Ma Chun-Wang

The Symmetry Energy from the Neutron-Rich Nucleus Produced in the Intermediate-Energy 40,48Ca and 58,64Ni Projectile Fragmentation

In the framework of a modified Fisher model, using the isobaric yield ratio method, we investigate the fragments produced in the 140 A MeV 40,48Ca+9Be and 58,64Ni+9Be 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.

Isospin dependence of projectile-like fragment production at intermediate energies

The cross sections of fragments produced in 140 A MeV Ca + Be and Ni + Be reactions are calculated by the statistical abration-ablation(SAA) model and compared to the experimental results measured at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. The fragment isotopic and isotonic cross section distributions of Ca and Ca, Ni and Ni, Ca and Ni, and Ca and Ni are compared and the isospin dependence of the projectile fragmentation is studied. It is found that the isospin dependence decreases and disappears in the central collisions. The shapes of the fragment isotopic and isotonic cross section distributions are found to be very similar for symmetric projectile nuclei. The shapes of the fragment isotopic and isotonic distributions of different asymmetric projectiles produced in peripheral reactions are found very similar. The similarity of the distributions are related to the similar proton and neutron density distributions inside the nucleus in framework of the SAA model.

Residue Coulomb interaction among isobars and its influence in symmetry energy of neutron-rich fragment

The residue Coulomb interaction (RCI), which affects the result of symmetry-energy coefficient of neutronrich nucleus in isobaric yield ratio (IYR) method, is difficult to be determined. Four RCI approximations are investigated: (i) The M1-RCI adopting the a(c)/T (the ratio of Coulomb energy coefficient to temperature) determined from the IYR of mirror-nucleus fragments; (ii) The M2-RCI by fitting the difference between IYRs; (iii) The M3-RCI adopting the standard Coulomb energy at a temperature T = 2 MeV; and (iv) Neglecting the RCI among isobars. The M1-, M2- and M3-RCI are no larger than 0.4. In particular, the M2-RCI is very close to zero. The effects of RCI in a(sym)/T of fragment are also studied. The M1- and M4-a(sym)/T are found to be the lower and upper limitations of a(sym)/T, respectively. The M2-a(sym)/T overlaps the M4-a(sym)/T, which indicates that the M2-RCI is negligible in the IYR method, and the RCI among the three isobars can be neglected. The relative consistent low values of M3-a(sym)/T (7.5 +/- 2.5) are found in very neutron-rich isobars.

Surface and Volume Symmetry Energy Coefficients of a Neutron-Rich Nucleus

Using an isobaric method, the symmetry-energy coefficient (a(sym)) of a neutron-rich nucleus is obtained from experimental binding energies. The shell effects are shown in a(sym)*/A equivalent to 4a(sym)/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 (b(v)) and surface-symmetry coefficients (b(s)) of a neutron-rich nucleus are extracted from a(sym)*/A by a correlation a(sym)*/A = b(v)/A - b(s)/A (4/3). It is found that b(v) and b(s) decrease when the nucleus becomes more neutron-rich, and tend to saturate in the very neutron-rich nucleus. A linear correlation between b(v) and b(s) is obtained in nuclei with different neutron-excess I, and b(v) of I > 7 nuclei is found to coincide with the results of infinite nuclear matter a(sym) = 32 +/- 4 MeV, and b(s)/b(v) 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

The yields of fragments produced in the 60Ni+12C reactions at 80 A and 140 A MeV, and with maximum impact parameters of 1.5, 2 and 7.3 fm at 80 A MeV are calculated by the statistical abrasion-ablation model. The yields of fragments are analyzed by the isobaric yield ratio (IYR) method to extract the coefficient of symmetry energy to temperature (asym/T). The incident energy is found to influence asym/T very little. Its found that asym/T of fragments with the same neutron-excess I=N−Z increases when A increases, while asym/T of isobars decreases when A increases. The asym/T of prefragments is rather smaller than that of the final fragments, and the asym/T of fragments in small impact parameters is smaller than that of the larger impact parameters, which both indicate that asym/T decreases when the temperature increases. The choice of the reference IYRs is found to have influence on the extracted asym/T of fragments, especially on the results of the more neutron-rich fragments. The surface-symmetry energy coefficient (bs/T) and the volume-symmetry energy coefficient (bv/T) are also extracted, and the bs/bv is found to coincide with the theoretical results.

A Model Comparison Study of Fragment Production in 140 A MeV 58,64Ni+9Be Reactions*

The cross sections of fragments produced in the 140 A MeV58,64Ni+9 Be projectile fragmentation reactions are calculated by using the antisymmetrized molecular dynamics (AMD) model, the modified statistical abrasion-ablation (SAA) model, and the empirical EPAX2/EPAX3 formulae. The Gogny-g0 interaction is taken as the effective nucleon-nucleon interaction in the AMD calculation, and the decays of fragments obtained from the AMD results are calculated by using the GEMINI code. The calculated cross sections of fragments are compared.

Temperature of Heavy Fragments in Heavy-Ion Collisions

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 124,136Xe and 140A MeV 48Ca/64Ni 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.

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

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.

Investigation of neutron induced reactions on 23Na by using Talys1.4

The neutron induced reactions on Na-23 are investigated by using the Talys1.4 program. The calculated results for the Na-23(n, 2n)Na-22 reaction are found to agree with the experimental results. The cross sections of the residues of the (n, n), (n, gamma), (n, p), and (n, np) channels in the reactions are presented, and at the same time, the neutron induced reactions on Ne-22 are also investigated.

Isospin dependence of projectile fragmentation and neutron-skin thickness of neutron-rich nuclei

By investigating the cross section distributions of fragments produced in the 140 A MeV 40,48Ca+9Be and 1 A GeV 124,136Xe+Pb reactions, the isospin dependence of projectile fragmentation in fragment production is studied. In the framework of the statistical abrasion-ablation model, the 1 A GeV 136Xe+ 208Pb reaction is calculated. By adjusting the diffuseness parameter in neutron density distribution of 136Xe, we find the isospin dependence of projectile fragmentation in fragment production is sensitive to the neutron-skin thickness of the projectile nucleus.