Isospin Diffusion Research Articles

Probing the high-density symmetry energy from subthreshold hyperon production in heavy-ion collisions

The hyperon dynamics in heavy-ion collisions near threshold energy has been investigated within the quantum molecular dynamics transport model. The isospin and momentum dependent hyperon-nucleon potential and the threshold energy correction on the hyperon elementary cross section are included in the model. It is found that the high-density symmetry energy is dependent on the isospin ratios Σ−/Σ+ and Ξ−/Ξ0, in particular in the domain of high kinetic energies. The isospin diffusion in heavy-ion collisions influences the neutron/proton ratio in the high-density region. The Σ−/Σ+ ratio depends on the stiffness of symmetry energy, in particular at the beam energy below the threshold value (Eth=1.58 GeV), i.e., the kinetic energy spectra of the single ratios, excitation functions and energy spectra of the double ratios in the isotopic reactions of 108Sn + 112Sn, 112Sn + 112Sn, 124Sn + 124Sn and 132Sn + 124Sn. The double strangeness ratio Ξ−/Ξ0 weakly depends on the symmetry energy because of the hyperon-hyperon collision mainly contributing the Ξ production below the threshold energy (Eth = 3.72 GeV).

Nuclear symmetry energy at work in heavy ion reactions: new results from the INDRA-FAZIA apparatus

The recently coupled INDRA-FAZIA apparatus offers unique opportunities to investigate heavy ion collisions at Fermi energies by combining the optimal identification capabilities of FAZIA and the large angular coverage of INDRA. We present a selection of the results of the analysis of the first experimental campaign performed with INDRA-FAZIA, in which the four reactions 58,64Ni+58,64Ni have been studied at two different beam energies (32 and 52 MeV/nucleon) in the intermediate energy regime. The present work is focused on the isospin diffusion effects in semiperipheral and peripheral collisions. A stronger isospin equilibration is found at 32 MeV/nucleon than at 52 MeV/nucleon, as expected due to a shorter projectile-target interaction time in the latter case.

Experimental study of isospin transport with Ca40,48+Ca40,48 reactions at 35 MeV/nucleon

We investigate the isospin transport with 40,48 Ca+ 40,48 Ca reactions at 35 MeV/nucleon, measured with the coupling of the VAMOS high acceptance spectrometer and the INDRA charged particle multidetector. Using the quasi-projectile remnant measured with VAMOS and carefully selected light-charged-particles measured in coincidence with INDRA, a reconstruction method is applied to estimate the excited quasi-projectile (QP) on an event-by-event basis. The isospin diffusion is investigated using the isospin transport ratio with the asymmetry $\delta$ = (N -- Z)/A of the projectile as an isospin-sensitive observable and the total transverse energy of Z $\le$ 2 nuclei for experimental centrality sorting. The experimental isospin transport ratios present, for both the reconstructed QP and its remnant, a clear evolution towards isospin equilibration with increasing dissipation of the collision while the full equilibration is not reached. A smoother evolution with less discrepancies between the two mixed systems in the case of the reconstructed QP is also observed. The isospin migration is investigated using the neutron-to-proton ratio of the light-charged-clusters and the velocity of the QP remnant as a sorting parameter. More particularly, we focused on an angular region centered around the mid-rapidity of the reaction so as to characterize the low-density neck emissions. A systematic neutron-enrichment is observed and interpreted as a consequence of isospin migration, more particularly for the symmetric systems which present no isospin gradient between the projectile and the target. We also noticed that the ^{2}H and ^{4}He particles exhibit very close multiplicities independently of the sorting variable for the symmetric systems.

Isospin blocking and its effects in heavy-ion collisions

A concept of \emph{isospin blocking} in the process of isospin diffusion in heavy-ion collisions is raised. Generally, in the process of isospin diffusion, isospin asymmetry would diffuse from the place with large asymmetry to the place with small asymmetry. However, our study shows that the isospin diffusion could be blocked in case the local value of the symmetry energy is larger. We dub this phenomenon ``isospin blocking''. To check this behavior, in the framework of an Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, isospin diffusions in the isotope Sn+Sn reactions at 270 MeV/nucleon are studied. It is shown that the value of the after-diffusion asymmetry is distinctly blocked if the local symmetry energy is large. The effects of the isospin blocking on the isospin asymmetry of dilute and dense matter and the final $\pi^-/\pi^+$ ratio in heavy ion collisions are demonstrated.

