A systematic study of the in-medium correction factor ($F$) on nucleon-nucleon elastic cross section is performed within the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. The effects of the beam energy dependence of $F$ on the directed, elliptic flow and nuclear stopping in $^{197}$Au+$^{197}$Au collisions with energy ranging from $0.09$ to $0.8A$ GeV are explored. It is found that the directed, elliptic flow and nuclear stopping at relatively low energies are very sensitive to $F$, and the sensitivity gradually weakens with increasing beam energy. The beam energy dependent in-medium correction factor $F$ is deduced from the comparison of the excitation functions of the directed, elliptic flow and nuclear stopping between the calculated results and the FOPI experimental data.
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 …
Data on stopping in intermediate-energy central heavy-ion collisions are analyzed following transport theory based on the Boltzmann equation. In consequence, values of nuclear shear viscosity are inferred. The inferred values are significantly larger than obtained for free nucleon dispersion relations and free nucleon-nucleon cross sections.
By considering three different Nucleon-Nucleon (NN) elastic differential cross sections: the Cugnon \emph{et al.} parameterized differential cross section [Nucl. Instrum. Methods Phys. Res., Sect. \textbf{B111}, 215 (1996)], and the differential cross section derived from the collision term of the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation proposed by Mao \emph{et al.} [Z.\ Phys.\ A {\bf 347}, 173 (1994)], as well as the isotropic differential cross section, within the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, the influence …
Nuclear stopping in the heavy ion collisions over a beam energy range from SIS, AGS up to SPS is studied in the framework of the modified UrQMD transport model, in which mean field potentials of both formed and "pre-formed" hadrons (from string fragmentation) and medium modified nucleon-nucleon elastic cross sections are considered. It is found that the nuclear stopping is influenced by both the stiffness of the equation of state and the medium modifications of nucleon-nucleon cross sections at SIS energies. At the high SPS energies, the two-bump structure is shown in the experimental rapidity…
Three typical algorithms of Pauli blocking in the quantum molecular dynamics type models are investigated in the nuclear matter, the nucleus and the heavy ion collisions. The calculations in nuclear matter show that the blocking ratios obtained with the three algorithms are underestimated 13-25\% compared to the analytical values of blocking ratios. For the finite nucleus, the spurious collisions occur around the surface of the nucleus owing to the defects of Pauli blocking algorithms. In the simulations of heavy ion collisions, the uncertainty of stopping power from different Pauli blocking a…
In-medium nucleon-nucleon scattering cross sections are explored by comparing results of quantum molecular dynamics simulations to data on stopping and on elliptic and directed flow in intermediate-energy heavy-ion collisions. The comparison points to in-medium cross sections which are suppressed at low energies but not at higher energies. Positive correlations are found between the degree of stopping and the magnitudes of elliptic and directed flows.
With the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, a systematic investigation of the effects of in-medium nucleon-nucleon ($NN$) elastic cross section on the collective flow and the stopping observables in $^{197}\text{Au}+^{197}\text{Au}$ collisions at beam energies from 40 to 150 MeV/nucleon is performed. Simulations with the medium correction factor $\mathcal{F}=σ^{\text{in-medium}}_{NN}/σ^{\text{free}}_{NN}=0.2,~0.3,~0.5$, and the one obtained with the FU3FP1 parametrization which depends on both the density and the momentum are compared to th…
We address the stopping in heavy-ion induced reactions around the Fermi energy using central collisions recorded with \emph{INDRA} $4π$ array. The stopping is minimal around the Fermi energy and corresponds to the disappearance of the Mean-Field effects and the appearance of nucleon-nucleon elastic collisions. This phenomenon is attributed to a change in the dissipation regime going from 1-body (Mean-Field) dissipation at low incident energy to 2- body (nucleonic collisions) above the Fermi energy. A connection to the in-medium transport properties of nuclear matter is proposed and comprehensi…
We present transport calculations for heavy ion reactions in which the mean field and the in-medium nucleon-nucleon cross section are consistently based on the same effective interaction, i.e. the in-medium T-matrix from microscopic Dirac-Brueckner calculations. Doing so, the stopping in central reactions in terms of the recently proposed $var_{\rm tl}$ observable and the correlation to the behavior of the directed flow is investigated. The relation to the nuclear shear viscosity is discussed.
