Isospin- and momentum-dependent interaction in isospin-dependent quantum molecular dynamics

An isospin-dependent quantum molecular dynamical model （IQMD） is developed, with the isospin degree of freedom in the momentum-dependent interaction（MDI） included in IQMD, to obtain an isospin- and momentum-dependent interaction （IMDI） in IQMD. We investigate the effect of IMDI on the isospin fractionation ratio and its dynamical mechanism in the intermediate energy heavy ion collisions. It is found that the IMDI induces the significant reductions in the isospin fractionation ratio for all of beam energies, impact parameters, neutron-proton ratios and mass number of colliding systems. However, the strong dependence of isospin fractionation ratio on the symmetrical potential is preserved, with the isospin degree of freedom included in the MDI, i.e. the isospin fractionation ratio is still a good probe for extracting the information about the equation of state of isospin asymmetrical nuclear matter.

Isospin and Symmetry Structure in ^(36)Ar

The interacting boson model-3(IBM-3) has been used to study the isospin excitation states and electromag-netic transitions for ^(36)Ar nucleus.The mixed symmetry states and superdeformed band at low spin are also analyzed.The theoretical calculations are in agreement with experimental data,and the ^(36)Ar is superdeformed rotational nucleusclose to the SU(3) limit.The present calcula,tions indicate that the 2_4^+ state is the lowest mixed symmetry state and thelowest isospin T=1 excitation state and at about 6.2 MeV,and the bandhead of superdeformed band is 0_2^+ state.

Isospin effects on intermediate mass fragments at intermediate energy-heavy ion collisions

In this study,we investigated the isospin properties of intermediate mass fragments(IMFs)for the central collisions of^(112,124)Sn+^(112,124)Sn at a beam energy of50 MeV per nucleon using an improved quantum molecular dynamics model(ImQMD)coupled with a sequential decay model(GEMINI).Three observables were analyzed:(1)the average center-of-mass kinetic energy per nucleon<Ec.m./A>of fragments as a function of their charge number Z;(2)the average neutron number to proton number ratio(<N>/Z)of fragments with a given charge number Z as a function of their center-of-mass kinetic energy per nucleon(Ec.m./A);and(3)the average total neutron number to total proton number ratio(ΣN/ΣZ)and double ratio(DR(N/Z))of IMFs with Z=3-8 as a function of their center-of-mass kinetic energy per nucleon Ec.m./A.Our calculations revealed that the sensitivity of the isospin properties of IMFs relative to the stiffness of the symmetry energy remains even after sequential decay.By comparing the calculations ofΣN/ΣZ and DR(N/Z)with the data,it was found that the soft symmetry energy,i.e.,γ=0.5,is favored.

Probing neutron–proton effective mass splitting using nuclear stopping and isospin mix in heavy-ion collisions in GeV energy region

The ramifications of the effective mass splitting on the nuclear stopping and isospin tracer during heavy-ion collisions within the gigaelectron volt energy region are studied using an isospin-dependent quantum molecular dynamics model.Three isotope probes,i.e.,a proton,deuteron,and triton,are used to calculate the nuclear stopping.Compared to the mn*>mp*case,the mn*<mp*parameter results in a stronger stopping for protons but a weaker stopping for tritons.The calculations of the isospin tracer show that the mn*>mp*parameter results in a higher isospin mix than the mn*<mp*parameter.The rapidity and impact parameter dependences of the isospin tracer are also studied.A constraining of the effective mass splitting using the free nucleons with high rapidity and in a central rather than peripheral collision is suggested.

Secondary decay effects of the isospin fractionation in the projectile fragmentation at GeV/nucleon

The isospin fractionations in 124Sn,107Sn+120Sn at 600 MeV/nucleon,and 136Xe,124Xe+208Pb at 1000 MeV/nucleon are investigated by the isospin-dependent quantum molecular dynamics model coupled with the statistical code GEMINI.The yield ratio as a function of the binding energy difference for light mirror nuclei 3H/3He,7Li/7Be,11B/11C,and 15N/15O is applied to estimate the ratio between neutrons and protons in the gas of the fragmenting system.By comparing the estimated values resulting from the simulations with and without the GEMINI code,it was found that the secondary decay distorts the signal of the isospin fractionation.To minimize the secondary decay effects,the yield ratio of the light mirror nuclei 3H/3He as well as its double ratio between two systems with different isospin asymmetries of the projectiles is recommended as robust isospin observables.

