Study of collective flows of protons and \pi^{-} -mesons in p+C, Ta and He+Li, C collisions at momenta of 4.2, 4.5 and 10 AGeV/c

Study of collective flows of protons and -mesons in p+C, Ta and He+Li, C collisions at momenta of 4.2, 4.5 and 10 AGeV/c

L. Chkhaidze High Energy Physics Institute of Tbilisi State University, Georgia corresponding author E-mail: ichkhaidze@yahoo.com    G. Chlachidze Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA    T. Djobava High Energy Physics Institute of Tbilisi State University, Georgia    A. Galoyan Veksler and Baldin Laboratory of High Energy Physics, Joint Institute for Nuclear Research, Dubna, Russia    L. Kharkhelauri High Energy Physics Institute of Tbilisi State University, Georgia    R. Togoo Institute of Physics and Technology of the Mongolian Acad. Sci., Ulan Bator, Mongolia    V. Uzhinsky Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia corresponding author E-mail: uzhinsky@jinr.ru
Received: date / Revised version: date
Abstract

Collective flows of protons and -mesons are studied at the momenta of 4.2, 4.5 and 10 AGeV/c for p+C, Ta and He+Li, C interactions. The data were obtained from the streamer chamber (SKM-200-GIBS) and from the Propane Bubble Chamber (PBC-500) systems utilized at JINR. A method of Danielewicz and Odyniec has been employed in determining a directed transverse flow of particles. The values of the transverse flow parameter and the strength of the anisotropic emission were defined for each interacting nuclear pair. It is found that the directed flows of protons and pions decrease with increasing the energy and the mass numbers of colliding nucleus pairs. The -meson and proton flows exhibit opposite directions in all studied interactions, and the flows of protons are directed in the reaction plane. The Ultra-relativistic Quantum Molecular Dynamical Model (UrQMD) coupled with the Statistical Multi-fragmentation Model (SMM), satisfactorily describes the obtained experimental results.

pacs:
25.70.-z and 25.75.Ld

1 Introduction

One of the central goals of the high-energy heavy-ion collision research is a determination of the properties of nuclear matter at densities and temperatures higher than that in the ground-state nuclei. Asymmetry of produced particle emission relative to the reaction plane observed in nucleus-nucleus interactions is explained by the collective flows of the particles. Theoretically, those flows can be linked to the fundamental properties of nuclear matter and, in particular, to the equation of state (EOS) R1 (). Two types of asymmetries were identified. The former is a directed flow R2 () in the reaction plane, associated with the matter ”bouncing-off” within the hot participant region of overlap between colliding nuclei. The latter is a squeeze-out R3 () of the hot matter directed perpendicular to the reaction plane within the participant region. When energy increases into ultra-relativistic values the squeeze-out turns into an in-plane elliptic flow.

Many different methods have been proposed for studying the flow effects in relativistic nuclear collisions, of which the most commonly employed ones are the directed transverse momentum analysis technique developed by Danielewicz and Odyniec R4 () and the method of the Fourier expansion for azimuthal distributions proposed by Demoulins et al. and Voloshin and Zhang R5 (). Quantitatively, the anisotropic flow is characterized by coefficients in the Fourier expansion of the azimuthal dependence of the invariant yield of particles relative to the reaction plane R6 (). A first coefficient, , is usually called a directed flow parameter, and a second coefficient, , is called an elliptic flow parameter. To improve anisotropic flow measurements, advanced methods based on multi-particle correlations (cumulants) have been developed to suppress non-flow contribution, which are not related to the initial geometry R7 (). Most of the data below 4 AGeV in the literature were, in fact, analyzed by the method of Danielewicz and Odyniec R4 (). The advantage of this method is that it can be employed even at small statistics, which is typical for film detectors. That is why we have chosen the method of Danielewicz for the analysis of our data from film detectors in order to investigate the directed flow of protons and -mesons in the colliding systems p+C, Ta and He+Li, C.

The collective flow of charged particles has been first observed at the Bevalac by the Plastic Ball and Streamer Chamber Collaborations. The flow continued to be explored at Berkeley and at GSI, and further at AGS and at CERN/SPS accelerators. By now, the collective flow effects were investigated in nucleus-nucleus interactions over a wide range of energies, from hundreds of MeV up to 5.02 TeV U1 ()R12 (). Measurements of multi-particle azimuthal correlations (cumulants) for charged particles in Pb+Pb collisions at = 2.76 TeV and in p+Pb collisions at = 5.02 TeV have been carried out at ALICE, ATLAS and CMS LHC experiments. They help address the question of whether there is an evidence for global, flow-like, azimuthal correlations in these systems.

