From a Bayesian analysis of the electric dipole polarizability, the constrained energy of isovector giant dipole resonance, the peak energy of isocalar giant quadrupole resonance and the constrained energy of isocalar giant monopole resonance in $^{208}$Pb, we extract the isoscalar and isovector effective masses in nuclear matter at saturation density $ρ_0$ as $m_{s,0}^{\ast}/m=0.87_{-0.04}^{+0.04}$ and $m_{v,0}^{\ast}/m = 0.78_{-0.05}^{+0.06}$ at $90\%$ confidence level. The obtained constraints on $m_{s,0}^{\ast}$ and $m_{v,0}^{\ast}$ lead to a positive isospin splitting of nucleon effective mass in asymmetric nuclear matter of isospin asymmetry $δ$ at $ρ_0$ as $m_{n-p}^* / m=(0.20^{+0.15}_{-0.14})δ$. In addition, the symmetry energy at the subsaturation density $ρ^{\ast}=0.05~\mathrm{fm}^{-3}$ is determined to be $E_{\mathrm{sym}}(ρ^{\ast})=16.7\pm1.3$ MeV at $90\%$ confidence level.
We study the isospin effects of the mean field and two-body collision on the nucleon emissions at the intermediate energy heavy ion collisions by using an isospin dependent transport theory. The calculated results show that the nucleon emission number $N_{n}$ depends sensitively the isospin effect of nucleon nucleon cross section and weakly on the isospin dependent mean field for neutron-poor system in higher beam energy region . In particular, the correlation between the medium correction of two-body collision and the momentum dependent interaction enhances the dependence of nucleon emission …
We classify $A$--nucleon forces according to their isospin dependence and discuss the most general isospin structure of the three--nucleon force. We derive the leading and subleading isospin--breaking corrections to the three--nucleon force using the framework of chiral effective field theory.
Traditionally isospin violation (charge symmetry breaking and charge dependence) has been modeled by the exchange of mesons between two nucleons. Sources of isospin violation in these models include meson mass differences, meson mixing (of pseudoscalar, vector, and axial-vector mesons) and isospin violating couplings of mesons with nucleons. I will review the calculated results of this theoretical approach and the NN data on isospin violation.
The effects of the symmetry potential and the isospin dependent in-medium nucleon-nucleon (NN) cross section on the number of proton(neutron) emissions N$_p(N_n$) are studied respectively within an isospin-dependent quantum molecular dynamics (IQMD) model. The isospin dependent in-medium NN cross section is found to have a strong influence on N$_p(N_n$) but N$_p(N_n$) is not sensitive to the symmetry potential for the neutron-deficient colliding system at relatively high energies.We propose to make use of the N$_p(N_n$) as a probe to extract information on the isospin dependent in-medium NN cr…
We study the sensitivity of isospin dependence of nucleon-nucleon cross section and symmetry energy on the collective transverse in-plane flow. We find that collective transverse flow in Ca+Ca reactions shows great sensitivity to isospin dependence of nn cross section and symmetry energy.
After reviewing our microscopic approach to nuclear and neutron-rich matter, we focus on how nucleon-nucleon scattering is impacted by the presence of a dense hadronic medium, with special emphasis on the case where neutron and proton densities are different. We discuss in detail medium and isospin asymmetry effects on the total elastic cross section and the mean free path of a neutron or a proton in isospin-asymmetric nuclear matter. We point out that in-medium cross sections play an important role in heavy-ion simulations aimed at extracting constraints on the symmetry potential. We argue th…
We investigate nucleon mass splitting at finite isospin chemical potential in the frame of two flavor Nambu--Jona-Lasinio model. It is analytically proved that, in the phase with explicit isospin symmetry breaking the proton mass decreases and the neutron mass increases linearly in the isospin chemical potential.