Within a Boltzmann transport model, we demonstrate correlation between stopping observables and shear viscosity in central nuclear collisions at intermediate energies (on the order of 10 to 1000 MeV/nucleon). The correlation allows us to assess the viscosity of nuclear matter, by tuning the in-medium nucleon-nucleon cross section in our transport model to agree with nuclear stopping data. We also calculate the ratio of shear viscosity to entropy density to determine how close the system is to the universal quantum lower limit proposed in the context of ultrarelativistic heavy ion collisions.
Accessing nucleon transversity with one-point energy correlators
Fudan University（复旦大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles（加州大学洛杉矶分校马尼·L·巴乌米克理论物理研究所）；Center for Frontiers in Nuclear Science, Stony Brook University（纽约州立大学石溪分校核科学前沿中心）；Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Fudan University（复旦大学核物理与离子束应用教育部重点实验室）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（国家自然科学基金委与复旦大学上海理论核物理研究中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
It is argued that the experimentally observed baryon stopping may indicate (within the present experimental uncertainties) a non-monotonous behaviour as a function of the incident energy of colliding nuclei. This can be quantified by a midrapidity reduced curvature of the net-proton rapidity spectrum. The above non-monotonous behaviour reveals itself as a "zig-zag" irregularity in the excitation function of this curvature. The three-fluid dynamic calculations with a hadronic equation of state (EoS) fail to reproduce this irregularity. At the same time, the same calculations with an EoS involvi…
We show how exclusive vector meson production off light ions can be used to probe the spatial distribution of small-$x$ gluons in the deuteron and $^3$He wave functions. In particular, we demonstrate how short range repulsive nucleon-nucleon interactions affect the predicted coherent $J/Ψ$ production spectra. Fluctuations of the nucleon substructure are shown to have a significant effect on the incoherent cross section above $|t|\gtrsim 0.2\,\mathrm{GeV}^2$. By explicitly performing the JIMWLK evolution, we predict the $x$-dependence of coherent and incoherent cross sections in the EIC energy …
The role of momentum dependent interactions is studied in nuclear stopping at intermediate energy using an isospin-dependent quantum molecular dynamics model. Present calculations are performed at incident energy between 50 and 1000 MeV/nucleon. Our findings show that nuclear stopping is sensitive towards the impact parameter, incident energies as well as towards the mass of the colliding system. Further, the degree of stopping is suppressed by the inclusion of momentum dependent interactions, whereas the particle production is not affected by the MDI.
Using an isospin-dependent quantum molecular dynamics (IQMD) model, nuclear stopping is analyzed in asymmetric colliding channels by keeping the total mass fixed. The calculations have been carried by varying the asymmetry of the colliding pairs with different neutron-proton ratios in center of mass energy 250 MeV/nucleon and by switching off the effect of Coulomb interactions. We find sizable effect of asymmetry of colliding pairs on the stopping and therefore on the equilibrium reached in a reaction.
Nuclear stopping in heavy ion collisions (HIC) has been studied by means of rapidity distribution and asymmetry of nucleon momentum distribution. It is an important quantity in determining the outcome of a reaction. Fen Fu {\it et al.,} \cite{2} calculate both the radial flow and the degree of nuclear stopping in Pb + Pb and Ni + Ni at 0.4, 0.8 and 1.2 GeV/neucleon. They found that the expansion velocity as well as the degree of nuclear stopping are higher in the heavier system at all energies.
Generalized parton distributions (GPDs) encoding multidimensional information of hadron partonic structure appear as the building blocks in a factorized description of hard exclusive reactions. The nucleon GPDs have been accessed by deeply virtual Compton scattering and deeply virtual meson production with lepton beam. A complementary probe with hadron beam is the exclusive pion-induced Drell-Yan process. We discuss recent theoretical advances on describing this process in terms of the partonic subprocess convoluted with the nucleon GPDs and the pion distribution amplitudes. Furthermore, we me…
The present thesis deals with the theoretical study of multi-fragmentation and its related phenomena's like directed transverse flow, rapidity distribution, elliptical flow and nuclear stopping in intermediate energy heavy-ion collisions for asymmetric colliding nuclei. We aim to discuss the role of Coulomb interactions, nuclear equations of state (NEOS) and various rapidity bins by taking mass asymmetry into account.