In order to study the properties of nucleus-nucleus interactions, the collective flows of protons, pions and hyperons were previously investigated R13 ()R16 () by the authors of the present paper at beam energies of 3.4 and 3.7 AGeV. According to the study, the flow parameters of protons and negative pions increase at an increase of the mass of projectile and target nuclei () in H + C, He + C, C + C, C + Ne, H + Ta, He + Ta, C + Cu, and C + Ta collisions. It was interesting to study characteristics of the collective flow in nucleon-nucleus interactions also.

It is worth to mention that the values of the elliptic flow excitation function obtained by us for protons correspond to quite an interesting energy region. According to the investigations of Au+Au collisions at AGS R17 (), an evolution from a negative ( 0) to positive ( 0) elliptic flow was observed at an energy interval of 2.0 Ebeam 8.0 GeV/nucleon and an apparent transition energy 4 GeV/nucleon was pointed. Therefore, our results are also interesting for enrichment of the existing results in the above mentioned energy region.

The collective flows are well established in collisions of heavy nuclei, while the information is very limited for interactions of light and medium projectile nuclei with various target nuclei. The results obtained in our paper will bring a new light on the nature of the flows.

In this paper, we present the collective flow analysis results of protons and -mesons for different projectile-target combinations at the laboratory momenta of 4.2, 4.5 and 10 AGeV/c. The data were obtained from the experimental setups of JINR, Dubna. Moreover, the characteristics of protons and -mesons, produced in the collisions, were determined and provided for comparison at different energies. The experimental results are compared with the predictions of the Ultra-relativistic Quantum Molecular Dynamics Model (UrQMD) R18 () in combination with the Statistical Multi-fragmentation Model (SMM) R19 ().

2 Experimental data

The data were obtained from the SKM-200-GIBS streamer chamber

The SKM-200-GIBS experiment is based on a 2 m streamer chamber placed in the magnetic field of 0.8 T and on a triggering system. An inelastic trigger was used to select the events. The streamer chamber R20 () was exposed by a beam of He nuclei accelerated up to 4.5 AGeV/c in the JINR synchrophasotron. The thickness of Li and C solid targets (in the form of a disc) were 1.5 and 0.2 g/cm, correspondingly. The analysis produced 4020 events of He+Li and 2127 events of He+C collisions.

The 2-meter long Propane Bubble Chamber (PBC-500) was placed in the magnetic field of 1.5 T. The procedures for separating out the p+C collisions in propane (CH) and the data processing details, including particle identification and corrections, were described in R21 (). The analysis produced 5882 (10775 events in CH) and 16509 (28703 events in CH) events of p+C interactions at the momentum of 4.2 and 10 GeV/c, correspondingly, and 2342 events of p+Ta (at 10 GeV/c) collisions. The protons with momentum p150 MeV/c were not detected 150 200 MeV/c within the PBC-500 as far as their track lengths are less than 2 mm (p+C interactions), and protons with p200 MeV/c were absorbed in Ta target plate (the detector biases). Thus, the protons with momentum larger than 150 MeV/c were registered in p+C interactions, and the protons with p250 MeV/c in p+Ta collisions.

The following factors were considered at estimations of systematic errors for the both set-ups: the contamination of non-beam particles (contamination due to interactions of other projectile nuclei with a charge less than required, Z Z), the choice of the effective area for registration of collisions, secondary interactions in the target, absorption of slow mesons in the target, contamination of and particles, visual identification of mesons, scanning losses (including tracks with a large angles at the plane of photography). For SKM-200-GIBS experiment the corrections due to the trigger, selecting inelastic and central collisions, were added, while for PBC-500 the corrections for the selection of interactions with carbon nuclei from the collisions with propane nuclei were taken into account. The most important corrections were connected with the scanning losses which mainly reduce the number of the observed secondary particles. All the factors led to a systematic uncertainty of meson average multiplicity on the level 24.5 %. For the analysis presented in our paper, we study kinematic properties of mesons and protons in narrow intervals of rapidity. In each rapidity bin the statistical errors were in 34 times larger than the pointed systematic uncertainty. Thus, we will not consider the systematic errors further.

