The formation of deuterons in heavy-ion collisions at relativistic energies is investigated by employing two recently advanced models -- the Minimum Spanning Tree (MST) method and the coalescence model by embedding them in the PHQMD and the UrQMD transport approaches. While the coalescence mechanism combines nucleons into deuterons at the kinetic freeze-out hypersurface, the MST identifies the clusters during the different stages of time evolution. We find that both clustering procedures give very similar results for the deuteron observables in the UrQMD as well as in the PHQMD environment. Moreover, the results agree well with the experimental data on deuteron production in Pb+Pb collisions at $\sqrt{s_{NN}} = 8.8$ GeV (selected for the comparison of the methods and models in this study). A detailed investigation shows that the coordinate space distribution of the produced deuterons differs from that of the free nucleons and other hadrons. Thus, deuterons are not destroyed by additional rescattering.
We study (anti)deuteron formation rates in heavy-ion collisions in the framework of a wave-function based coalescence model. The main feature of our model is that nucleons are emitted from the whole spherically symmetric fireball volume, while antinucleons are emitted only from a spherical shell close to the surface. In this way, the model accounts for nucleon-antinucleon annihilations in the center of the reaction at lower beam energies. Comparison with experimental data on the coalescence parameter in the range $\sqrt{s_{NN}}= 4.7-200$ GeV allows us to extract radii of the respective source …
We investigate the collision energy dependence of deuteron and antideuteron emission in the RHIC-BES low- to mid-energy range $\sqrt{s_{NN}} = 4.6-200$ GeV where the formation rate of antinuclei compared to nuclei is strongly suppressed. In the coalescence picture, this can be understood as bulk emission for nuclei in contrast to surface emission for antinuclei. By comparison with experimental data on the coalescence parameter $B_2$, we are able to extract the respective source geometries. This interpretation is further supported by results from the UrQMD transport model, and establishes the f…
UrQMD phase-space coalescence calculations for the production of deuterons are compared with available data for various reactions from the GSI/FAIR energy regime up to LHC. It is found that the production process of deuterons, as reflected in their rapidity and transverse momentum distributions in p+p, p+A and A+A collisions at a beam energies starting from the GSI energy regime around 1 AGeV and up to the LHC, are in good agreement with experimental data. We further explore the energy and centrality dependence of the d/p ratios. Finally, we discuss anti-deuteron production for selected system…
Coalescence has long been used to describe the production of light (anti-)nuclei in heavy ion collisions. The same underlying mechanism may also exist in jets when a proton and a neutron are close enough in phase space to form a deuteron. We model deuteron production in jets by applying an afterburner to protons and neutrons produced in PYTHIA for $p$+$p$ collisions at a center of mass energy $\sqrt{s} =$ 7 TeV. PYTHIA provides a reasonable description of the proton spectra and the shape of the deuteron spectrum predicted by the afterburner is in agreement with the data. We show that the rise …
Using a dynamical model based on the $NN \to dπ$, $NNN \to dN$, and $NNπ\to dπ$ reactions and measured proton and pion transverse momentum spectra and elliptic flows, we study the production of deuterons and their elliptic flow in heavy ion collisions at RHIC. The results are compared with those from the coalescence model. The deviation of deuteron elliptic flow from the constituent nucleon number scaling expected from the coalescence model and the comparison with the experimental data are discussed in connection to the allowed nucleon phase space in these reactions.