Generalized parton distributions (GPDs) encoding multidimensional information of hadron partonic structure appear as the building blocks in a factorized description of hard exclusive reactions. The nucleon GPDs have been accessed by deeply virtual Compton scattering and deeply virtual meson production with lepton beam. A complementary probe with hadron beam is shown to be the exclusive pion-induced Drell-Yan process, $π^- p \to μ^+ μ^- n$, as demonstrated by recent theoretical advances on describing this process in terms of QCD factorization as the partonic subprocess convoluted with the nucle…
A novel stochastic technique combining a dilute source grid of $\mathbb{Z}_3$ noise with iterative momentum-smearing is used to study the proton correlation function at rest and in boosted frames on two lattice volumes. The technique makes use of the baryonic version of the so-called one-end trick, and the decomposition into signal and noise terms of the resulting stochastic proton correlation function is made explicit. The number and location of the source points in the dilute grid should be chosen so that the benefits of averaging over many locations overcomes the additional statistical erro…
Using the isospin dependent quantum molecular dynamics model, we study the effect of charge asymmetry and isospin dependent cross-section on nuclear stopping and multiplicity of free nucleons and LMF's. Simulations were carried out for the reactions $^{124}X_{m}+^{124}X_{m}$, where m varies from 47 to 59 and for $^{40}Y_{n}+^{40}Y_{n}$, where n varies from 14 to 23. Our study shows that nuclear stopping as well as the production of LMF's depend strongly on the isospin of the cross-section.
We study the nuclear stopping in high energy nuclear collisions using the constituent quark model. It is assumed that wounded nucleons with different number of interacted quarks hadronize in different ways. The probabilities of having such wounded nucleons are evaluated for proton-proton, proton-nucleus and nucleus-nucleus collisions. After examining our model in proton-proton and proton-nucleus collisions and fixing the hadronization functions, it is extended to nucleus-nucleus collisions. It is used to calculate the rapidity distribution and the rapidity shift of final state protons in nucle…
Generalized parton distributions (GPDs) encoding multidimensional information of hadron partonic structure appear as the building blocks in a factorized description of hard exclusive reactions. The nucleon GPDs have been accessed by deeply virtual Compton scattering and deeply virtual meson production with lepton beam. A complementary probe with hadron beam is the exclusive pion-induced Drell-Yan process. In this paper, we discuss recent theoretical advances on describing this process in terms of nucleon GPDs and pion distribution amplitudes. Furthermore, we address the feasibility of measurin…
Using the isospin-dependent quantum molecular dynamical (IQMD) model, we systematically study the role of momentum dependent interactions in global stopping and analyze the effect of symmetry energy in the presence of momentum dependent interactions. For this, we simulate the reactions by varying the total mass of the system from 80 to 394 at different beam energies from 30 to 1000 MeV/nucleon over central and semi-central geometries. The study is carried in the presence of momentum dependent interactions and symmetry energy by taking into account hard equation of state. The nuclear stopping i…
We present a complete systematics (excitation function, impact parameter, system size, isospin asymmetry, and equations of state dependences) of global stopping and fragment production for heavy-ion reactions in the energy range between 50 and 1000 MeV/nucleon in the presence of symmetry energy and an isospin-dependent cross section. It is observed that the degree of stopping depends weakly on the symmetry energy and strongly on the isospin-dependent cross section. However, the symmetry energy and isospin-dependent cross section has an effect of the order of more than 10% on the emission of li…
Using a relativistic transport (ART) model, we study the stopping power, the formation of superdense hadronic matter as well as the strength of transverse and radial flow in central Au+Au collisions at beam momentum from 2 to 12 GeV/c per nucleon. We find that complete stopping is achieved in the whole beam momentum range. In particular, the proton rapidity distribution scaled by the beam rapidity is independent of the beam momentum, and this is in agreement with the experimental findings. Also, a large volume of superdense hadronic matter with a local energy density exceeding that expected fo…