A study of the collective flow phenomenon needs an ”event-by-event” analysis, which requires the exclusive analysis of each individual collision. In this connection, there has been a necessity to perform identification of mesons in order to separate mesons from the positive charged particles. The procedure has been done as described below.

In what concerning He+Li, C collisions, identification of positive charged particles never has been done yet, and we have carried out our effectively mesons identification for the first time. It was assumed, that and mesons hit a given cell of the plane (P, P) with equal probability in collisions of isospin-symmetrical nuclei. Thus [13], it was assumed that a proton yield in a given cell () of the P–P plane is presented as:

where is a number of positively charged tracks in the cell, and is a number of negative charged tracks in the cell. As known [13], the procedure works quite well for inclusive distributions. In our case, we randomly choose how to treat a given positive charged track. We treated the track as a proton one with a probability , and as a meson one with the probability .

Since mesons and protons in the Propane Bubble Chamber (p+C, Ta collisions) have been identified in the narrow interval of momenta (up to 0.7 GeV/c), it was necessary the additional ”identification” of particles with higher momenta. It was done as follow: The momentum distributions (spectra) of positive and negative particles was divided into 10 intervals for p0.750 GeV/c. The distributions were created for isospin-symmetrical collisions (). Using them, the probabilities and were determined. According to the probabilities, the positive charged tracks with p0.750 GeV/c were subdivided into ”protons” and ” mesons”. The results of the ”identification” for He+Li, C and p+Ta collisions are presented in Figs 1, 2 for inclusive distributions in a comparison with the UrQMD model predictions. One can see that the spectrum of mesons well agrees with the experimental spectrum (distribution) of mesons and with the simulated spectrum of mesons.

For the flow analysis, minimum four participant protons, N 4, (the remaining protons after the ”identification”) were required in event. In the experiment, the positively charged projectile fragmentation products were identified as those characterized by the momentum p3.5 GeV/c (4.2 AGeV/c, 4.5 AGeV/c) or p7 GeV/c (10 AGeV/c) and emission angle 3.5 and the target fragmentation products – by the momentum p 0.25 GeV/c in the target rest frame.

3 The directed flows of protons and -mesons

It has been investigated that the directed flow of protons and mesons in the colliding systems p+C, Ta and He+Li, C employed a method of Danielewicz and Odyniec R4 (). The method relies on summation over transverse momenta of selected particles in the events. In an experiment, no determination of the impact parameter is possible. Therefore, instead of , a vector sum of transverse momenta of projectile and target nuclear fragments or participant protons is used. The fragmentation regions of projectile and target nuclei were outside the acceptance regions of experimental setups in some experiments and, therefore, the reaction plane was defined by the second approach using the participant protons. The second approach is preferable also for the light nuclear systems, because the multiplicity of the participant protons is larger than the number of detected nuclear fragments. Therefore, the participant protons were used in our study for the reaction plane determination.

The analysis was carried out in the laboratory system. To eliminate the correlation of a particle with itself (autocorrelations) at a study of proton flows, we estimated the reaction plane for each proton in the event with a contribution of that proton removed from the definition of the reaction plane. The reaction plane is spanned by the impact parameter vector and the beam axis. Within the transverse momentum method, the direction of is estimated event-by-event in terms of the vector constructed from the proton transverse momenta:

(1)

where is a weight factor of i-th particle, = y - y, y is a rapidity of i-th participating proton, and y is an average rapidity of the participant protons in an event R22 (). The values of averaged over all events are shown in Figs. 3, 4 by arrows.

The projection of a transverse momentum of a particle onto the estimated reaction plane is:

(2)

The dependence of the projection on the rapidity was constructed for each collision systems. For further analysis, the average transverse momentum in the reaction plane, , is obtained by averaging over all events in the corresponding intervals of rapidity. Due to finite number of particles used in constructing of the vector in (1), the estimated reaction plane fluctuates in the azimuth around the direction of the true reaction plane. Because of those fluctuations, the component of a particle momentum in the true reaction plane is systematically larger than the component in the estimated plane:

(3)

where is the angle between the true and estimated reaction planes. The overall correction factor = 1 cos is a subject of a large uncertainty R4 (); R14 (), especially for low multiplicity events. In R4 () the method for the definition of the correction factor has been proposed. Each event is randomly divided into two almost equal sub-events and the vectors and are constructed.

