Flow Of Nucleons Research Articles

In-medium nucleon-nucleon cross section in nuclear matter

In-medium nucleon-nucleon ($NN$) cross sections at various densities and isospin asymmetries are investigated systematically in the framework of the Brueckner-Hartree-Fock approach. The calculations are base on the exact treatment of the center-of-mass momentum instead of the total momentum approximation employed in previous works. The neutron-proton in-medium cross section is shown to exhibit nearly isospin asymmetry independence. For convenience in application, analytical formulas embodying the medium correction to free $NN$ cross section with parameters calibrated to the calculated results have been provided. Using these formulas, the transverse and elliptic flows of emitted nucleons in heavy-ion collisions are studied within the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model. We find the medium effect of the cross section from the $G$ matrix contributes to the transverse and elliptic flows oppositely to and obviously smaller than that from the effective mass. In addition, the present microscopic in-medium cross sections can significantly revise the predictions of the transverse and elliptic flows compared to the in-medium cross sections previously adopted in transport models for heavy-ion collisions.

Nuclear Bubble Configuration in Heavy-Ion Collisions

We study the effects of a bubble configuration in a nucleus on heavy-ion collisions at a few tens and hundreds A MeV. We first investigate the bubble structure of 206Hg using the relativistic continuum Hartree–Bogoliubov theory and then study the 206Hg + 208Pb and 206Hg+206Hg reactions using the DaeJeon–Boltzmann–Uehling–Uhlenbeck (DJBUU) transport model. To see the role of the bubble structure, we consider the maximum density of the produced nuclear matter, directed flow of neutrons and protons, and π−/π+ ratio. We observe that the maximum density is smaller with a bubble nucleus, and the directed flow of nucleons and π−/π+ ratio may depend on the bubble structure.

Harmonic flow correlations in Au+Au reactions at 1.23 AGeV: a new testing ground for the equation-of-state and expansion geometry

Correlations between the harmonic flow coefficients v_1, v_2, v_3 and v_4 of nucleons in semi-peripheral Au+Au collisions at a beam energy of 1.23 AGeV are investigated within the hadronic transport approach ultra-relativistic quantum molecular dynamics (UrQMD). In contrast to ultra-relativistic collision energies (where the flow coefficients are evaluated with respect to the respective event plane), we predict strong correlations between the flow harmonics with respect to the reaction plane. Based on an event-by-event selection of the midrapidity final state elliptic flow of nucleons we show that as a function of rapidity, (I) the sign of the triangular flow changes, (II) that the shape of v_4 changes from convex to concave, and (III) that v_3propto v_1v_2 and v_4propto v_2^2 for all different event classes, indicating strong correlations between all investigated harmonic flow coefficients.

Magnetic field effects on photon emission in intermediate energy heavy-ion collisions

Photon production cross section in heavy-ion collisions is estimated by employing the elementary process of proton-neutron bremsstrahlung in a Boltzmann-Uehling-Uhlenbeck model. With taking the electromagnetic field into account for simulating the reactions, the magnetic effects are considered in different impact parameter regions for the collisions of 14N + 208Pb at incident energy of 40 MeV/nucleon in the laboratory system. We investigated the energy spectra, production rates, and the polar angular distributions of photons. In particular, the directed flow $ v_{1}$ and elliptic flow $ v_{2}$ are extracted for both photons and free nucleons. In contrast with unaffected nucleon flows by the magnetic field, photon flows do display magnetic field effect.

Probing the density dependence of the symmetry energy by nucleon flow

In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, sensitive regions of some nucleon observables to the nuclear symmetry energy are studied. It is found that the symmetry energy sensitive observable n/p ratio in the $^{132}$Sn+$^{124}$Sn reaction at 0.3 GeV/nucleon in fact just probes the density-dependent symmetry energy below the density of $1.5\rho_0$ and effectively probes the density-dependent symmetry energy around or somewhat below the saturation density. Nucleon elliptic flow can probe the symmetry energy from the low-density region to the high-density region when changing the incident beam energies from 0.3 to 0.6 GeV/nucleon in the semi-central $^{132}$Sn+$^{124}$Sn reaction. And nucleon transverse and elliptic flows in the semi-central $^{197}$Au+$^{197}$Au reaction at 0.6 GeV/nucleon are more sensitive to the high-density behavior of the nuclear symmetry energy. One thus concludes that nucleon observables in the heavy reaction system and with higher incident beam energy are more suitable to be used to probe the high-density behavior of the symmetry energy. The present study may help one to get more specific information about the density-dependent symmetry energy from nucleon flow observable in heavy-ion collisions at intermediate energies.