The correlation between the nuclear stopping and the scale invariant nucleon sideward flow at energies ranging from those available at the GSI heavy ion synchrotron (SIS) to those at the CERN Super Proton Synchrotron (SPS) is studied within ultrarelativistic quantum molecular dynamics (UrQMD). The universal behavior of the two experimental observables for various colliding systems and scale impact parameters are found to be highly correlated with each other. As there is no phase transition mechanism involved in the UrQMD, the correlation may be broken down by the sudden change of the bulk prop…
We investigate possible effects of correlations between stopped nucleons on higher order proton cumulants at low energy heavy-ion collisions. We find that fluctuations of the number of wounded nucleons $N_{\mathrm{part}}$ lead to rather nontrivial dependence of the correlations on the centrality; however, this effect is too small to explain the large and positive four-proton correlations found in the preliminary data collected by the STAR collaboration at $\sqrt{s}=7.7$ GeV. We further demonstrate that, by taking into account additional proton clustering, we are able to qualitatively reproduce…
We study nuclear stopping in central collisions for heavy-ion induced reactions in the Fermi energy domain, between $15$ and $100$ A\,\textrm{MeV}. Using the large dataset of exclusive measurements provided by the $4π$ array \emph{INDRA}, we determine the relative degree of stopping as a function of system mass and bombarding energy. We show that the stopping can be directly related to the transport properties in the nuclear medium. By looking specifically at free nucleons (here protons), we present for the first time a comprehensive body of experimental results concerning the mean free path, …
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 …
Within an isospin- and momentum-dependent transport model using as an input nucleon density profiles from Hartree-Fock calculations based on a modified Skyrme-like (MSL) model, we study how to eliminate the influence of neutron-skin size difference of initial colliding nuclei in probing the nuclear symmetry energy. Within the current experimental uncertainty range of neutron-skin size of $^{208}$Pb, the Pb+Pb collisions are performed in semicentral and peripheral collisions with impact parameters of 5 and 9fm and at beam energies from 50 MeV/nucleon to 1000 MeV/nucleon, respectively. It is sho…
With the semiclassical Landau-Vlasov transport model we studied the stopping observable $R_E$, the energy-based isotropy ratio, for the $^{129}$Xe\,+\,$^{120}$Sn reaction at beam energies spanning 12$A$ to 100$A$ MeV. We investigated the impacts of the nonlocality of the nuclear mean field, of the in-medium modified nucleon-nucleon ($NN$) cross section and of the reaction centrality. A fixed set of model parameters yields $R_E$ values that favorably compare with the experimental ones, but only for energies below the Fermi energy $E_F$. Above $E_F$ agreement is readily possible, but by a smooth…
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…
Static and dynamical aspects of nuclear systems are described through an extended time-dependent mean-field approach. The foundations of the formalism are presented, with highlights on the estimation of average values and their corresponding dispersions. In contrast to semiclassical transport models, the particular interest of this description lies on its intrinsic quantal character. The reliability of this approach is discussed by means of stopping-sensitive observables analysis in heavy-ion collisions in the range of 20 to 120 MeV per nucleon.
Simplified approach to extracting nucleon transversity in collinear factorization using near-side energy-energy correlators
University of California, Los Angeles（加州大学洛杉矶分校）；Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles（加州大学洛杉矶分校马尼·L·巴乌米克理论物理研究所）；Center for Frontiers in Nuclear Science, Stony Brook University（石溪大学核科学前沿中心）；Temple University（天普大学）；Lebanon Valley College（黎巴嫩谷学院）
For high energy nucleus-nucleus collisions, we show that a combination of space-momentum correlations characteristic of radial expansion together with the correlation between the position of a nucleon in the nucleus and its stopping, results in a very specific rapidity dependence of directed flow: a reversal of sign in the mid-rapidity region. We support our argument by RQMD model calculations for Au+Au collisions at $\sqrt s$ = 200 AGeV.