Then the distribution of the azimuthal angle between these two vectors was obtained, and the average cos was determined. cos for all considered interactions are given in Table 1. Figs. 3, 4 show dependencies of the average in-plane transverse-momentum components on the rapidity for protons and -mesons in p+C, Ta and He+Li, C collisions. The values of the flow parameter , which are the slopes of at its mid-rapidity cross-over, are given in Table 1. All presented error bars are only statistical ones.

The flow analysis was done also for the changed requirement for the determination of the reaction plane, namely for N 3. In this case the absolute values of the directed flow parameter for protons have been obtained 82.7 4.3 MeV/c (N=1720 after cut) for He+Li, C and 76.8 4.9 MeV/c (N=1541 after cut) for p+Ta collisions. One can see from Table 1, that the change of the selection criterion of the events for the flow analysis does not affect significantly the values of the flow parameters, while the errors of F increases for the criterion N 4 due to the decrease of statistics: for He+Li, C collisions 80.9 16.2 MeV/c (N=786 after cut) and for p+Ta collisions 76.1 5.3 MeV/c (N=1141 after cut).

In view of the strong coupling between the nucleon and pion, it is interesting to know, if pions also have a collective flow behaviour in that presented nuclear systems and how is the pion flow related to the nucleon one. An answer to this question is given in Table 1. The pion’s flow has been observed with respect to the reaction plane determined by participant protons.

One can see from the Table 1 and Figures 3, 4 that the mesons flows are smaller than the proton ones. It is apparent that the mesons and protons flow are in the opposite in-plane directions, in the forward and backward hemispheres, in all nuclear systems. The flow parameter absolute values for mesons and protons decrease with increasing of projectile momentum and of mass numbers of target nuclei, what is opposite the results in nucleus-nucleus collisions (H + C, He + C, C + C,H + Ta, He + Ta, and C + Ta collisions) obtained at the same energy and on the same setup R14 (), R16 (). Interestingly, the proton and mesons collective flow parameters in He+C collisions of SKM-200-GIBS with the pure, solid thin targets are comparable with those from collisions with CH (PBC-500, our earlier results) R16 (). Both results are in agreement within errors.

The obtained experimental results from p+C, Ta and He+Li, C collisions are compared with predictions of the UrQMD model coupled with the SMM model. Detailed descriptions of the UrQMD and SMM models can be found in R18 () and R19 (), correspondingly. The UrQMD model is a microscopic transport model based on the covariant propagation of all hadrons on classical trajectories in combination with stochastic binary scatterings, colour string formation and resonance decay. We added the SMM model to the UrQMD model to improve simulations of a baryon production in target and projectile fragmentation regions. There is no a strong subdivision between the participating protons and protons created at the de-excitation of nuclear residuals. The SMM allows a simulation of the evaporated proton production, and UrQMD generates the participating protons. Thus, we have in the model events all processes presented at the experiment.

The UrQMD model is designed as a multi-purpose tool for studying a wide variety of heavy ion related effects ranging from multi-fragmentation and collective flow to particle productions and correlations in the energy range from SIS to RHIC. In the used version of the UrQMD model (1.3) with addition of the SMM, we consider potential interactions between nucleons and excitations of the residual nuclei. These allowed one to determine the reaction plane by the participant protons.

The incorporation of UrQMD and SMM was done as it was proposed in Ref. Kh1 (); Kh2 (). The UrQMD calculation was carried out up to the transition time fm/c. After that the minimum spanning tree method Kh3 () was employed for determination of prefragments. It was assumed that two nucleons form a cluster, if a distance between their centers is lower than fm. The choice of the parameters ( and ) was considered in Ref. Kh1 (); Kh2 (). The procedure allowed to determine mass numbers, charges, energies and momenta of pre-fragments. The energy and momentum of a prefragment were transformed to the prefragment rest frame using the Lorentz transformation. The excitation energy of the hot prefragment was calculated as a difference between the binding energy of the pre-fragment and the binding energies of this pre-fragment in its ground state. Skyrme, Yukawa and Coulomb potentials were used at a calculation of the binding energy. The Pauli potential was not accounted. A ”hard” Skyrme-type EoS with the nuclear incompressibility was used. Decay of the prefragments was simulated by SMM.