First results from the INDRA-FAZIA apparatus on isospin diffusion in Ni58,64+Ni58,64 systems at Fermi energies

An investigation of the isospin equilibration process in the reactions Ni58,64+Ni58,64 at two bombarding energies in the Fermi regime (32 and 52 MeV/nucleon) is presented. Data have been acquired during the first experimental campaign of the coupled INDRA-FAZIA apparatus in GANIL. Selecting from peripheral to semicentral collisions, both the neutron content of the quasiprojectile residue and that of the light ejectiles coming from the quasiprojectile evaporation have been used as probes of the dynamical process of isospin diffusion between projectile and target for the asymmetric systems. The isospin transport ratio technique has been employed. The relaxation of the initial isospin imbalance with increasing centrality has been clearly evidenced. The isospin equilibration appears stronger for the reactions at 32 MeV/nucleon, as expected due to the longer projectile-target interaction time than at 52 MeV/nucleon. Coherent indications of isospin equilibration come from the quasiprojectile residue characteristics and from particles ascribed to the quasiprojectile decay.6 MoreReceived 23 May 2022Accepted 26 July 2022DOI:https://doi.org/10.1103/PhysRevC.106.024603©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEquations of state of nuclear matterLow & intermediate energy heavy-ion reactionsNuclear fragmentationNuclear reactionsTechniquesSpectrometers & spectroscopic techniquesNuclear Physics

Constraining the density dependence of the symmetry energy: the isospin transport ratio revisited

The isospin diffusion of the quasi-projectile formed in the on reactions in the Fermi energy domain is investigated in the framework of the Boltzmann–Uehling–Uhlenbeck transport model. The well known isospin transport ratio observable is revisited, with the aim of insuring an optimal comparison between experimental data and theoretical calculations and reducing the present uncertainties in the extraction of empirical equation of state parameters. We show that isospin transport ratios are sensitive to all the low order isovector parameters (E sym, L sym and K sym, but the quantitative results depend on the choice of the isospin sensitive observable. We demonstrate that realistic models of the equation of state, covering the uncertainty that presently affects the theoretical description of neutron stars static observables, can be effectively discriminated by isospin diffusion experiments, provided the neutron to proton ratio of the projectile remnant is precisely measured as a function of centrality.

Isospin diffusion measurement from the direct detection of a quasiprojectile remnant

The neutron-proton equilibration process in 48 Ca+ 40 Ca at 35 MeV/nucleon bombarding energy has been experimentally estimated by means of the isospin transport ratio. Experimental data have been collected with a subset of the FAZIA telescope array, which permitted to determine Z and N of detected fragments. For the first time, the QP evaporative channel has been compared with the QP break-up one in a homogeneous and consistent way, pointing out to a comparable n-p equilibration which suggests close interaction time between projectile and target independently of the exit channel. Moreover, in the QP evaporative channel n-p equilibration has been compared with the prediction of the Antisymmetrized Molecular Dynamics (AMD) model coupled to the GEMINI statistical model as an afterburner, showing a larger probability of proton and neutron transfers in the simulation with respect to the experimental data.

Dynamics of light hypernuclei in collisions of $$^{197}$$Au+$$^{197}$$Au at GeV energies

The dynamics of light hypernuclei and nuclear clusters produced in $^{197}$Au+$^{197}$Au collisions has been investigated thoroughly with a microscopic transport model. All possible channels of hyperon production and transportation of hyperons in nuclear medium are implemented into the model. The light complex fragments are recognized with the Wigner density approach at the stage of freeze out in nuclear collisions. The isospin diffusion in the collisions is responsible for the neutron-rich cluster formation. The collective flows of nuclear clusters are consistent with the experimental data from FOPI collaboration. It is found that the influence of the hyperon-nucleon potential on the free hyperons is negligible, but available for the light hypernuclide formation. The directed and elliptic flows of $^{3}_{\Lambda}$H and $^{4}_{\Lambda}$H at incident energies of 2, 2.5, 3, 3.5 and 4 GeV/nucleon are investigated thoroughly and manifest the same structure with the nuclear clusters. The hypernuclear yields are produced in a wide rapidity and momentum regime with increasing the beam energy.