The in-medium neutron-proton, proton-proton(neutron-neutron) scattering cross sections($σ_{np}^{*}$, $σ_{pp(nn)}^{*}$) are studied based on QHD-II type Lagrangian within the framework of the microscopic transport theory. The results demonstrate that, for free nucleon-nucleon scattering cross sections, the isospin dependence is dominantly caused by $ρ$ meson field. The medium correction of nucleon-nucleon scattering cross sections is also isospin dependent, $σ_{np}^{*}$ depends on the baryon density weakly and $σ_{pp(nn)}^{*}$ depends on the baryon density significantly, which is due to the dif…
The effect of different isospin-dependent cross-section on directed flow is studied for variety of systems(for which experimental balance energies are available) using an isospin-dependent Quantum Molecular Dynamic (IQMD) model. We show that balance energies are sensitive towards isospin-dependent cross-sections for light systems, while nearly no effect exist for heavier nuclei. A reduced cross-section $σ= 0.9σ_{NN}$ with stiff equation of state is able to explain experimental balance energies in most of systems. A power law behaviour is also given for the mass dependence of balance energy, wh…
We use the method of QCD sum rules in the presence of an external pion field to investigate isospin symmetry breakings in pion-nucleon couplings. Possible manifestations of such isospin symmetry breaking are examined in the context of low-energy nucleon-nucleon ($NN$) scattering. We discuss numerical results in relation to both the existing data and other theoretical predictions.
Based on an isospin dependent quantum molecular dynamics model we studied the influence of a medium correction of an isospin dependent nucleon nucleon cross section on the fragmentation at the intermediate energy heavy ion collisions. We found that the medium correction from an isospin dependent nucleon nucleon cross section increases the dependence of the fragmentation on the isospin effect of in-medium nucleon nucleon cross section, at the same time, the momentum dependent interaction (MDI) produces also an important role for enhancing the influence of the medium correction on the isospin ef…
We study the effect of isospin projections on a two source picture of coherent pions coming from nucleon-antinucleon annihilation. We show that important Hanbury-Brown Twiss correlations among like charge pion pairs compared with unlike arise from these isospin projections.
The influence of medium correction from an isospin dependent nucleon nucleon cross section on the fragmentation and nucleon emission in the intermediate energy heavy ion collisions was studied by using an isospin dependent quantum molecular dynamical model (IQMD). We found that the medium correction enhances the dependence of multiplicity of intermediate mass fragment $N_{imf}$ and the number of nucleon emission $N_{n}$ on the isospin effect of the nucleon nucleon cross section,while the momentum dependent interaction (MDI) produces also an important role for enhancing the influence of the med…
We examine the effect of isospin-violating meson-nucleon coupling constants on low-energy pion-nucleon scattering. We compute the couplings in the context of a nonrelativistic quark model. The difference between the up and down constituent masses induces a coupling of the neutral pion to the proton that is slightly larger than the corresponding one for the neutron. This difference generates a large isospin-violating correction---proportional to the isospin-even contribution arising from the nucleon Born terms---to the charge-exchange ($π^{-}p \rightarrow π^{0}n$) amplitude. In contrast to the …
We study the leading isospin-breaking contributions to the two-nucleon two-pion exchange potential due to explicit Delta degrees of freedom in chiral effective field theory. In particular, we find important contributions due to the delta mass splittings to the charge symmetry breaking potential that act opposite to the effects induced by the nucleon mass splitting.