We have checked out that the UrQMD model without the potential interactions (cascade mode of UrQMD) does not predict any anisotropic flows for proton interactions with light nuclei. An inclusion of the potential interactions leads to the flows, and allows one to estimate the excitation energy of nuclear remnant. Evaporated protons, neutrons and nuclear fragments are produced at a de-excitation of the remnants. The average kinetic energy of the evaporated protons is below 30 MeV. An accounting of the protons does not have an essential influence on our results.

20000 (4.2 GeV/c) and 60000 (10 GeV/c) events have been generated for p+C interactions, 15000 (4.5 AGeV/c), 8000 (4.5 AGeV/c) and 7230 (10 GeV/c) events for He+Li, C and p+Ta collisions, correspondingly, by using the enlarged UrQMD model (UrQMD+SMM). The experimental conditions and selection criteria are applied to the generated events. For UrQMD+SMM events the projection of the transverse momentum onto true reaction plane was determined. The values of the flow parameter F are extracted for protons and -mesons from the dependencies of on rapidity y for each nuclear pair (Table 1). As seen, there is a good agreement between the experimental and theoretical values (Figs. 3, 4).

The reduced magnitude of the average pion momentum component in the reaction plane compared to the proton one was seen before at Bevalac, GSI-SIS, CERN-SPS and STAR R9 (); R23 (); R24 (). Historically, the pattern of pion emission relative to the reaction plane has been first studied at Bevalac by the Streamer Chamber Group and later by the EOS collaboration R25 (). In the investigations at Bevalac and Saturne, projection of the pion transverse momentum onto the reaction plane was examined. The direction of the pion flow opposite to the proton flow, the so called anti-flow, was seen before in either asymmetric or symmetric systems R9 (); R25 (); R26 (). However, we are unaware of observation of the pion anti-flow in a strongly asymmetric system such as our p+Ta one.

The anti-correlation of nucleons and pions was explained in R27 () by the effect of multiple N scattering. However, in R28 () it is shown that the anti-correlation is a manifestation of the nuclear shadowing of the target and projectile spectators through both pion re-scattering and re-absorptions. Quantitatively, the shadowing can produce the in-plane transverse momentum components comparable to the momenta itself and, thus, much larger than the components due to the collective motion for pions R29 (). In our opinion, our results indicate that the flow behaviour of mesons is a result of the nuclear shadowing effect.

4 Proton elliptic flow

We have studied a proton elliptic flow in p+C (4.2 and 10 GeV/c), He+Li, C (4.5 AGeV/c) and p+Ta (10 GeV/c) collisions. The azimuthal distributions of the protons were obtained and presented in Figs 5, 6 where is the angle between the transverse momentum of each particle in the event and the reaction plane (cos = /). The azimuthal angular distributions show maxima at =90 and 270 with respect to the event plane. The maxima are associated with a preferential particle emission perpendicular to the reaction plane (squeeze-out). To treat the data in a quantitative way, the azimuthal distributions were fitted with the Fourier cosine-expansion (given the system invariance under reflections with respect to the reaction plane).

(4)

The squeeze-out signature is a negative value of the coefficient , which is a measure of the strength of the anisotropic emission. The elliptic anisotropy, quantified in terms of the coefficient (=2), extracted from the azimuthal distributions of the protons with respect to the reaction plane at mid-rapidity is given in Table 2.

The obtained experimental results have been compared with the calculations of the UrQMD+SMM model. The experimental selection criteria were applied to the generated events. The elliptic flow parameters with respect to the true reaction plane were calculated (Table 2) for UrQMD+SMM events too. A good agreement between experimental and theoretical distributions has been obtained for the proton elliptic flow in the above mentioned collisions (Figs 5, 6).

The absolute value of the proton elliptic flow parameter increases with the growth of momenta per nucleon in our collisions (Table 2). According to the investigations of Au+Au collisions at AGS R17 (), the sign of the elliptic flow changes at an apparent transition energy of E 4 GeV/nucleon. All considered theoretical scenarios R34 () properly describe the change of sign at the incident energy decrease below = 3.5 GeV. In heavy ion collisions the squeeze-out of particles from interaction zone takes place due to a shadowing of particles production in the reaction plane by the nuclear residuals. At higher energies the shadowing decreases, and the squeeze-out flow is changed into the elliptic flow. In the interactions studied by us (p+C and p+Ta collisions at 4.2 and 10 GeV/c, correspondingly, there are no projectile remnants. Thus, it is natural that the sign of the observed elliptic flow does not change.

