and statistical models, etc, are briefly introduced. The typical applications of Shannon information theory in HICs are collected, which cover the chaotic behavior in branching process of hadron collisions, the liquid-gas phase transition in HICs, and the isobaric difference scaling phenomenon for intermediate mass fragments produced in HICs of neutron-rich systems. Even though the present applications in heavy-ion collision physics are still relatively simple, it would shed light on key questions we are seeking for. It is suggested to further develop the information entropy methods in nuclear reactions models, as well as to develop new analysis methods to study the properties of nuclear matters in HICs, especially the evolution of dynamics system.

Using an isobaric method, the symmetry-energy coefficient (asym) of a neutron-rich nucleus is obtained from experimental binding energies. The shell effects are shown in a*sym/A ≡ 4asym/A of nuclei. A (sub)magic neutron magic number N = 40 is suggested in a very neutron-rich nucleus, and a*sym/A of a nucleus is found to decrease when its mass increases. The a*sym/A of a very neutron-rich nucleus with large mass saturates. The volume-symmetry coefficients (bv) and surface-symmetry coefficients (bs) of a neutron-rich nucleus are extracted from a*sym/A by a correlation a*sym/A = bv/A − bs/A4/3. It is found that bv and bs decrease when the nucleus becomes more neutron-rich, and tend to saturate in the very neutron-rich nucleus. A linear correlation between bv and bs is obtained in nuclei with different neutron-excess I, and bv of I > 7 nuclei is found to coincide with the results of infinite nuclear matter asym = 32 ± 4 MeV, and bs/bv of the nucleus is found to coincide with the results of the finite-range liquid-drop model results.

Symmetry energy from neutron-rich fragments in heavy-ion collisions,and its dependence on incident energy, and impact parameters * MA Chun-Wang( ) 1;1) SONG Heng-Li( )

The longitudinal momentum distribution (P // ) of fragments after one-proton removal from 23 Al and reaction cross sections (σR) for 23,24 Al on carbon target at 74A MeV have been measured. The 23,24 Al ions were produced through projectile fragmentation of 135A MeV 28 Si primary beam using RIPS fragment separator at RIKEN. P // is measured by a direct time-of-flight (TOF) technique, while σR is determined using a transmission method. An enhancement in σR is observed for 23 Al compared with 24 Al. The P // for 22 Mg fragments from 23 Al breakup has been obtained for the first time. FWHM of the distributions has been determined to be 232±28 MeV/c. The experimental data are discussed by using Few-Body Glauber model. Analysis of P // demonstrates a dominant d-wave configuration for the valence proton in ground state of 23 Al, indicating that 23 Al is not a proton halo nucleus.

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The heavy fragments in heavy-ion collisions are finally formed after the hot prefragments undergo sequential decay, of whom the temperature should be much lower than that of prefragments. Using the double ratio (DR) method, the isotopic thermometer (Tiso) for heavy fragment is constructed using the yield of heavy isotopes. Tiso of heavy fragment is obtained by analyzing the measured data in the 1A GeV 124,136 Xe and 140A MeV 48 Ca/ 64 Ni reactions. Result shows that Tiso varies from 0.5 MeV to 10 MeV. But most Tiso is around 1 ± 0.5 MeV, which is much lower than temperature of light particles. Result also indicates that the difference between Tiso of heavy fragments in different reactions is very small, and Tiso is independent on the size of the reaction system, the incident energy and the neutron-richness of the projectile.