Recently, we have derived the leading and subleading isospin-breaking three-nucleon forces using the method of unitary transformation. In the present work we extend this analysis and consider the corresponding two-nucleon forces using the same approach. Certain contributions to the isospin-violating one- and two-pion-exchange potential have already been discussed by various groups within the effective field theory framework. Our findings agree with the previously obtained results. In addition, we present the expressions for the subleading charge-symmetry-breaking two-pion exchange potential wh…
Modern nucleon-nucleon (NN) potentials, which accurately fit the nucleon-nucleon scattering phase shifts, contain terms which break isospin symmetry. The effects of these symmetry violating terms on the bulk properties of nuclear matter are investigated. The predictions of the charge symmetry breaking (CSB) terms are compared with the Nolen-Schiffer (NS) anomaly regarding the energies of neighboring mirror nuclei. We find that, for a quantitative explanation of the NS anomaly, it is crucial to include CSB in partial waves with $L>0$ (besides $^1S_0$) as derived from a microscopic model for CSB…
We report quantum Monte Carlo calculations of single-$Λ$ hypernuclei for $A<50$ based on phenomenological two- and three-body hyperon-nucleon forces. We present results for the $Λ$ separation energy in different hyperon orbits, showing that the accuracy of theoretical predictions exceeds that of currently available experimental data, especially for medium-mass hypernuclei. We show the results of a sensitivity study that indicates the possibility to investigate the nucleon-isospin dependence of the three-body hyperon-nucleon-nucleon force in the medium-mass region of the hypernuclear chart, whe…
The degree of isospin fractionation is measured by $(N/Z)_{n}$ / $(N/Z)_{N_{imf}}$, where $(N/Z)_{n}$ and $(N/Z)_{N_{imf}}$ are the saturated neutron-proton ratio of nucleon emissions (gas phase) and that of fragment emissions (liquid phase) in heavy ion collision at intermediate energy . The calculated results by using the isospin-dependent quantum molecular dynamics model show that the degree of isospin fractionation is sensitive to the neutron-proton ratio of colliding system but insensitive to the difference between the neutron-proton ratio of target and that of projectile. In particular, …
Using isospin dependent quantum molecular dynamical model, the studies of the isospin effect on preequilibrium nucleon emission in heavy ion collisions under different entrance channel conditions show that the ratio of preequilibrium neutron number to proton number depends strongly on symmetry potential, beam energy, and the ratio of neutron to proton of the colliding system, but weakly on isospin dependent in-medium nucleon-nucleon cross sections, impact parameter, Pauli potential, and momentum dependent interaction in the energy region from 45MeV/u up to 150 MeV/u where the dynamics is domin…
A spin-isospin dependent Three-Dimensional approach based on momentum vectors for formulation of the three-nucleon bound state is presented in this paper. The three-nucleon Faddeev equations with two-nucleon interactions are formulated as a function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angle between them with the inclusion of the spin-isospin quantum numbers, without employing a partial wave decomposition. As an application the spin-isospin dependent Faddeev integral equations are solved with Bonn-B potential. Our result for the Triton binding energy wit…
We discuss the role of the three-nucleon isospin T=3/2 amplitude in elastic neutron-deuteron scattering and in the deuteron breakup reaction. The contribution of this amplitude originates from charge-independence breaking of the nucleon-nucleon potential and is driven by the difference between neutron-neutron (proton-proton) and neutron-proton forces. We study the magnitude of that contribution to the elastic scattering and breakup observables, taking the locally regularized chiral N4LO nucleon-nucleon potential supplemented by the chiral N2LO three-nucleon force. For comparison we employ also…
Within a transport model using as the input nucleon momentum profiles from a parameterized isospin-dependent single-nucleon momentum distribution with a high momentum tail induced by short-range correlations, we employ the $^{197}$Au + $^{197}$Au collisions at 400 MeV/nucleon to examine on one hand effects of the short-range correlations on the pion and flow observables in probing the nuclear symmetry energy, and on the other hand how reliable are this isospin-dependent single-nucleon momentum distribution as well as the corresponding parameter settings. Besides significant effects of the shor…