5 Conclusion

The directed transverse collective flows of protons and mesons and elliptic flow of protons emitted from p+C (4.2 and 10 GeV/c), He+Li, C (4.5 AGeV/c) and p+Ta (10 GeV/c) collisions have been studied. In more detail:

1) The p+C system is the lightest studied one, and the p+Ta system is an extremely asymmetrical system in which collective flow effects (directed and elliptic) are detected for protons and pions. As shown, the mesons exhibit an opposite directed flow with that for protons in all colliding systems. The absolute value of the directed flow parameter decreases with increase of projectile momenta in p+C collisions for the protons from 125.2 7.2 MeV/c at 4.2 GeV/c down to 85.7 5.8 MeV/c at 10 GeV/c. The values for mesons are -21.6 11.1 MeV/c at 4.2 GeV/c and -16.1 5.4 MeV/c at 10 GeV/c. Also, decreases with increasing the mass numbers of the target nuclei, for protons from 85.7 5.8 MeV/c (p+C, 10 GeV/c) down to 76.1 5.3 MeV/c (p+Ta, 10 GeV/c), and almost does not change for mesons -19.7 4.8 MeV/c (p+C, 10 GeV/c) and -18.8 4.8 MeV/c (p+Ta, 10 GeV/c). The results for nucleon-nucleus collisions are opposite the results in nucleus-nucleus interactions obtained at the same energy and on the same experimental setup.

2) It should be mentioned that no change of the sign of the proton elliptic flow has been observed in p+C, Ta nucleon-nucleus collisions in the projectile momentum range of 4 10 GeV/c. The absolute value of the proton elliptic flow parameter in p+C collisions increases with projectile momentum from -0.053 0.020 at 4.2 GeV/c up to -0.071 0.013 at 10 GeV/c. Also, almost does not change with increase of the mass numbers of the target nuclei at 10 GeV/c: -0.071 0.013 (p+C) and -0.071 0.016 (p+Ta).

An agreement between experimental and theoretical (UrQMD+SMM) collective flow distributions has been obtained for particles in the above mentioned interactions.

Acknowledgements

One of us (L. Ch.) would like to thank the board of directors of the Laboratory of Information Technologies (LIT) of JINR for the warm hospitality.

This work was partially supported by the Georgian Shota Rustaveli National Science Foundation under Grant DI/38/6-200/13.

The authors are thankful to heterogeneous computing (HybriLIT) team of the Laboratory of Information Technologies of JINR for support of our calculations.

