Pion Production In Heavy Ion Collisions Research Articles

Collision integral with momentum-dependent potentials and its impact on pion production in heavy-ion collisions

Collision integral with momentum-dependent potentials and its impact on pion production in heavy-ion collisions

In-medium $$\Delta (1232)$$ potential, pion production in heavy-ion collisions and the symmetry energy

Using the dcQMD transport model, the isoscalar and isovector in-medium potentials of the $\Delta$(1232) baryon are studied and information regarding their effective strength is obtained from a comparison to experimental pion production data in heavy-ion collisions below 800 MeV/nucleon impact energy. The best description is achieved for an isoscalar potential moderately more attractive than the nucleon optical potential and a rather small isoscalar relative effective mass m$^*_\Delta \approx$ 0.45. For the isovector component only a constraint between the potential's strength at saturation and the isovector effective mass difference can be extracted, which depends on quantities such as the slope of the symmetry energy and the neutron-proton effective mass difference. These results are incompatible with the usual assumption, in transport models, that the $\Delta$(1232) and nucleon potentials are equal. The density dependence of symmetry energy can be studied using the high transverse momentum tail of pion multiplicity ratio spectra. Results are however correlated with the value of neutron-proton effective mass difference. This region of spectra is shown to be affected by uncertain model ingredients such as the pion potential or in-medium correction to inelastic scattering cross-sections at levels smaller than 10$\%$. Extraction of precise constraints for the density dependence of symmetry energy above saturation will require experimental data for pion production in heavy-ion collisions below 800 MeV/nucleon impact energy and experimental values for the high transverse momentum tail of pion multiplicity ratio spectra accurate to better than 5$\%$.

Scaling of factorial moments in cumulative variables

A search for power-law fluctuations within the framework of the intermittency method is ongoing to locate the critical point of the strongly interacting matter. In particular, experimental data on proton and pion production in heavy-ion collisions are analyzed in transverse-momentum, pT, space.In this regard, we have studied the dependence of the second scaled factorial moment F2 of particle multiplicity distribution on the number of subdivisions of transverse momentum-interval used in the analysis. The study is performed using a simple model with a power-law two-particle correlation function in pT. We observe that F2 values depend on the size and position of the pT interval. However, when we convert the non-uniform transverse-momentum distribution to uniform one using cumulative transformation, F2 calculated in subdivisions of the cumulative pT becomes independent of the cumulative-pT interval. The scaling behaviour of F2 for the cumulative variable is observed. Moreover, F2 follows a power law with the number of subdivisions of the cumulative-pT interval with the intermittency index close to the correlation function's exponent.

Modeling pion production in heavy-ion collisions at intermediate energies

Pion production in nucleus-nucleus collisions at intermediate energies was modeled in the framework of the Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model. The effects of nucleon-nucleon short-range correlations in initialization and mean-field potential, isospin-dependent in-medium baryon-baryon elastic and inelastic cross sections and pion in-medium effect are all considered in this model. It is found that the ratio and yields of $\pi^{-}$and $\pi^{+}$ in Au+Au reaction at 400 MeV/nucleon reproduce the FOPI/GSI data very well especially with a soft symmetry energy in the present transport model. Predictions on the single and double $\pi^{-}/\pi^{+}$ ratio are made for the isotope reaction systems $^{132}\rm {Sn}+^{124}\rm {Sn}$ and $^{108}\rm {Sn}+^{112}\rm {Sn}$ at 300 MeV/nucleon since related experiments are being carried out at RIKEN/Japan.

Preequilibrium particle emissions and in-medium effects on the pion production in heavy-ion collisions

Within the framework of the Lanzhou quantum molecular dynamics (LQMD) transport model, pion dynamics in heavy-ion collisions near threshold energies and the emission of preequilibrium particles (nucleons and light complex fragments) have been investigated. A density, momentum and isospin dependent pion-nucleon potential based on the $\Delta$-hole model is implemented in the transport approach, which slightly leads to the increase of the $\pi^{-}/\pi^{+}$ ratio, but reduces the total pion yields. It is found that a bump structure of the $\pi^{-}/\pi^{+}$ ratio in the kinetic energy spectra appears at the pion energy close to the $\Delta$(1232) resonance region. The yield ratios of neutrons to protons from the squeeze-out particles perpendicular to the reaction plane are sensitive to the stiffness of nuclear symmetry energy, in particular at the high-momentum (kinetic energy) tails.