The isospin dependence of the nucleon effective mass is investigated in the framework of the Dirac Brueckner-Hartree-Fock (DBHF) approach. The definition of nucleon scalar and vector effective masses in the relativistic approach is clarified. Only the vector effective mass is the quantity related to the empirical value extracted from the analysis in the nonrelatiistic shell and optical potentials. In the relativistic mean field theory, where the nucleon scalar and vector potentials are both energy independent, the neutron vector potential is stronger than that of proton in the neutron rich nuc…
The calculation of the energy-, density-, and isospin-dependent $Δ$ production cross sections in nucleon-nucleon (NN) scattering $σ^*_{NN\rightarrow NΔ}$ has been performed within the framework of the relativistic BUU approach. The N$Δ$ cross sections are calculated in Born approximation taking into account the effective mass splitting of the nucleons and $Δ$s in asymmetric matter. Due to the different mass splitting for neutron, proton and differently charged $Δ$s, it is shown that, similar to the NN elastic ones, the reductions of N$Δ$ inelastic cross sections in isospin-asymmetric nuclear m…
We review the present status of the nucleon effective mass splitting $puzzle$ in asymmetric matter, with controversial predictions within both non-relativistic $and$ relativistic approaches to the effective in medium interactions. Based on microscopic transport simulations we suggest some rather sensitive observables in collisions of asymmetric (unstable) ions at intermediate ($RIA$) energies: i) Energy systematics of Lane Potentials; ii) Isospin content of fast emitted nucleons; iii) Differential Collective Flows. Similar measurements for light isobars (like $^3H-^3He$) could be also importan…
The discrepancy between experimental data and theoretical calculations in one-nucleon removal reactions at intermediate energies (quantified by the so-called "quenching factors") and its dependence on the isospin asymmetry of the nuclei has been an open problem in nuclear physics for the last fifteen years. In this work, we propose an explanation for this long-standing problem, which relies on the inclusion of the process of core destruction due to its interaction with the removed nucleon. To include this effect, we extend the commonly used eikonal formalism via an effective nucleon density, a…
Based on an improved isospin- and momentum-dependent interaction, we have studied the qualitative effect of isospin splitting of nucleon effective mass on the specific shear viscosity of neutron-rich nuclear matter from a relaxation time approach. It is seen that for $m_n^\star>m_p^\star$, the relaxation time of neutrons is smaller and the neutron flux between flow layers is weaker, leading to a smaller specific shear viscosity of neutron-rich matter compared to the case for $m_n^\star<m_p^\star$. The effect is larger in nuclear matter at higher densities, lower temperatures, and larger isospi…
A representation without explicit use of the isospin formalism is developed for the precise study of few-nucleon systems, and the advantages of the proposed approach are demonstrated. Using the example of three-nucleon systems with central exchange NN-interaction potentials of the general type, the complete equivalence is shown for the both approaches with and without the isospin formalism. The new systems of equations contain a less number of components as compared to the commonly used ones and are more suitable for precise study of few-nucleon systems, in particular, within variational appro…
The asymptotic time derivative of the total dipole signal is proposed as an useful observable to investigate on Isospin equilibration phenomenon in multi-fragmentation processes. The study has been developed to describe charge/mass equilibration processes involving the gas and liquid "phases" of the total system formed during the early stage of a collision. General properties of this observable and the links with others isospin dependent phenomena are discussed. In particular, the $^{40}Cl+^{28}Si$ system at 40 MeV/nucleon is investigated by means of semiclassical microscopic many-body calcula…
We studied the influence of a momentum dependent interaction in the context of isopspin effects on fragmentation and dissipation in intermediate energy heavy ion collisions by using an isospin dependent quantum molecular dynamics model. It is shown that the nuclear stopping, the number of nucleons emitted ,and the multiplicity of intermediate mass fragments are larger with a momentum dependent interaction than without. In particular, the differences for these observables, when using an isospin dependent in-medium nucleon nucleon cross section versus an isospin independent one, are also larger …
The nuclear density functional framework, based on chiral dynamics and the symmetry breaking pattern of low-energy QCD, is extended to the description of collective nuclear excitations. Starting from the relativistic point-coupling Lagrangian previously introduced [Nucl. Phys. A770 (2006) 1], the proton-neutron (quasiparticle) random phase approximation is formulated and applied to investigate the role of chiral pion-nucleon dynamics in excitation modes involving spin and isospin degrees of freedom, e.g. isobaric analog states and Gamow-Teller resonances.