Isospin dependence of projectile fragmentation at hundreds of MeV/u * * Supported by the National Natural Science Foundation of China (11875328, 11605296, 11635003)

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.

Nuclear neck-density determination at Fermi energy with CHIMERA detector

Binary collisions of either stable or radioactive heavy ions at Fermi energies allow to study the nuclear reaction mechanisms under dynamical conditions of non-equilibrium and the formation of transient pieces of nuclear matter of very short mean life times at sub-normal density. An important role in the evolutionary phase of the collision is played by the gradient of the nuclear density affecting the isospin asymmetry of the reaction products by typical transport phenomena such as the isospin diffusion and drift. Experimental determination of the value of the nuclear matter density in the early phase of the collision is a crucial step towards understanding the underlying mechanism responsible for the production of clusters. In this paper a method for evaluating the nuclear density in semi-peripheral collisions in the reaction $$^{124}Sn + ^{64}Ni$$ at 35 MeV/nucleon as studied with the CHIMERA multi-particle detector is described.

Constraints on the symmetry energy and its associated parameters from nuclei to neutron stars

The symmetry energy obtained with the effective Skyrme energy density functional is related to the values of isoscalar effective mass and isovector effective mass, which is also indirectly related to the incompressibility of symmetric nuclear matter. In this work, we analyze the values of symmetry energy and its related nuclear matter parameters in five-dimensional parameter space by describing the heavy ion collision data, such as isospin diffusion data at 35 MeV/u and 50 MeV/u, neutron skin of $^{208}\mathrm{Pb}$, and tidal deformability and maximum mass of neutron star. We obtain the parameter sets which can describe the isospin diffusion, neutron skin, tidal deformability, and maximum mass of neutron star, and give the incompressibility ${K}_{0}=250.23\ifmmode\pm\else\textpm\fi{}20.16$ MeV, symmetry energy coefficient ${S}_{0}=31.35\ifmmode\pm\else\textpm\fi{}2.08$ MeV, the slope of symmetry energy $L=59.57\ifmmode\pm\else\textpm\fi{}10.06$ MeV, isoscalar effective mass ${m}_{s}^{*}/m=0.75\ifmmode\pm\else\textpm\fi{}0.05$, and quantity related to effective mass splitting ${f}_{I}=0.005\ifmmode\pm\else\textpm\fi{}0.170$. At two times normal density, the symmetry energy we obtained is in 35--55 MeV. To reduce the large uncertainties of ${f}_{I}$, more critical works in heavy ion collisions at different beam energies are needed.

Constraints on symmetry energy and n/p effective mass splitting with improved quantum molecular dynamics model

A new version of improved quantum molecular dynamics model that includes standard Skyrme interactions has been developed. Based on the new code,four commonly used parameter sets,SLy4,SkI2,SkM*and Gs are adopted in the improved quantum molecular dynamics model and the isospin sensitive observables,namely isospin transport ratios,single and double ratios of the yields of neutrons and protons are investigated. The isospin transport ratios are strongly sensitive to the slope of symmetry energy,and are not very sensitive to the nucleon effective mass splitting. On the other hand,the high energy neutrons and protons yields ratios from reactions at different incident energies provide a good observable to the momentum dependence of nucleon effective mass splitting. By comparing our calculations with the data,we find that the constrained L value(the slope of density dependence of symmetry energy) is about ~46 MeV when the Skyrme type interaction is considered in transport models,and the isospin diffusion data prefer to mn*mp*,but it is not a strong constraint with deep χ2minimum.