Enhancement of elliptic flow can signal a first-order phase transition in high-energy heavy-ion collisions

The beam energy dependence of the elliptic flow,$v_2$, is studied in mid-central Au+Au collisions in the energy range of $3\leq \sqrt{s_{NN}} \leq 30$ GeV within the microscopic transport model JAM. The results of three different modes of JAM are compared; cascade-,hadronic mean field-, and a new mode with modified equations of state, with a first order phase transition (1.O.P.T.) and with a crossover transition. The standard hadronic mean field suppresses $v_2$, while the inclusion of the effects of a 1.O.P.T. (and also of a crossover transition) does enhance $v_2$ at $\sqrt{s_{NN}}<30$ GeV. The enhancement or suppression of the scaled energy flow, dubbed "elliptic flow"is understood as being due to out of plane- flow, i.e. $v_2<0$, dubbed out of plane - "squeeze-out", which occurs predominantly in the early, compression stage. Subsequently, the in-plane flow dominates, in the expansion stage, $v_2 > 0$. The directed flow, dubbed "bounce- off", is an independent measure of the pressure, which quickly builds up the transverse momentum transfer in the reaction plane. When the spectator matter leaves the participant fireball region, where the highest compression occurs, a hard expansion leads to larger $v_2$. A combined analysis of the three transverse flow coefficients, radial $v_0$-, directed $v_1$- and elliptic $v_2$- flow, in the beam energy range of $3\leq\sqrt{s_{NN}}\leq10$ GeV, distinguishes the different compression and expansion scenarios: a characteristic dependence on the early stage equation of state is observed. The enhancement of both the elliptic and the transverse radial flow and the simultaneous collapse of the directed flow of nucleons offers a clear signature if 1.O.P.T. is realized at the highest baryon densities created in high energy heavy-ion collisions.

Simulating spin dynamics with spin-dependent cross sections in heavy-ion collisions

We have incorporated the spin-dependent nucleon-nucleon cross sections into a Boltzmann-Uehling-Uhlenbeck transport model for the first time, using the spin-singlet and spin-triplet nucleon-nucleon elastic scattering cross sections extracted from the phase-shift analyses of nucleon-nucleon scatterings in free space. We found that the spin splitting of the collective flows is not affected by the spin-dependent cross sections, justifying it as a good probe of the in-medium nuclear spin-orbit interaction. With the in-medium nuclear spin-orbit mean-field potential that leads to local spin polarization, we found that the spin-averaged observables, such as elliptic flows of free nucleons and light clusters, becomes smaller with the spin-dependent differential nucleon-nucleon scattering cross sections.

Erratum to: Influence of the time-step on the production of free nucleons and pions from heavy-ion collisions around 1 GeV/nucleon

By considering different values of the time-step for the potential updates in the ultra-relativistic quantum molecular dynamics (UrQMD) model, we examine its influence on observables, such as the yield and collective flow of nucleons and pions from heavyion collisions around 1 GeV/nucleon. It is found that these observables are affected to some extent by the choice of the time-step, and the impact of the time-step on the pion-related observables is more visible than that on the nucleon-related ones. However, its effect on the π −/π + yield ratio and elliptic flow difference between neutrons and protons, which have been taken as sensitive observables for probing the density-dependent nuclear symmetry energy at high densities, is fairly weak.

Influence of the time-step on the production of free nucleons and pions from heavy-ion collisions around 1 GeV/nucleon

By considering different values of the time-step for the potential updates in the ultra-relativistic quantum molecular dynamics (UrQMD) model, we examine its influence on observables, such as the yield and collective flow of nucleons and pions from heavyion collisions around 1 GeV/nucleon. It is found that these observables are affected to some extent by the choice of the time-step, and the impact of the time-step on the pion-related observables is more visible than that on the nucleon-related ones. However, its effect on the π−/π+ yield ratio and elliptic flow difference between neutrons and protons, which have been taken as sensitive observables for probing the density-dependent nuclear symmetry energy at high densities, is fairly weak.