22aAB-10 重イオン衝突における核子のダイナミクスとπ中間子生成

22aAB-10 重イオン衝突における核子のダイナミクスとπ中間子生成

Phase transitions in dense matter and the maximum mass of neutron stars

The recent precise measurement of the mass of pulsar PSR J1614$-$2230, as well as observational indications of even more massive neutron stars, has revived the question of the composition of matter at the high densities prevailing inside neutron-star cores. We study the impact on the maximum possible neutron-star mass of an "exotic" core consisting of non-nucleonic matter. For this purpose, we study the occurrence of a first-order phase transition in nucleonic matter. Given the current lack of knowledge of non-nucleonic matter, we consider the stiffest possible equation of state subject only to the constraints of causality and thermodynamic stability. The case of a hadron-quark phase transition is discussed separately. The purely nucleonic matter is described using a set of unified equations of state that have been recently developed to permit a consistent treatment of both homogeneous and inhomogeneous phases. We then compute the mass-radius relation of cold nonaccreting neutron stars with and without exotic cores from the Tolman-Oppenheimer-Volkoff equations. We find that even if there is a significant softening of the equation of state associated with the actual transition to an exotic phase, there can still be a stiffening at higher densities closer to the center of the star that is sufficient to increase the maximum possible mass. However with quarks the maximum neutron-star mass is always reduced by assuming that the sound speed is limited by $c/\sqrt{3}$ as suggested by QCD calculations. In particular, by invoking such a phase transition, it becomes possible to support PSR J1614$-$2230 with a nucleonic equation of state that is soft enough to be compatible with the kaon and pion production in heavy-ion collisions.

Dynamics of pion production in heavy-ion collisions around1A GeV energies

Within the framework of the improved isospin-dependent quantum molecular dynamics model, the dynamics of pion emission in heavy-ion collisions in the region of $1$$A$ GeV energies as a probe of nuclear symmetry energy at suprasaturation densities is investigated systematically. The total pion multiplicities and the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ yields are calculated for selected Skyrme parameters SkP, SLy6, Ska, and SIII and also for the cases of different stiffness of symmetry energy with the parameter SLy6. The influence of Coulomb potential, symmetry energy, and in-medium pion potential on the pion production is investigated and compared to each other by analyzing the distributions of transverse momentum and longitudinal rapidity and also the excitation functions of the total pion and the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio. The directed flow, elliptic flow, and polar-angle distributions are calculated for the cases of different collision centralities and also the various stiffnesses of the symmetry energies. A comparison of the calculations with the available experimental data is performed.

On the role of Δ-resonance in the pion production in collisions of heavy intermediate-energy ions in the hydrodynamic approach

Pion production in heavy-ion collisions is considered within the hydrodynamic approach. It is shown that consideration of pion production as a result of Δ-resonance decay (Δ → N + π) leads to hardening of the high-energy “tails” of subthreshold pions.

Pion Production in Heavy-Ion Collisions in the 1 A GeV Region

Within the framework of the improved isospin dependent quantum molecular dynamics (ImIQMD) model, pion emission in heavy-ion collisions in the region 1 A GeV is investigated systematically, in which the pion is considered to be mainly produced by the decay of resonances Δ(1232) and N* (1440). The in-medium dependence and Coulomb effects of pion production are included in the calculation. Total pion multiplicity and π−/π+ yields are calculated for the reaction 197Au+197Au in central collisions for selected Skyrme parameters SkP, SLy6, Ska, SIII and compared with the measured data of the FOPI collaboration.

Near-threshold pion production with radioactive beams

Using an isospin- and momentum-dependent transport model we study near-threshold pion production in heavy-ion collisions induced by radioactive beams at the planned rare isotope accelerator (RIA). We revisit the question of probing the high-density behavior of nuclear symmetry energy E{sub sym}({rho}) using the {pi}{sup -}/{pi}{sup +} ratio. It is found that both the total and differential {pi}{sup -}/{pi}{sup +} ratios remain sensitive to the E{sub sym}({rho}) when the momentum-dependence of both the isoscalar and isovector potentials are consistently taken into account. Moreover, the multiplicity and spectrum of {pi}{sup -} mesons are found more sensitive to the E{sub sym}({rho}) than those of {pi}{sup +} mesons. Finally, effects of the Coulomb potential on the pion spectra and {pi}{sup -}/{pi}{sup +} ratio are also discussed.

Quenching of resonance production in heavy-ion collisions at 1–2 A GeV

We study the pion production in heavy-ion collisions at SIS energies within the coupled resonance BUU model. The standard calculation overpredicts the pion multiplicity in the central Au+Au collision at 1 A GeV by about a factor of 2, which is interpreted as a signature for the quenching of the resonance production/absorption in nucleon–nucleon collisions at high nuclear density. Results of the calculations taking into account a specific form of quenching are presented for pion spectra from light and heavy systems as well as for the pion in-plane and out-of-plane flow.

Estimating the particle-antiparticle correlation effect for pion production in heavy-ion collisions

Estimation of the back-to-back pi-pi correlations arising due to evolution of the pionic field in the course of pion production process is given for central heavy nucleus collisions at moderate energies.

Pion-production in heavy-ion collisions at SIS energies

Pion-production in heavy-ion collisions at SIS energies

Coherent, semicoherent and incoherent pion production in heavy-ion reactions

Two types of coherent pion production in heavy-ion collisions are studied and calculations are performed for 12C against 12C collisions. The first one, doubly coherent production, produces a pion in one nucleus leaving it in its ground state, while the second nucleus is excited to the 1 +, T = 1 state. The second process, semicoherent production, also leaves in its ground state the nucleus where the pion is produced while the second one is broken. The cross sections for forward pions are compared to the standard incoherent production process. We observe that at energies below 130 MeV/ A the semicoherent process dominates the cross section for forward pion angles while at large energies around 800 MeV/ A it represents a fraction of around 30% of the incoherent cross section. The doubly coherent process leads to smaller cross sections, still in the measurable range for energies above 200 MeV/ A.