Reexamining the isospin-relaxation time in intermediate-energy heavy-ion collisions

Isospin relaxation times characterizing isospin transport processes between the projectile and the target with different $N/Z$ ratios and that between the neck and the spectator with different isospin asymmetries and densities in intermediate-energy heavy-ion collisions are studied within an isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model using the lattice Hamiltonian approach. The respective roles and time scales of the isospin diffusion and drift as the major mechanisms of isospin transport in intermediate-energy heavy-ion collisions are discussed. Effects of nuclear symmetry energy and neutron-proton effective mass splitting on the isospin relaxation times are examined.

Relativistic Brueckner-Hartree-Fock theory in nuclear matter without the average momentum approximation

Brueckner-Hartree-Fock theory allows to derive the $G$-matrix as an effective interaction between nucleons in the nuclear medium. It depends on the center of mass momentum $\bm{P}$ of the two particles and on the two relative momenta $\bm{q}$ and $\bm{q'}$ before and after the scattering process. In the evaluation of the total energy per particle in nuclear matter usually the angle averaged center of mass momentum approximation has been used. We derive in detail the exact expressions of the angular integrations of the momentum $\bm{P}$ within relativistic Brueckner-Hartree-Fock (RBHF) theory, especially for the case of asymmetric nuclear matter. In order to assess the reliability of the conventional average momentum approximation for the binding energy, the saturation properties of symmetric and asymmetric nuclear matter are systematically investigated based on the realistic Bonn nucleon-nucleon potential. It is found that the exact treatment of the center of mass momentum leads to non-negligible contributions to the higher order physical quantities. The correlation between the symmetry energy $E_{\mathrm{sym}}$, the slope parameter $L$, and the curvature $K_{\mathrm{sym}}$ of the symmetry energy are investigated. The results of our RBHF calculations for the bulk parameters characterizing the equation of state are compared with recent constraints extracted from giant monopole resonance and isospin diffusion experiments.

Effect of isospin diffusion on the production of neutron-rich nuclei in multinucleon transfer reactions

The isospin dissipation dynamics in multinucleon transfer reactions has been investigated within the dinuclear system model. Production cross sections of neutron-rich isotopes around projectile-like and target-like fragments are estimated in collisions of $^{58,64}\mathrm{Ni}+^{208}\mathrm{Pb}$ and $^{78,86,91}\mathrm{Kr}+^{198}\mathrm{Pt}$ near Coulomb barrier energies. The isospin diffusion in the nucleon transfer process is coupled to the dissipation of relative motion energy and angular momentum of colliding system. The available data of projectile-like fragments via multinucleon transfer reactions are nicely reproduced. It is found that the light projectile-like fragments are produced in the neutron-rich region because of the isospin equilibrium in two colliding nuclei. However, the heavy target-like fragments tend to be formed on the neutron-poor side above the $\ensuremath{\beta}$-stability line. The neutron-rich projectiles move the maximal yields of heavy nuclei to the neutron-rich domain and are available for producing the heavy exotic isotopes, in particular around the neutron shell closure of $N=126$.

Correlation between symmetry energy and effectivek-mass splitting with an improved isospin- and momentum-dependent interaction

The isospin- and momentum-dependent interaction using the isospin-dependent quantum molecular dynamics model is improved. The momentum dependence of the interaction is fitted to the optical potentials extracted with proton-nucleus scattering data, while the isospin dependence is adjusted based on the current constraints on the symmetry energy and its density slope at normal density. The resulting parameters of the interaction are used to calculate the effective masses characterized by the nonlocality of the nuclear potential in the spatial coordinates (the so-called effective $k$ masses). It is found that this parametrization can reproduce the effective $k$ masses calculated by the Dirac-Brueckner-Hartree-Fock model. The current constraints on the total symmetry energy can accommodate a wide-range adjustment of the local symmetry energy and effective $k$-mass splitting. Four groups of parameters, which provide different density dependences of symmetry energy and effective $k$-mass splitting, are applied to investigate the isospin diffusion and neutron to proton double ratios in collisions involving $^{124}\mathrm{Sn}$ and $^{112}\mathrm{Sn}$ nuclei at 50 and 120 MeV/nucleon. Calculations confirm the sensitivity of symmetry energy to the isospin diffusion, but indicate the synchronous effects of symmetry energy and effective $k$-mass splitting on the double ratios.