Mass-splitting effect on flows in heavy-ion collisions in the Fermi-energy domain

In this work, based on one updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model in which the Skyrme-like (parabolic) isospin- and momentum-dependent interaction is included, the effect of the neutron-proton effective mass splitting (NPEMS) on flows in heavy-ion collisions at the Fermi-energy domain (between 40 and 100 MeV/nucleon) is focused. Using various Skyrme interactions (all exhibiting similar values of isoscalar incompressibility but very different NPEMS), both rapidity- and transverse-momentum-dependent directed and elliptic flows of free neutrons and protons are calculated. Our calculations show that the effect of NPEMS on the flows of free nucleons is more obvious at ${E}_{\mathrm{lab}}=100\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}/\mathrm{nucleon}$ than at $40 \mathrm{MeV}/\mathrm{nucleon}$. At ${E}_{\mathrm{lab}}=100\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}/\mathrm{nucleon}$, the directed flows of both neutrons and protons are easily affected by the NPEMS, while the elliptic flow of protons is not very sensitive to the NPEMS at both energies. It is suggested that the directed flow is better than the elliptic flow for probing the NPEMS.

3H/3He ratio as a probe of the nuclear symmetry energy at sub-saturation densities

Within the newly updated version of the Ultra-relativistic quantum molecular dynamics (UrQMD) model in which the Skyrme potential energy-density functional is introduced, the yield ratio between $^3$H and $^3$He clusters emitted from central $^{40}$Ca+$^{40}$Ca, $^{96}$Zr+$^{96}$Zr, $^{96}$Ru+$^{96}$Ru, and $^{197}$Au+$^{197}$Au collisions in the beam energy range from 0.12 to 1 GeV$/$nucleon is studied. The recent FOPI data for the $^3$H$/$$^3$He ratio are compared with UrQMD calculations using 13 Skyrme interactions (all exhibiting similar values of iso-scalar incompressibility but very different density dependences of the symmetry energy). It is found that the $^3$H$/$$^3$He ratio is sensitive to the nuclear symmetry energy at sub-saturation densities. Model calculations with moderately soft to linear symmetry energies are in agreement with the experimental FOPI data. This result is in line with both, the recent constraints on the low-density symmetry energy available in the literature and our previous results for the high-density symmetry energy obtained with the elliptic flow of free nucleons and hydrogen isotopes as a sensitive probe.

Effect of the spin-orbit interaction on flows in heavy-ion collisions at intermediate energies

The effect of the spin-orbit coupling in heavy ion collisions is investigated based on an updated version of the ultra-relativistic quantum molecular dynamics (UrQMD) model, in which the Skyrme potential energy density functional is employed. And in special, the spin-orbit coupling effects on the directed and elliptic flows of free nucleons emitted from $^{197}$Au+$^{197}$Au collisions as functions of both the beam energy and the impact parameter are studied. Our results show that the net contribution of the spin-orbit term to flows of nucleons is negligible, whereas a directed flow splitting between spin-up and spin-down nucleons is visible especially at large impact parameters and a peak of the splitting is found at the beam energy around 150 MeV$/$nucleon. We also found that the directed flow splitting between spin-up and spin-down neutrons is comparable with the neutron directed flow difference calculated by a soft and a stiff symmetry energy, indicating that the directed flow of neutrons cannot be used to pin down the stiffness of symmetry energy any more without considering the spin degree of freedom in models in case of spin polarization.

Constraining the high-density nuclear symmetry energy with the transverse-momentum-dependent elliptic flow

Within the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, the transverse-velocity dependence of the elliptic flow of free nucleons from $^{197}$Au+$^{197}$Au collisions at the incident energy 400 MeV$/$nucleon is studied within different windows of the normalized c.m. rapidity $y_0$. It is found that the elliptic flow difference $v_{2}^{n}$-$v_{2}^{p}$ and ratio $v_{2}^{n}$/$v_{2}^{p}$ of neutrons versus protons are sensitive to the density dependence of the symmetry energy, especially the ratio $v_{2}^{n}$/$v_{2}^{p}$ at small transverse velocity in the intermediate rapidity intervals $0.4<|y_0|<0.6$. By comparing either transverse-momentum dependent or integrated FOPI/LAND elliptic flow data of nucleons and hydrogen isotopes with calculations using various Skyrme interactions, all exhibiting similar values of isoscalar incompressibility but very different density dependences of the symmetry energy, a moderately soft to linear symmetry energy is extracted, in good agreement with previous UrQMD or T\"{u}bingen QMD model calculations but contrasting results obtained with $\pi^-/\pi^+$ yield ratios available in the literature.