Using a density matrix approach to describe the process of coalescence, we calculate the coalescence probabilities and invariant momentum spectra for deuterons and antideuterons. We evaluate our expressions with a hydrodynamically motivated parametrization for the source at freeze-out which implements rapid collective expansion of the collision zone formed in heavy ion collisions. We find that the coalescence process is governed by the same lengths of homogeneity which can be extracted from HBT interferometry. They appear in the absolute cluster yield via an effective volume factor as well as …
Two scenarios for cluster production have since long been discussed in the literature: i) direct emission of the clusters from a (grand canonical) thermal source or ii) subsequent formation of the clusters by coalescence of single nucleons. While both approaches have been successfully applied in the past it has not yet been clarified which of the two mechanisms dominates the cluster production. We propose to use recently developed event-by-event techniques to study particle multiplicity fluctuations on nuclear clusters and employ this analysis to the deuteron number fluctuations to disentangle…
The production of light nuclei in relativistic heavy-ion collisions is well described by both the thermal model, where light nuclei are in equilibrium with hadrons of all species present in a fireball, and by the coalescence model, where light nuclei are formed due to final-state interactions after the fireball decays. We present and critically discuss the two models and further on we consider two proposals to falsify one of the models. The first proposal is to measure a yield of exotic nuclide $^4{\rm Li}$ and compare it to that of $^4{\rm He}$. The ratio of yields of the nuclides is quite di…
Collective flows of protons and deuterons for Au + Au collisions at beam energy $E_{beam}$ = 1.23 $A$ GeV were simulated by an Isospin dependent Quantum Molecular Dynamics (IQMD) model. Two coalescence models, namely naive coalescence and dynamical coalescence models, for the formation of deuterons are compared. After reasonable match of rapidity spectra of protons and deuterons to the High Acceptance DiElectron Spectrometer (HADES) data is reached, we apply an event-plane method to calculate the first four-order collective flow coefficients as well as the ratios of $<v_4>/<v_2>^2$ and $<v_3>/…
Deuteron production in S and Pb induced collisions at beam energies of 200 and 160 AGeV is studied in the framework of the transport theoretical approach RQMD. Strong transverse flow invalidates the differential coalescence formula in momentum space. The transverse momentum integrated $d$ yields scale in a broad rapidity interval with the squared proton densities and inversely with the produced particle rapidity densities. This kind of scaling can be linked to constant relative sizes of nucleon and pion sources at freeze-out. With increasing projectile mass the nucleon source blows up stronger…
The deuteron coalescence parameter $B_2$ in proton+proton and nucleus+nucleus collisions in the energy range of $\sqrt{s_{NN}}=$ 900 - 7000 GeV for proton+proton and $\sqrt{s_{NN}}=$ 2 - 2760 GeV for nucleus+nucleus collisions is analyzed with the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model, supplemented by an event-by-event phase space coalescence model for deuteron and anti-deuteron production. The results are compared to data by the E866, E877, PHENIX, STAR and ALICE experiments. The $B_2$ values are calculated from the final spectra of protons and deuterons. At low…
The hadronic transport model \textsc{art} is extended to include the production and annihilation of deuterons via the reactions $BB \leftrightarrow dM$, where $B$ and $M$ stand for baryons and mesons, respectively, as well as their elastic scattering with mesons and baryons in the hadronic matter. This new hadronic transport model is then used to study the transverse momentum spectrum and elliptic flow of deuterons in relativistic heavy ion collisions, with the initial hadron distributions after hadronization of produced quark-gluon plasma taken from a blast wave model. The results are compare…
Production of deuterons by coalescence has an important influence on the moments of the observed proton number distribution. Therefore, this effect must be taken into account when physics conclusions about baryon number fluctuation are drawn from the measurement of proton number fluctuations. We also show that a measurement of the third and fourth moments of the deuteron number distribution would allow to distinguish whether deuterons are produced statistically or by coalescence.