Probing the medium effect and isospin dependence of the in-medium nucleon-nucleon cross section in heavy ion collisions

Probing in-medium nucleon-nucleon （NN） cross section σ1/NN（α） in heavy ion collisions has been investigated by means of the isospin-dependent quantum molecular dynamics （IQMD） with the isospin- and momentum-dependent interaction （IMDI（T））. It is found that there are the very obvious medium effect and the sensitive isospin-dependence of nuclear stopping R on the in-medium NN cross section α1/NN（α） in the nuclear reactions induced by halo-neutron projectile and the same-mass stable projectile. However, R induced by the neutron-halo projectile is obviously lower than that induced by the corresponding stable projectile. In particular, there is a very obvious dependence of R on the medium effect of σ1/NN（α） in the whole beam energy region for the above two kinds of projectiles. Therefore, the comparison between the results of R＇s in the reactions induced by the neutron-halo projectile and the corresponding same-mass stable projectile is a more favourable probe for extracting the information of σ1/NN（α） because of adding a new judgement.

A New Approach to Mesons’ States and Their Dependence on Spin and Isospin: A Mathematical Study

The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the authors’ name: Alireza Heidari and Seyedali Vedad. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.5 412-419, 2012, has been removed from this site.

1-3 In-medium and Isospin Effects on Pion Production in Heavy-ion Collisions Near Threshold Energies

Properties of hadrons in nuclear medium is interest in studying the Quantum Chromodynamics (QCD) structure in dense matter, in particular related to the chiral symmetry restoration, phase-transition from quark-gluon plasma to hadrons, dynamics of hypernucleus formation, nuclear equation of state (EoS), etc. High energy heavy-ion collisions in terrestrial laboratory provide a unique possibility to study the in-medium properties of hadrons in dense nuclear matter and to extract the high-density behavior of the nuclear symmetry energy (isospin asymmetri part of EoS). The dynamics of pseudoscalar mesons in heavy-ion collisions and the in-medium properties in dense nuclear matter have been investigated with the Lanzhou quantum molecular dynamics (LQMD) transport model[1].

Isospin splitting of nucleon effective mass and isospin effect in heavy-ion collisions

Two different isospin splittings of nucleon effective mass in nuclear medium as the form of mn*>mp* and mn*<mp* have been implemented in an isospin and momentum dependent transport model.Their impacts on the isospin emission in heavy-ion collisions is investigated thoroughly.It is found that the yield ratios of energetic neutrons to protons squeezed out during the compression stage of two colliding nuclides are sensitive to the isospin splitting.The elliptic flows of free nucleons are also to be promising observables for extracting the nucleon effective mass splitting.Further experimental measurements are being expected,in particular at the CSR-CEE platform in Lanzhou.Several observables are proposed for constraining the density dependence of symmetry energy,such as the transverse flow difference of neutrons and protons,double ratios of n/p and π-/π+,excitation functions of π-/π+ and K0/K+.

Directed flow of isospin sensitive fragments within a modified clusterization algorithm in heavy-ion collisions

By extending the minimum spanning tree(MST)clusterization algorithm for the binding energy cut,the isospin asymmetry dependence of directed flow for isospin sensitive isobar pairs(neutrons-protons,3H-3He) is studied from low towards high incident energies.The modified clusterization method(MSTB) has the advantage to identify the fragments at quite early time.It enhances(reduces) the production of free nucleons(fragments) over MST method.The directed flow of isobaric pair3H-3He is more sensitive towards isospin asymmetry caused by MSTB than isobaric pair n-p.This sensitivity becomes quite strong towards the high incident energy and neutron-rich reaction system.In conclusion,the inclusion of binding energy in clusterization method for the flow studies has been uniquely important for understanding the isospin physics,especially for high density behavior of symmetry energy.