Nucleon flow in the process of evolution from dinucleus to mononucleus investigated with a dynamic model

Nucleon flow in the process of evolution from dinucleus to mononucleus is studied by means of the coupled Langevin equations in the three-dimensional collective space of the radial, neck, and asymmetry degrees of freedom for the systems ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ and ${}^{58}\mathrm{Fe}+{}^{248}\mathrm{Cm}$. For a comparison, the dynamic evolution of the neck is also investigated with the Langevin equations in the two-dimensional collective space of the radial and neck for these two reaction systems. The results show that nucleon flow is strongly damped in the stage of the dinuclear system due to the large dissipation associated with the mass asymmetry degree of freedom. The evaporation residue (ER) cross sections for the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ and ${}^{58}\mathrm{Fe}+{}^{248}\mathrm{Cm}$ reactions are evaluated by means of the modified fusion-by-diffusion (FBD) model, in which the injection distance distributions in the asymmetric fission valley obtained from the dynamic calculations are integrated. The theoretical excitation functions of the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ reaction are in good agreement with the experimental data. For the ${}^{58}\mathrm{Fe}+{}^{248}\mathrm{Cm}$ reaction, the maximum ER cross sections in 3$n$- and 4$n$-evaporation channels calculated with the three-dimensional Langevin equations are, respectively, $0.008$ and $0.020$ fb. We have demonstrated that the effect of drift and diffusion towards a more symmetric configuration on the ER cross sections is counterbalanced by that of diffusion towards a more asymmetric one. The ER excitation functions calculated with the two approaches are similar, which means that the impact of the nucleon flow during the process of neck evolution on the formation probability of superheavy nuclei is small in the framework of the dynamic model. In this sense, the frozen approximation of mass asymmetry in the FBD model should be reasonable in the hot fusion reactions.

Cold fusion reaction of58Fe+208Pb analyzed by a generalized model of fusion by diffusion

A generalized version of the fusion by diffusion model is proposed, in which evolution from dinuclear to mononuclear regimes is taken into account in terms of the coupled Langevin equations in the three-dimensional collective space of neck, radial, and asymmetric degrees of freedom. By simulating numerically these dynamic equations, the probability distribution of ${s}_{\mathrm{inj}}$, the separation between the surfaces of two approaching nuclei at the injection point in the asymmetric fission valley, is obtained. From the injection points, the system starts its climb uphill over the saddle point in the presence of thermal fluctuation; thus for very heavy systems the injection-point distance is a very critical constituent in the calculations of fusion probability. The present model is applied for the study of the mass asymmetric system ${}^{58}\mathrm{Fe}\phantom{\rule{0.16em}{0ex}}+{\phantom{\rule{0.16em}{0ex}}}^{208}$Pb. The excitation function for the ${}^{208}$Pb(${}^{58}$Fe,$n$)${}^{265}$Hs reaction is calculated and compared with the experimental data. By comparing the theoretical results with and without taking the asymmetric degree of freedom into account, we have arrived at the conclusion that nucleon flow between the asymmetric reaction partners in the early stage of the fusion process plays an important role in the formation of superheavy nuclei in the cold fusion reactions.

Effective mass splitting of neutron and proton and isospin emission in heavy-ion collisions

Within the framework of an isospin and momentum dependent transport model, the emissions of isospin particles (nucleons and light clusters) squeezed out in heavy-ion collisions are investigated as probes of the poorly known symmetry energy at high baryon density. Two different mass splittings of neutrons and protons in nuclear medium as mn⁎>mp⁎ and mn⁎<mp⁎ are used in the model and their influence on the isospin emission in heavy-ion collisions is discussed thoroughly. The competition between the stiffness and the momentum dependence of the symmetry potential on reaction dynamics are compared and systematically analyzed. It is found that the difference of the neutron and proton directed flows and the transverse momentum distribution of the neutron/proton ratio are sensitive to the stiffness of the symmetry energy, which cannot be changed with the controversial effective mass splitting. The elliptic flows of free nucleons at high transverse momentum within mid-rapidity emission are to be promising observables as distinguishing the nucleon effective mass splitting.