Light (anti-)nuclei in relativistic heavy-ion collisions are considered to be formed by the coalescence mechanism of (anti-)nucleons in the present work. Using a dynamical phase-space coalescence model coupled with a multi-phase transport (AMPT) model, we explore the formation of light clusters such as deuteron, triton and their anti-particles in different centralities for $^{197}$Au + $^{197}$Au collisions at $\sqrt{s_{NN}} = 39$ GeV. The calculated transverse momentum spectra of protons, deuterons, and tritons are comparable to those of experimental data from the RHIC-STAR collaboration. Bot…
The production of light nuclei in relativistic heavy-ion collisions is well described by both the thermal model, where light nuclei are in equilibrium with all other hadron species present in a fireball, and by the coalescence model, where light nuclei are formed due to final state interactions after the fireball decays. A method is proposed to falsify one of the models. We suggest to measure a hadron-deuteron correlation function which carries information about the source of the deuterons and allows one to determine whether a deuteron is directly emitted from the fireball or if it is formed a…
We explore the directed, elliptic, triangular and quadrangular flow of deuterons in Au+Au reactions at a beam energy of 1.23 AGeV within the UrQMD approach. These investigations are of direct relevance for the HADES experiment at GSI that has recently presented first data on the flow of light clusters in Au+Au collisions at 1.23 AGeV. To address the deuteron flow, UrQMD has been extended to include deuteron formation by coalescence. We find that this ansatz provides a very good description of the measured deuteron flow data, if a hard equation of state is used for the simulation. In addition w…
We present predictions for the formation of (anti)nuclear bound states in Au+Au central collisions at $\sqrt{s}=200A$ GeV. The coalescence afterburner was applied to the freeze-out phase space distributions of nucleons provided by the transport model, RQMD version 2.4. We study the sensitivity of the deuteron spectra to space-momentum correlations. It is found that the deuteron transverse momentum distributions are strongly affected by the nucleon space-momentum correlations.
The deuteron binding energy is only 2.2 MeV. At the same time, its yield in Pb+Pb collisions at $\sqrt{s_{NN}} = $2.76 TeV corresponds to a thermal yield at the temperature around 155 MeV, which is too hot to keep deuterons bound. This puzzle is not completely resolved yet. In general, the mechanism of light nuclei production in ultra-high energy heavy ion collisions remains under debate. In a previous work [1] we suggest a microscopic explanation of the deuteron production in central ultra-relativistic Pb+Pb collisions, the main mechanism being $πpn \leftrightarrow πd$ reactions in the hadron…
Using a microscopic transport model together with a coalescence after-burner, we study the formation of deuterons in Au + Au central collisions at $\sqrt{s}=200 AGeV$. It is found that the deuteron transverse momentum distributions are strongly affected by the nucleon space-momentum correlations, at the moment of freeze-out, which are mostly determined by the number of rescatterings. This feature is useful for studying collision dynamics at ultrarelativistic energies.
We use a Bayesian-calibrated multistage viscous hydrodynamic model to explore deuteron yield, mean transverse momentum and flow observables in LHC Pb-Pb collisions. We explore theoretical uncertainty in the production of deuterons, including (i) the contribution of thermal deuterons, (ii) models for the subsequent formation of deuterons (hadronic transport vs coalescence) and (iii) the overall sensitivity of the results to the hydrodynamic model -- in particular to bulk viscosity, which is often neglected in studies of deuteron production. Using physical parameters set by a comparison to only …
The study of the cosmic-ray deuteron and antideuteron flux receives an increasing interest in current astrophysics investigations. For both cases an important contribution is expected from the nuclear interactions of primary cosmic rays with intergalactic matter. In this work, deuteron and antideuteron production from 20 to 2.6$\times$10$^{7}$ GeV beam energy in p+p and p+A collisions were simulated using EPOS-LHC and Geant4's FTFP-BERT Monte Carlo models by adding an event-by-event coalescence model afterburner. These estimates depend on a single parameter ($p_0$) obtained from a fit to the d…
Within the ultra-relativistic quantum molecular dynamics (UrQMD) model, in which the Lorentz-covariant treatment of nuclear mean-field potential is considered, the fluctuations of net-baryon, net-charge and deuterons multiplicity distributions in Au+Au head-on collisions at $\sqrt{s_{NN}}=3.0-5.0$ GeV are calculated. The results show that the nuclear mean-field potential can significantly enhance the magnitude of baryon number fluctuations in narrow rapidity windows, and this enhancement rapidly weakens with increasing beam energy. However, for proton and net-charge number fluctuations, the me…
We present predictions for the formation of (anti)nuclear bound states in nucleus-nucleus reactions at RHIC energies. he phase space coalescence method is used in combination with RQMD-v2.4 transport calculations to demonstrate the relevance of particle production as well as the longitudinal and transverse flow components. The formation of deuterons follows an approximate scaling law proportional to the relative freeze-out densities of nucleons and produced secondaries. For antideuterons, an additional suppression appears that is proportional to the number of nucleons, pointing toward multiple…
We explore the influence of deuteron formation in the late stage of nucleus-nucleus reactions on the fluctuations observed in the final net-proton yields around midrapidity. At each investigated energy, the produced (anti-)proton yield at chemical freeze-out is assumed to fluctuate according to a Poisson distribution and in each event the probability for deuteron formation by coalescence is proportional to $(dN_{\mathrm{proton}}/dy)^2$. The protons that are then clustered in deuterons are usually not included in the experimental measurement of the net-proton fluctuations, therefore, we subtrac…
We describe a direct method to reconstruct the transverse proton source formed in a relativistic heavy ion collision, making use of experimentally measured proton and deuteron spectra and assuming that deuterons are formed via two-nucleon coalescence. We show that an ambiguity with respect to the source temperature still persists and we indicate a possible solution to the problem.