We investigate the equation of state of asymmetric nuclear matter and its isospin dependence in various spin-isospin $ST$ channels within the framework of the Brueckner-Hartree-Fock approach extended to include a microscopic three-body force (TBF). It is shown that the potential energy per nucleon in the isospin-singlet T=0 channel is mainly determined by the contribution from the tensor SD coupled channel. At high densities, the TBF effect on the isospin-triplet T=1 channel contribution turns out to be much larger than that on the T=0 channel contribution. At low densities around and below th…
We have studied the influences of isospin symmetry breaking of nucleon-nucleon interaction on the various properties of asymmetrical nuclear matter and $β$-stable matter. For asymmetrical nuclear matter, it is found that by including this isospin symmetry breaking, the changes of bulk properties increase by increasing both density and asymmetry parameter. However, these effects on the total energy and equation of state of $β$-stable matter are ignorable. For asymmetrical nuclear matter, the validity of the empirical parabolic law in the isospin symmetry breaking case is shown. It is observed t…
Within an isospin and momentum dependent transport model, the dynamics of isospin particles (nucleons and light clusters) in Fermi-energy heavy-ion collisions are investigated for constraining the isospin splitting of nucleon effective mass and the symmetry energy at subsaturation densities. The mass splitting of $m^{*}_{n}>m^{*}_{p}$ and $m^{*}_{n}<m^{*}_{p}$ in nuclear matter and the different stiffness of symmetry energy are used in the model. The single and double neutron to proton ratios of free nucleons and light particles are thoroughly investigated in the isotopic nuclear reactions of …
We have introduced a spin-isospin dependent three-dimensional approach for formulation of the three-nucleon scattering. Faddeev equation is expressed in terms of vector Jacobi momenta and spin-isospin quantum numbers of each nucleon. Our formalism is based on connecting the transition amplitude $T$ to momentum-helicity representations of the two-body $t$-matrix and the deuteron wave function. Finally the expressions for nucleon-deuteron elastic scattering and full breakup process amplitudes are presented.
We study the effect of isospin degree of freedom on the balance energy (E$_{bal}$) as well as its mass dependence throughout the mass range 48-270 for two sets of isobaric systems with N/Z = 1 and 1.4 at different colliding geometries ranging from central to peripheral ones. Our findings reveal the dominance of Coulomb repulsion in isospin effects on E$_{bal}$ as well as its mass dependence throughout the range of the colliding geometry. Our results also indicate that the effect of symmetry energy and nucleon-nucleon cross section on E$_{bal}$ is uniform throughout the mass range and throughou…
Partial-wave decomposition of isospin-projected subleading three-nucleon contact interactions
European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT ∗ ) and Fondazione Bruno Kessler（欧洲核物理及相关领域理论研究中心和布鲁诺·凯塞尔基金会）；Department of Mathematics and Physics “E. De Giorgi”, University of Salento（萨莱托大学“E. 德乔治”数学与物理系）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Lecce（意大利国家核物理研究所莱切分部）
In the simulation of intermediate energy heavy ion collisions by using the isospin dependent quantum molecular dynamics, the isospin effect on the process of multifragmentation and dissipation has been studied. It is found that the multiplicity of intermediate mass fragments $N_{imf}$ for the neutron-poor colliding system is always larger than that for the neutron-rich system, while the quadrupole of single particle momentum distribution $Q_{zz}$ for the neutron-poor colliding system is smaller than that of the neutron-rich system for all projectile-target combinations studied at the beam ener…
Within the framework of ImQMD05, we study several isospin sensitive observables, such as DR(n/p) ratios, isospin transport ratio (isospin diffusion), yield ratios for LCPs between the projectile region and mid-rapidity region for the reaction systems Ni+Ni, Zn+Zn, Sn+Sn at low-intermediate energies. Our results show that those observables are sensitive to the density dependence of symmetry energy, and also depend on the cluster formation mechanism. By comparing these calculations to the data, the information of the symmetry energy and reaction mechanism is obtained.