Pion-production in heavy-ion collisions at SIS energies

We investigate the production of pions in heavyion collisions in the energy range of 1–2 GeV/A. The dynamics of the nucleus-nucleus collisions is described by a set of coupled transport equations of the Boltzmann-Uehling-Uhlenbeck type for baryons and mesons. Besides theN(938) and theΔ(1232) we also take into account nucleon resonances up to masses of 1.95 GeV/c2 as well asπ-,η- andρ-mesons. We study in detail the influence of the higher baryonic resonances and the 2π-production channels (NN→NNππ) on the pion spectra in comparison toπ − data fromAr+KCl collisions at 1.8 GeV/A andπ 0-data forAu+Au at 1.0GeV/A. We, furthermore, present a detailed comparison of differential pion angular distributions with the BEVALAC data forAr+KCl at 1.8 GeV/A. The general agreement obtained indicates that the overall reaction dynamics is well described by our novel transport approach.

Energy-dependent effects in coherent pion production

Theoretical calculations have been done for the coherent production of pions in the exclusive reaction 12C + 12 C → 12 C (15.11 MeV) + 12C + π0 at 100 and 250 MeV/nucleon. An analysis is made on how three-body kinematics and other energy dependencies affect the various factors that enter the calculation for the pion differential cross section. Momentum and momentum-transfer diagrams are constructed that show pictorially how projectile- and target-generated pions differ in their intermediate states, even though they lead to the same final states. It is shown how three-body kinematics affect the exchange-process amplitudes that account for projectile- and target-generated pions. Also, the energy dependencies found in the delta width and phase-space factors are assessed as to their relative importance. Momentum robbing and kickback effects to the final-state nuclei from the produced pion are discussed. These effects are shown to give an asymmetry in the pion angular distribution. The study of three-body kinematics and its associated energy dependencies under the Born approximation is considered to be an important first step in the understanding of coherent pion production in heavy-ion collisions, before the complicating features of absorption and distortion are introduced. Even though the pion is much lighter than either of the two equal-mass, final-state nuclei, observable asymmetries are seen in the pion angular distribution that are caused by the produced pion.

Eta and dilepton production in heavy-ion reactions

We present a nonperturbative dynamical study of η-meson and pion production in heavy-ion collisions from 1 to 2 GeV/ A bombarding energy. The dynamical evolution of the nucleus-nucleus collision is described by a transport equation of the Boltzmann-Uehling-Uhlenbeck type evolving phase-space distribution functions for nucleons, Δ's, N(1440)'s, N(1535)'s, pions and η′s with their isospin degrees of freedom. Furthermore, we present results for differential dilepton yields in heavy-ion collisions at bombarding energies of 1 and 2 GeV/ A incorporating all known sources for dilepton production. We investigate in particular the sensitivity of the calculated yields to predicted changes of the ρ-meson in dense matter and discuss the feasibility to measure the time-like electromagnetic form factor of hadrons and their medium-dependence through the observation of dileptons.

ETA and dilepton production in heavy-ion reactions

We present a nonperturbative dynamical study of η-meson and pion production in heavy-ion collisions from 1 to 2 GeV/A bombarding energy. The dynamical evolution of the nucleus-nucleus collision is described by a transport equation of the Boltzmann-Uehling-Uhlenbeck type evolving phase-space distribution functions for nucleons, Δ's, N(1440)'s, N(1535)'s, pions and η's with their isospin degrees of freedom. We also study the effect of pion and Δ selfenergies on the pion dynamics. Though quite substantial medium modifications are incorporated, the pion spectra and yields show only a weak sensitivity on the in-medium effects. Furthermore, we present results for differential dilepton yields in heavy-ion collisions at bombarding energies of 1 and 2 GeV/A incorporating all known sources for dilepton production. We investigate in particular the sensitivity of the calculated yields to predicted changes of the ρ meson in dense matter and discuss the feasibility to measure the time-like electromagnetic form factor of hadrons and their medium-dependence through the observation of dileptons.

Eta and dilepton production in heavy-ion reactions

We present a nonperturbative dynamical study of η-meson and pion production in heavy-ion collisions from 1 to 2 GeV/A bombarding energy. The dynamical evolution of the nucleus-nucleus collision is described by a transport equation of the Boltzmann-Uehling-Uhlenbeck type. Our model evolves phase-space distribution functions for nucleons, Δ's, N(1440)'s, N(1535)'s, pions and η's with their isospin degrees of freedom. Furthermore, we show results for dilepton yields in heavy-ion collisions at bombarding energies of 1 and 2 GeV/A. All known sources of dileptons are taken into account. We investigate in particular the sensitivity of the calculated yields to predicted changes of the ϱ meson in dense matter and discuss the feasibility to measure the time-like electromagnetic form factor of hadrons and their medium-dependence through the observation of dileptons.