The antideuteron production rate at high-energy heavy ions collisions is calculated basing on the concept of anti-d formation by antinucleons which move in the mean field of the fireball constituents (mainly pions). The explicit formula is presented for the coalescence parameter B_2 in terms of deuteron binding energy and fireball volume.
We present a detailed comparison of coalescence and thermal-statistical models for the production of (anti-)(hyper-)nuclei in high-energy collisions. For the first time, such a study is carried out as a function of the size of the object relative to the size of the particle emitting source. Our study reveals large differences between the two scenarios for the production of objects with extended wave-functions. While both models give similar predictions and show similar agreement with experimental data for (anti-)deuterons and (anti-)3He nuclei, they largely differ in their description of (anti…
We study the production of clusters and hypernuclei at midrapidity employing the Parton-Hadron-Quantum-Molecular-Dynamics (PHQMD) approach, a microscopic n-body transport model based on the QMD propagation of the baryonic degrees of freedom with density dependent 2-body potential interactions. In PHQMD the cluster formation occurs dynamically, caused by the interactions. The clusters are recognized by the Minimum Spanning Tree (MST) algorithm. We present the PHQMD results for cluster and hypernuclei formation in comparison with the available experimental data at relativistic energies. PHQMD al…
Using a transport model that includes a first-order chiral phase transition between the partonic and the hadronic matter, we study the development of density fluctuations in the matter produced in heavy ion collisions as it undergoes the phase transition, and their time evolution in later hadronic stage of the collisions. Using the coalescence model to describe the production of deuterons and tritons from nucleons at the kinetic freeze out, we find that the yield ratio $ N_\text{t}N_\text{p}/ N_\text{d}^2$, where $N_\text{p}$, $N_\text{d}$, and $N_\text{t}$ are, respectively, the proton, deute…
With the kinetic freeze-out nucleons and antinucleons obtained from the quark combination model, we study the production of light nuclei and antinuclei in the (anti-)nucleon coalescence mechanism in relativistic heavy ion collisions. We derive analytic formulas of the momentum distributions of different light nuclei and apply them to compute transverse momentum ($p_T$) spectra of (anti-)deuterons ($d$, $\bar d$) and (anti-)tritons ($t$, $\bar t$) in Au-Au collisions at $\sqrt{s_{NN}}=$7.7, 11.5, 19.6, 27, 39, 54.4 GeV. We find that the experimental data available for these $p_T$ spectra can be…
We study the collision energy dependence of (anti-)deuteron and (anti-)triton production in the most central Au+Au collisions at $\sqrt{s_\mathrm{NN}}=$ 7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV, using the nucleon coalescence model. The needed phase-space distribution of nucleons at the kinetic freeze-out is generated from a new 3D hybrid dynamical model (\texttt{iEBE-MUSIC}) by using a smooth crossover equation of state (EoS) without a QCD critical point. Our model calculations predict that the coalescence parameters of (anti-)deuteron ($B_2(d)$ and $B_2(\bar{d})$) decrease monotonically as t…
A direct method to reconstruct the transverse structure of the baryon source formed in a relativistic heavy ion collision is presented. The procedure makes use of experimentally measured proton and deuteron spectra and assumes that deuterons are formed via two-nucleon coalescence. The transverse density shape and flow profile are reconstructed for Pb+Pb collisions at the CERN-SPS. The ambiguity with respect to the source temperature is demonstrated and possible ways to resolve it are discussed.