We report variational calculations of symmetric nuclear matter and pure neutron matter, using the new Argonne v18 two-nucleon and Urbana IX three-nucleon interactions. At the equilibrium density of 0.16 fm^-3 the two-nucleon densities in symmetric nuclear matter are found to exhibit a short-range spin-isospin structure similar to that found in light nuclei. We also find that both symmetric nuclear matter and pure neutron matter undergo transitions to phases with pion condensation at densities of 0.32 fm^-3 and 0.2 fm^-3, respectively. Neither transtion occurs with the Urbana v14 two-nucleon in…
The isospin splitting of the nucleon mean field is derived from the Brueckner theory extended to asymmetric nuclear matter. The Argonne V18 has been adopted as bare interaction in combination with a microscopic three body force. The isospin splitting of the effective mass is determined from the Brueckner-Hartree-Fock self-energy: It is linear acording to the Lane ansatz and such that $m^*_n > m^*_p$ for neutron-rich matter. The symmetry potential is also determined and a comparison is made with the predictions of the Dirac-Brueckner approach and the phenomenological interactions. The theoretic…
The Microscopic Otical Model Potential is evaluated within a relativistic scheme which provides a natural and consistent relation between the spin-orbit part and the central part of the potential. The Dirac-Brueckner-Hartree-Fock (DBHF) approach provides such a microscopic relativistic scheme, which is based on a realistic nucleon-nucleon interaction and reproduce the saturation properties of symmetric nuclear matter without any adjustable parameter. Its solution using the projection technique within the subtracted T-matrix (STM) representation provides a reliable extension to asymmetric nucle…
We use QCD sum rules for the three point function of a pseudoscalar and two nucleonic currents in order to estimate the charge dependence of the pion nucleon coupling constant coming from isospin violation in the strong interaction. The effect can be attributed primarily to the difference of the quark condensates <ubar u> and <dbar d>. Assuming that the pi0 is a pure isostate we obtain for the splitting between the coupling of proton and neutron to the neutral pion an interval of [0.008 ; 0.023], the uncertainties coming mainly from the input parameters. In order to obtain the coupling to a ph…
We had previously used techniques involving isospin to count the number of states for three identical fermions in a single j shell with total angular momentum I=j. We generalize this to all I, but the main thrust of this work is to consider now a 4-fermion system. As before, one evaluates the eigenvalues of the Hamiltonian \sum_{i<j}[a + bt(i)t(j)] both from an isospin point of view and an angular momentum point of view. In the 4-particle case, we get a more limited result than in the 3-particle case, namely the number of T=0 states minus twice the number of T=2 states, all of a given angular …
Based on a chiral approach to nuclear matter, we calculate the quartic term in the expansion of the equation of state of isospin-asymmetric nuclear matter. The contributions to the quartic isospin asymmetry energy $A_4(k_f)$ arising from $1π$-exchange and chiral $2π$-exchange in nuclear matter are calculated analytically together with three-body terms involving virtual $Δ(1232)$-isobars. From these interaction terms one obtains at saturation density $ρ_0 = 0.16\,$fm$^{-3}$ the value $A_4(k_{f0})= 1.5\,$MeV, more than three times as large as the kinetic energy part. Moreover, iterated $1π$-exch…
This paper presents reaction cross section predictions. These predictions are the result of a continuous pipeline which originates from a microscopic nuclear interaction. Density parameters and effective nucleon-nucleon cross sections (both involved in the reaction calculations) are by-products of the same equation of state. First, we perform tests of sensitivity to medium effects using reactions involving 208-Pb, a stable but weakly isospin-asymmetric nucleus. We also show predictions for collisions of some neutron-rich isotopes of Calcium and Argon. We observe significant sensitivity of the …
Within a transport model we search for potential probes of the isospin dependence of the in-medium nucleon-nucleon (NN) cross sections. Traditional measures of the nuclear stopping power are found sensitive to the magnitude but they are ambiguous for determining the isospin dependence of the in-medium NN cross sections. It is shown that isospin tracers, such as the neutron/proton ratio of free nucleons, at backward rapidities/angles in nuclear reactions induced by radioactive beams in inverse kinematics is a sensitive probe of the isospin dependence of the in-medium NN cross sections. At forwa…
The relativistic optical model potential (OMP) for nucleon-nucleus scattering is investigated in the framework of Dirac-Brueckner-Hartree-Fock (DBHF) approach using the Bonn-B One-Boson- Exchange potential for the bare nucleon-nucleon interaction. Both real and imaginary parts of isospin-dependent nucleon self-energies in nuclear medium are derived from the DBHF approach based on the projection techniques within the subtracted T -matrix representation. The Dirac potentials as well as the corresponding Schrodinger equivalent potentials are evaluated. An improved local density approximation is e…
We analyze isospin breaking through quark mass differences and virtual photons in the pion-nucleon scattering lengths in all physical channels in the framework of covariant baryon chiral perturbation theory.