Influence of Skyrme-type interaction on HICs observables

A new version of the improved quantum molecular dynamics model has been developed by including Skyrme type momentum dependent interaction. 12 Skyrme like parameter sets {K0, S0, L, m ∗, m ∗} are adopted in the transport model code to calculate the isospin diffusion, single and double ratios of transverse emitted nucleons, neutron proton isoscaling ratios. The calculations and correlation analysis evidence that isospin diffusion observable at lower beam energy is sensitive to the slope of symmetry energy and m ∗. The high energy neutrons and protons yield ratios from reactions at different incident energies provide a sensitive observable to study the nucleon effective mass splitting, at higher beam energy. The properties of isospin asymmetric nuclear equation of state is of fundamental importance in our understanding of nature’s asymmetric objects including neutron stars as well as heavy nuclei with very different number of neutrons and protons. Currently, there exist, lot of effective interaction parameter sets [1, 2], for fitting the ground-state properties of stable nuclei, symmetric and asymmetric nuclear matter. It also leads very different neutron Equation of state which may have different nuclear matter (NM) parameters, such as incompressibility K0, isoscalar effective mass m ∗ ,s ymmetry energy coef fi cientS0, slope of symmetry energy L and isovector effec

Covariance analysis of symmetry energy observables from heavy ion collision

Using covariance analysis, we quantify the correlations between the interaction parameters in a transport model and the observables commonly used to extract information of the Equation of State of Asymmetric Nuclear Matter in experiments. By simulating 124Sn + 124Sn, 124Sn + 112Sn and 112Sn + 112Sn reactions at beam energies of 50 and 120 MeV per nucleon, we have identified that the nucleon effective mass splitting is most strongly correlated to the neutrons and protons yield ratios with high kinetic energy from central collisions especially at high incident energy. The best observable to determine the slope of the symmetry energy, L, at saturation density is the isospin diffusion observable even though the correlation is not very strong (∼0.7). Similar magnitude of correlation but opposite in sign exists for isospin diffusion and nucleon isoscalar effective mass. At 120 MeV/u, the effective mass splitting and the isoscalar effective mass also have opposite correlation for the double n/p and isoscaling p/p yield ratios. By combining data and simulations at different beam energies, it should be possible to place constraints on the slope of symmetry energy (L) and effective mass splitting with reasonable uncertainties.

Isospin transport phenomena and odd-even staggering in84Kr+112,124Sn collisions at 35 AMeV

Experimental results concerning isospin transport phenomena and odd-even staggering in Z and N distributions are presented. Data refer to 84Kr+112,124Sn collisions at 35AMeV and they were collected with a high resolution FAZIA telescope, able to isotopically resolve ions up to Z ∼ 20. Evidences of isospin diffusion and drift obtained from the /Z behaviour of the detected fragments are discussed. The odd-even staggering both in Z and N is compared with experimental data available in literature, finding that it shows a common trend in different reaction types.

Constraints on nucleon effective mass splitting with heavy ion collisions

A new version of the improved quantum molecular dynamics model has been developed to include standard Skyrme interactions. Four commonly used Skyrme parameter sets, SLy4, SkI2, SkM* and Gs are adopted in the transport model code to calculate the isospin diffusion observables as well as single and double ratios of transverse emitted nucleons. While isospin diffusion observables are sensitive to the symmetry energy term, they are not very sensitive to the nucleon effective mass splitting parameters in the interactions. Our calculations show that the high energy neutrons and protons and their ratios from reactions at different incident energies provide a robust observable to study the momentum dependence of the symmetry potential which leads to the effective mass splitting. However the sensitivity of effective mass splitting effect on the double n/p yield ratios decreases with increasing beam energy, even though high energy protons and neutrons are produced more abundantly at high beam energy. Our calculations show that the optimum incident energy to study nucleon effective masses is between 100–200 MeV per nucleon.