This document presents a numerical study of the effects of high density nuclear reactions, pycnonuclear reactions, on the evolution of white dwarfs that accrete matter from a companion star. Primarily we seek observable properties that might be different when we include these nuclear reactions with varying microphysical assumptions. These different assumptions include effective nucleon-nucleon interactions, lattice structures and crystal polarization characteristics. Our results indicate that, although we find some significant differences in pycnonuclear reaction rates, the differences do not …
The equation of state (EOS) of nuclear matter, i.e., the thermodynamic relationship between the binding energy per nucleon, temperature, density, as well as the isospin asymmetry, has been a hot topic in nuclear physics and astrophysics for a long time. The knowledge of the nuclear EOS is essential for studying the properties of nuclei, the structure of neutron stars, the dynamics of heavy ion collision (HIC), as well as neutron star mergers. HIC offers a unique way to create nuclear matter with high density and isospin asymmetry in terrestrial laboratory, but the formed dense nuclear matter e…
Dynamics of central collisions of heavy nuclei in the energy range from few tens of MeV/nucleon to a couple of GeV/nucleon is discussed. As the beam energy increases and/or the impact parameter decreases, the maximum compression increases. It is argued that the hydrodynamic behavior of matter sets in the vicinity of balance energy. At higher energies shock fronts are observed to form within head-on reaction simulations, perpendicular to beam axis and separating hot compressed matter from cold. In the semicentral reactions a weak tangential discontinuity develops in-between these fronts. The ho…
A two phase cascade is presented for the treatment of ultra-high energy ion-ion collisions at energies from 17-200 GeV. First a high energy, fast cascade is performed, in which original baryons and freed hard partons, if any, collide. This stage ignores energy loss from soft (slow) processes. In this first version no hard processes, aside from Drell-Yan production, are included. The space-time history of the hard phase is then used as input to reconstruct soft energy-loss, which occurs over a longer time scale. Soft meson production is therefore treated as coherent over groups of interacting n…
In nuclear collisions induced by stable or radioactive neutron-rich nuclei a transient state of nuclear matter with an appreciable isospin asymmetry as well as thermal and compressional excitation can be created. This offers the possibility to study the properties of nuclear matter in the region between symmetric nuclear matter and pure neutron matter. In this review, we discuss recent theoretical studies of the equation of state of isospin-asymmetric nuclear matter and its relations to the properties of neutron stars and radioactive nuclei. Chemical and mechanical instabilities as well as the…
In the space environment, instruments onboard of spacecrafts can be affected by displacement damage due to radiation. The differential scattering cross section for screened nucleus--nucleus interactions - i.e., including the effects due to screened Coulomb nuclear fields -, nuclear stopping powers and non-ionization energy losses are treated from about 50 keV/nucleon up to relativistic energies.
The cross section for back-to-back hadron pair production in $e^+e^-$ annihilation provides access to the dihadron fragmentation functions (DiFF) needed to extract nucleon parton distribution functions from the semi-inclusive deep inelastic scattering (SIDIS) experiments with two detected final state hadrons. Particular attention is given to the so-called interference DiFF (IFF), which makes it possible to extract the transversity parton distribution of the nucleon in the collinear framework. However, previously unnoticed discrepancies were recently highlighted between the definitions of the I…
The strong nuclear interaction between nucleons (protons and neutrons) is the effective force that holds the atomic nucleus together. This force stems from fundamental interactions between quarks and gluons (the constituents of nucleons) that are described by the equations of Quantum Chromodynamics (QCD). However, as these equations cannot be solved directly, physicists resort to describing nuclear interactions using effective models that are well constrained at typical inter-nucleon distances in nuclei but not at shorter distances. This limits our ability to describe high-density nuclear matt…
We present UrQMD predictions for the comparison of the recently measured Ag+Ag and Au+Au runs at a beam energy of $E_\mathrm{lab}$ = 1.23~$A$GeV explored by the HADES experiment. To this aim, different centrality definitions are investigated: We suggest that in the case of particle production, both systems should be compared at the same number of participating nucleons, while for a comparison of the (elliptic) flow, a selection on the initial state eccentricity - as in high energy reaction - is better suited. Generally, we find good agreement between both system, if these centrality criteria a…