Effects of Isospin on Pre-scission Particle Multiplicity of Heavy Systems and ItsExcitation Energy Dependence

Isospin effects on particle emission of fissioning isobaric sources 202Fr, 202po, 202Tl and isotopic sources 189,202,212Po, and its dependence on the excitation energy are studied via Smoluchowski equations. It is shown that with increasing the isospin of fissioning systems, charged-particle emission is not sensitive to the strength of nuclear dissipation. In addition, we have found that increasing the excitation energy not only increases the influence of nuclear dissipation on particle emission but also greatly enhances the sensitivity of the emission of pre-scission neutrons or charged particles to the isospin of the system. Therefore, in order to extract dissipation strength more accurately by taking light particle multiplicities it is important to choose both a highly excited compound nucleus and a proper kind of particles for systems with different isospins.

Roles of Isospin in Evaporation Residue Cross Section as a Probe of Nuclear Dissipation

<Abstract>The influence of isospin on the excess of evaporation residue cross section over its standard statistical-model value for nuclei ^(194)Pb,^(200)Pb,and ^(206)pb is studied via a Langevin equation coupled with a statistical decay model.The magnitude of this excess for a low-isospin fissioning nucleus is shown to be larger and its dependence on the nuclear viscosity coefficient to be stronger than those of a high-isospin fissioning nucleus.These results suggest that to obtain a more accurate information of viscosity coefficient inside the saddle point by measuring evaporation residue cross sections, we had better choose those compound systems with small isospin.

Isospin-conserving hadronic decay of the D_(s1)(2460) into D_(s)π^(+)π^(-)

The internal structure of the charm-strange mesons D_(s0)^(*)(2317)and D_(s1)(2460)are the subject of intensive studies.Their widths are small because they decay dominantly through isospinbreaking hadronic channels D_(s0)^(*)(2317)^(+)→D_(s)^(+)π^(0) and D _(s1)(2460)^(+)→D_(s)^(*+)π^(0).The D_(s1)(2460)can also decay into the hadronic final states D_(s)^(+)ππ,conserving isospin.In that case there is,however,a strong suppression from phase space.We study the transition D_(s1)(2460)^(+)→D_(s)^(+)π^(+)π^(-)in the scenario that the D_(s1)(2460)is a D^(*)K hadronic molecule.The ππ final state interaction is taken into account through dispersion relations.We find that the ratio of the partial widths of the Γ(D_(s1)(2460)^(+)→D_(s)^(+)π^(+)π^(-)) / Γ(D_(s1)(2460)^(+)→D_(s)^(*+)π^(0))obtained in the molecular picture is consistent with the existing experimental measurement.More interestingly,we demonstrate that theπ+π−invariant mass distribution shows a double bump structure,which can be used to disentangle the hadronic molecular picture from the compact state picture for the D_(s1)(2460)^(+).Predictions on the B_(s1)^(0)→B_(s)^(0)π^(+)π^(-)are also made.

Isospin effects of the Skyrme potential and the momentum dependent interaction at intermediate energy heavy ion collisions

We improve the isospin dependent quantum molecular dynamical model by including isospin effects in the Skyrme potential and the momentum dependent interaction to obtain an isospin dependent Skyrme potential and an isospin dependent momentum interaction. We investigate the isospin effects of Skyrme potential and momentum dependent interaction on the isospin fractionation ratio and the dynamical mechanism in intermediate energy heavy ion collisions. It is found that the isospin dependent Skyrme potential and the isospin dependent momentum interaction produce some important isospin effects in the isospin fractionation ratio.

Isospin effects of projectile fragmentation in a Boltzmann-Langevin approach

The isospin effects of projectile fragmentation at intermediate energies are investigated using an isospin-dependent Boltzmann-Langevin model.The collisions of mass-symmetric reactions including 58Fe,58Ni+58Fe,and Ni at intermediate energies,in the 30 to 100 MeV/A range,are studied for different symmetry energies.Yield ratios of the isotopic,isobaric,and isotonic pairs of fragments from the intermediate-mass region using three symmetry energies are extracted as functions of the N/Z ratio of the composite systems in the entrance channel and the incident energies.It is found that the yield ratios are sensitive to symmetry energies,especially for neutron-rich systems,and the calculations using soft symmetry energy are closer to the experimental data.The isospin effect is stronger for the soft symmetry energy,owing to the competition of the repulsive Coulomb force and the symmetry energy attractive force on the proton.For the first time,the splits are presented,revealing a transition from the isospin equilibrium at lower energies to translucency at intermediate energies.The results show a degree of transparency in that intermediate mass fragments undergo a transition from dependence on the composite systems in the entrance channel to reliance on the projectile and target nuclei.