In this article we investigate the structure of the non-local part of the symmetry term, that leads to a splitting of the effective masses of protons and neutrons in asymmetric matter. Based on microscopic transport simulations we suggest some rather sensitive observables in collisions of neutron-rich (unstable) ions at intermediate ($RIA$) energies. In particular we focus the attention on pre-equilibrium nucleon emissions. We discuss interesting correlations between the N/Z content of the fast emitted particles and their rapidity or transverse momentum, that show a nice dependence on the pres…
In this contribution, we review the most important physics presented originally in our recent publications. Some new analyses, insights and perspectives are also provided. We showed recently that the symmetry energy $E_{sym}(ρ)$ and its density slope $L(ρ)$ at an arbitrary density $ρ$ can be expressed analytically in terms of the magnitude and momentum dependence of the single-nucleon potentials using the Hugenholtz-Van Hove (HVH) theorem. These relationships provide new insights about the fundamental physics governing the density dependence of nuclear symmetry energy. Using the isospin and mo…
With stochastic transport simulations we study in detail central and peripheral collisions at Fermi energies and suggest new observables, sensitive to the symmetry energy below normal density. As such we identify on one hand the isospin imbalance ratio, i.e. the relative amount of isospin equilibration in binary, peripheral reactions of nuclei with different isospin, as a function of the energy loss, which is sensitive to isospin diffusion; on the other hand the isospin asymmetry of an intermediate mass fragment (IMF) in symmetric collisions in ternary reactions, or more particularly, the rati…
Using an isospin-dependent quantum molecular dynamics, nuclear stopping in intermediate heavy ion collisions has been studied. The calculation has been done for colliding systems with different neutron-proton ratios in beam energy ranging from 15MeV/u to 150MeV/u. It is found that, in the energy region from above Fermi energy to 150MeV/u, nuclear stopping is very sensitive to the isospin dependence of in-medium nucleon-nucleon cross section, but insensitive to symmetry potential. From this investigation, we propose that nuclear stopping can be used as a new probe to extract the information on …
The isospin distribution of particles and fragments in collisions 96Ru+96Ru, 96Ru+96Zr, 96Zr+96Ru, and 96Zr+96Zr at beam energy 400 AMeV is studied with isospin dependent QMD model. We find that the rapidity distribution of differential neutron-proton counting in neutron rich nucleus-nucleus collisions at intermediate energies is sensitive to the isospin dependent part of nuclear potential. The study of the N/Z ratio of nucleons, light charged particles (LCP) and intermediate mass fragments (IMF) shows that the isospin dependent part of nuclear potential drives IMF to be more isospin symmetric…
Using the isospin dependent quantum molecular dynamics model, we study the effect of charge asymmetry and isospin dependent cross-section on $\frac{dN}{d(<Cos2ϕ>)}$ and $\frac{dN}{p_tdp_t}$. Simulations have been carried out for the reactions of $^{124}X_{m}+^{124}X_{m}$, where m = (47, 50 and 59) and $^{40}S_{16}+^{40}S_{16}$. Our study shows that these parameters depend strongly on the isospin of cross-section and charge asymmetry. The distribution of nucleons and fragments is not symmetric around the beam axis.
The dispersive optical model (DOM) as presently implemented can investigate the isospin (nucleon asymmetry) dependence of the Hartree-Fock-like potential relevant for nucleons near the Fermi energy. Data constraints indicate that a Lane-type potential adequately describes its asymmetry dependence. Correlations beyond the mean-field can also be described in this framework, but this requires an extension that treats the non-locality of the Hartree-Fock-like potential properly. The DOM has therefore been extended to properly describe ground-state properties of nuclei as a function of nucleon asym…
We study the mixing and the kinetic equilibration of projectile and target nucleons in relativistic heavy-ion collisions in the energy regime between 150~AMeV and 2~AGeV in a coupled-channel BUU (CBUU) approach. We find that equilibrium in the projectile-target degrees of freedom is in general not reached even for large systems at low energy where elastic nucleon-nucleon collisions dominate. Inelastic nucleon excitations are more favorable for equilibration and their relative abundance increases both with energy and mass. Experimentally, the projectile/target admixture can be determined by mea…