Nuclear in-medium effects and collective flows in heavy-ion collisions at intermediate energies

A recent updated version of the Lanzhou quantum molecular dynamics is reviewed, in which the momentum dependence of symmetry potential and the effective mass splitting of proton and neutron in nuclear medium are included in the model. The in-medium nucleon-nucleon (NN) elastic cross sections are evaluated with the scaling approach according to the effective mass and their influence on collective flows in heavy-ion collisions are discussed. The inelastic cross sections, in particular for the process of the channel N$\Delta\rightarrow$NN, are parameterized in accordance with the available experimental data. It is found that the in-medium cross sections play a significant role on isospin emissions and result in a flat distribution for transverse flows and elliptic flows of free nucleons comparing with the in-vacuum ones. The rapidity distribution of the difference between neutron and proton transverse flows is sensitive to the stiffness of nuclear symmetry energy as a promising observable, which can not be influenced by the in-medium effect and collision centrality. Furthermore, the elliptic flow of free energetic nucleons in the case of the mass splitting of $m_{n}^{\ast}>m_{p}^{\ast}$ is also related to the symmetry energy. However, the pion flows weakly depend on the symmetry energy and the mass splitting.

Isospin-dependent nucleon-nucleon cross section and the collective flow of nucleons in heavy-ion collision at intermediate energy

In this paper, the influences of the different forms of nucleon-nucleon (NN) cross sections on the rapidity distributions and the in-plane flows of nucleons in reactions 60Ca+60Ca and 60Ni+60Ni are studied by using IBUU04 transport model with the moment-dependent symmetry potential. The calculation results indicate that (1) the discrepancies of the rapidity distributions and in-plane flows corresponding to different forms of NN cross sections are large, (2) the sensitivity of the in-plane flow to the NN cross section still holds when the new form of moment-dependent symmetry energy is adopted, and (3) the influence of the N/P ratio of reaction systems on the transverse flow calculated with a certain NN cross section is more obvious when the incident energy is near the balance energy.

Beam fragmentation in heavy ion collisions with realistically correlated nuclear configurations

We develop a new approach to production of the spectator nucleons in the ultrarelativistic heavy ion collisions. The energy transfer to the spectator system is calculated using the Monte Carlo based on the updated version of our generator of configurations in colliding nuclei which includes a realistic account of short-range correlations in nuclei. The transferred energy distributions are calculated within the framework of the Glauber multiple-scattering theory, taking into account all individual inelastic and elastic collisions using an independent realistic calculation of the potential energy contribution of each of the nucleon-nucleon pairs to the total potential. We show that the dominant mechanism of the energy transfer is tearing apart pairs of nucleons with the major contribution coming from the short-range correlations. We calculate the momentum distribution of the directed flow of emitted nucleons which is strongly affected by short-range correlations, including its dependence on the azimuthal angle. In particular, we predict a strong angular asymmetry along the direction of the impact parameter $\text{b}$, providing a unique opportunity to determine the direction of $\text{b}$. Also, we predict a strong dependence of the shape of the nucleon momentum distribution on the centrality of the nucleus-nucleus collision.

Is the existence of a softest point in the directed flow excitation function an unambiguous signal for the creation of a quark–gluon plasma?

We investigate the claim that a minimum of the excitation function of the in-plane directed flow of nucleons in ultrarelativistic heavy-ion collisions is a ‘smoking gun’ signature for the creation of a quark–gluon plasma (QGP). Employing a non-equilibrium transport approach we demonstrate that such a minimum is expected in heavy ion collisions and not related to the formation of a QGP. The minimum has its origin in the interplay between a decreasing scattering angle of the elastic collisions with increasing beam energy, which lowers the in-plane flow, and the onset of particle production which increases the in-plane flow. Thus, the interpretation of this minimum as a ‘smoking gun’ signature for the creation of a QGP seems premature.