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU（2） NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 〈 0 and μI 〉0 in the phase diagram, and different values for the charged pion mass（or decay constant） and neutral pion mass（or decay constant） at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.

Coexistence of isospin I=0 and I=1 pairings in asymmetric nuclear matter

The coexistence of neutron-neutron(n-n),proton-proton(p-p),and neutron-proton(n-p)pairings is investigated by adopting an effective density-dependent contact pairing potential.These three types of pairings can coexist only if the n-p pairing is stronger than the n-n and p-p pairings for the isospin asymmetric nuclear matter.In addition,the existence of n-n and p-p pairs might enhance n-p pairings in asymmetric nuclear matter when the n-p pairing strength is significantly stronger than the n-n and p-p ones.Conversely,the n-p pairing is reduced by the n-n and p-p pairs when the n-p pairing interaction approaches n-n and p-p pairings.

Isospin dependence of projectile fragmentation at hundreds of MeV/u

By modeling the fragmentation process using a dynamic model and permitting only evaporation in the statistical code,the main features of a projectile fragmentation at 600 MeV/u were considered in our previous study[Phys.Rev.C,98:014610(2018)].In this study,we extend this to the isospin dependence of a projectile fragmentation at several hundreds of MeV/u.We searched for isospin observables related to the isospin fractionation to extract the symmetry energy,and found that at the pre-equilibrium stage of the collisions an isospin diffusion will take place and affect the isospin of the final fragments.The isospin fractionation plays a part during the fragmenting stage.Compared to the soft symmetry energy,the stiff symmetry energy provides a smaller repulsive force for neutrons and an attractive force for the protons in a neutron-rich system at a subnormal density,and hence causes a smaller isospin asymmetry of the gas phase,leaving a more neutron-rich liquid phase.An observable robust isospin is proposed to extract the slope of the symmetry energy at normal density based on the isospin dependence of the projectile fragmentation at hundreds of MeV/u.

Isospin and symmetry energy study in nuclear EOS

This paper summarizes the isoscaling and isospin related studies in asymmetry nuclear reactions by different dynamic and sta tistical models. Isospin dependent quantum molecular dynamics model (IQMD) and lattice gas model (LGM) are used to study the isoscaling properties and isoscaling parameters dependence on incident energies, impact parameters, temperature and other parameters. In the LGM model, the signal of phase transition has been found in free neutron (proton) chemical potential dif ference Δμn or Δμp as a function of temperature, or in free neutron and proton chemical potential difference Δμn-Δμp. Density dependence of symmetry energy coefficient Csym(ρ/ρ0) is also studied in the frame of LGM, with the potential parameters which can reproduce the nuclear ground state property, soft density dependence of symmetry energy is deduced from the sim ulation results. Giant dipole resonance (GDR) induced by isospin asymmetry in entrance channel is also studied via IQMD model, and the dynamic dipole resonance shows isospin sensitivity on the isospin asymmetry of entrance channel and sym metry energy of the nuclear equation of state (EOS). GDR can also be regarded as a possible isospin sensitive signature.

A phenomenological equation of state for isospin asymmetric nuclear matter

A phenomenological momentum-independent(MID) model is constructed to describe the equation of state(EOS) for isospin asymmetric nuclear matter,especially the density dependence of the nuclear symmetry energy Esym(ρ).This model can reasonably describe the general properties of the EOS for symmetric nuclear matter and the symmetry energy predicted by both the sophisticated isospin and momentum dependent MDI model and the Skyrme-Hartree-Fock approach.We find that there exists a nicely linear correlation between Ksym and L as well as between J0/K0 and K0,where L and Ksym represent,respectively,the slope and curvature parameters of the symmetry energy at the normal nuclear density ρ0,while K0 and J0 are,respectively,the incompressibility and the third-order derivative parameter of symmetric nuclear matter at ρ0.These correlations together with the empirical constraints on K0,L and Esym(ρ0) lead to an estimation of -477 MeV Ksat,2 -241 MeV for the second-order isospin asymmetry expansion coefficient for the incompressibility of asymmetric nuclear matter at the saturation point.