We study the momentum dependence of the production of light nuclei in high energy collisions in the nucleon coalescence/recombination mechanism. We derive formulas of the momentum distributions of deuterons ($d$) and helions ($^3$He). We obtain the analytic expressions of the coalescence factor $B_A$'s ($B_2$ for $d$ and $B_3$ for $^3$He) as functions of the collision system size and the momentum. We apply the deduced results to p-p, p-Pb and Pb-Pb collisions to naturally explain the interesting behaviors of $B_A$ observed in experiments at the CERN Large Hadron Collider.
Based on an improved multiphase transport (AMPT) model, which gives a good description of proton production with a smooth quark matter to hadronic matter transition in relativistic heavy ion collisions, we study deuteron and triton production from the coalescence of nucleons at the kinetic freezeout of these collisions. For Au+Au collisions at center-of-mass energies $\sqrt{s_\text{NN}}$ from 7.7 GeV to 200 GeV available at the Relativistic Heavy Ion Collider (RHIC), we find that the yield ratio $N_\text{t}N_\text{p}/N_\text{d}^2$ of proton, deuteron\com{,} and triton is essentially a constant…
Using the coalescence model based on the phase-space distributions of protons, neutrons, Lambdas and their antiparticles from a multiphase transport (AMPT) model, we study the production of deuteron, triton, helium 3, hypertriton, hyperhelium 3 and their antinuclei in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. The resulting transverse momentum spectra, elliptic flows and coalescence parameters for these nuclei are presented and compared with available experimental data. We also show the constituent number scaled elliptic flows of these nuclei and discuss their implications.
Using the coalescence model based on the phase-space distribution of nucleons from an extended blast-wave model that includes the space-momentum correlation of high momentum nucleons, we study the transverse momentum spectra and elliptic flows of deuteron and helium-3 in Pb+Pb collisions at the energy $\sqrt{s_{NN}}=2.76$ TeV. We find that the measured elliptic flows of deuteron can be satisfactorily described if nucleons of large transverse momenta are more spread in space when their momenta are more aligned along the reaction plane.
Within a transport model coupled with a microscopic coalescence model, the directed and elliptic flows of protons and deuterons as well as their scalling properties are studied in the centrality of 20-30% Au+Au collisions at $\sqrt{s_{\rm NN}}=2.4$ GeV. It is found that the flows as well as their scaling properties simulated with the isospin- and momentum-dependent nuclear mean field with an incompressibility $K_{0}=230$ MeV fit fairly the HADES data, while those simulated with the commonly used momentum-independent nuclear mean field with an incompressibility $K_{0}=380$ MeV can only fit part…
Deuteron coalescence, during relativistic nucleus-nucleus collisions, is carried out in a model incorporating a minimal quantal treatment of the formation of the cluster from its individual nucleons by evaluating the overlap of intial cascading nucleon wave packets with the final deuteron wave function. In one approach the nucleon and deuteron center of mass wave packet sizes are estimated dynamically for each coalescing pair using its past light-cone history in the underlying cascade, a procedure which yields a parameter free determination of the cluster yield. A modified version employing a …
Recent data on the deutron and $^3$He production in central Pb+Pb collisions at the CERN Super Proton Synchrotron (SPS) energies measured by the NA49 collaboration are analyzed within the model of the three-fluid dynamics (3FD) complemented by the coalescence model for the light-fragment production. The simulations are performed with different equations of state---with and without deconfinement transition. It is found that scenarios with the deconfinement transition are preferable for reproduction rapidity distributions of deuterons and $^3$He, the corresponding results well agree with the exp…