References

  • (1) H. Stcker et al., Phys. Rev. C f̱25, 1873 (1982)
  • (2) C. Hartnack et al., Nucl. Phys. A 538, 53c (1992)
  • (3) C. Hartnack et al., Mod. Phys. Lett. A 9, 1151 (1994)
  • (4) P. Danielewicz and G.Odyniec, Phys. Lett. B 157, 146 (1985)
  • (5) S. Voloshin, Y. Zhang, Z. Phys. C 70, 665 (1996)
  • (6) A. M. Poskanzer, S.A. Voloshin, Phys. Rev. C 58, 1671 (1998)
  • (7) A. Bilandzic, R. Snellings and S. Voloshinet, Phys. Rev. C 83,044913 (2010)
  • (8) W. Reisdorf and H.G. Ritter, Ann. Rev. Nucl. Part. Sci. 47, 663 (1997).
  • (9) N. Herrmann, J.P. Wessels, and T. Wienold, Ann. Rev. Nucl. Part. Sci. 49, 591 (1999).
  • (10) P. Senger and H. Strobele, J. Phys. G25, R59 (1999).
  • (11) FOPI Collaboration (W. Reisdorf et. al.), Nucl. Phys. A781, 459 (2007).
  • (12) C. Pinkenburg, et al., Nucl. Phys. A 698, 495 (2002)
  • (13) K. Ackermann et al., Phys. Rev. Lett. 86, 402 (2001)
  • (14) B.B. Abelev et. al., Phys. Rev. C 90, 054901 (2014)
  • (15) G. Aad et. al., Phys. Rev. C 90, 044906 (2014)
  • (16) S. Chatrchyan et. al., Phys. Lett. B 718, 795 (2013)
  • (17) L. Chkhaidze et al., Phys. Lett. B 479, 21 (2000)
    L.Chkhaidze, T. Djobava and L. Kharkhelauri, Phys. Part. Nucl. 2, 393 (2002)
  • (18) L. Chkhaidze et al., Nucl. Phys. A 794, 115 (2007)
  • (19) L. Chkhaidze et al., Nucl. Phys. A 831, 22 (2009)
  • (20) L. Chkhaidze et al., Phys. Rev. C 84, 064915 (2011)
  • (21) C. Pinkenburg et al., Phys. Rev. Lett. 83, 1295 (1999)
  • (22) S.A. Bass et al., Prog. Part. Nucl. Phys. 41, 225 (1998)
    M. Bleicher et al., J. Phys. G 25, 1859 (1999)
  • (23) A.S. Botvina et al., Nucl. Phys. A 475, 663 (1987)
  • (24) M. Anikina et al., Phys.Rev.C 33, 895 (1986)
    M. Anikina et al., JINR Preprint E1-84-785, Dubna, (1984)
  • (25) G.N. Agakishiev et al., Yad. Fiz. 43, 366 (1986)
    D. Armutlijski et al., Yad. Fiz. 45, 1047 (1987)
    A. Bondarenko et al., JINR Preprint P1-98-292, Dubna, (1998)
  • (26) D. Beavis et al., Phys. Rev. C 45, 299 (1992)
  • (27) Kh. Abdel-Waged, Phys. Rev. C 67, 064610 (2003)
  • (28) Kh. Abdel-Waged, J. Phys. G 31, 739 (2005)
  • (29) Ch. Hartnack, Rajeev K. Puri, J. Aichelin, J. Konopka, S.A. Bass, H. Stoecker, and W. Greiner, Eur. Phys. J. A1, 151 (1998)
  • (30) D. Brill et al., Z. Phys. A 357, 207 (1997)
  • (31) C. Ogilvie et al., Nucl. Phys. A 638, 57 (1998)
  • (32) J. Kintner et al., Phys. Rev. Lett. 78, 4165 (1997)
  • (33) J. Barrette et al., Phys. Rev. C 56, 3254 (1997)
  • (34) S. Bass, C. Hartnack, H. Stoecker and W. Greiner, Phys. Rev. C 51, 3343 (1995)
  • (35) B.A. Li, C.M. Ko, Phys. Rev. C 53, R22 (1996)
  • (36) P. Danielewicz, Phys. Rev., C 51, 716 (1995)
  • (37) Yu. B. Ivanov and A.A. Soldatov, Phys. Rev. C 91, 024915 (2015)
  • (38) Yu.B. Ivanov and Yu.B. Soldatov, Phys. Rev. C 91, 024914 (2015)

Figure and Table captions

Fig. 1. Distributions of -mesons () and -mesons (after the ”identification”) (), and -mesons (UrQMD+ SMM generated) () in He+Li, C collisions on total momentum (P) and transverse momentum (P).

Fig. 2. Distributions of -mesons (), -mesons (before the ”identification”) (), -mesons (after the corrections) () and -mesons (UrQMD+SMM generated) () in p+Ta collisions.

Fig. 3. The dependence of on the rapidity in p+C collisions at the momenta of 4.2 GeV/c and of 10 GeV/c for protons and mesons in experimental (, ) and UrQMD+SMM generated (, ) data, correspondingly. Straight solid lines stretches represent the slope of data at mid-rapidity, obtained by fitting the data with a 1-st order polynomial within the intervals of the rapidity. The curved lines guide the eye over data. Arrows indicate average y over the interactions.

Fig. 4. The dependence of on the rapidity in He+Li,C collisions at 4.5 AGeV/c and p+Ta interactions at 10 GeV/c for protons and -mesons in experimental (, ) and UrQMD+SMM generated (, ) data, correspondingly. Arrows indicate average y over the interactions.

Fig. 5. The azimuthal distributions with respect to the reaction plane in p+C collisions at the momenta of 4.2 GeV/c and of 10 GeV/c for protons. The curves are the result of the approximation by .

Fig. 6. The azimuthal distributions with respect to the reaction plane in He+Li, C collisions at 4.5 AGeV/c and p+Ta interactions at 10 GeV/c for protons in experimental () and UrQMD+SMM generated () data, correspondingly. The curves are the result of the approximation by .

Table 1. The numbers of experimental and UrQMD+
SMM events prior and after applying the cuts (see text) and the values of flow parameters for protons and -mesons.

Table 2. Characteristics of proton elliptic flow in the experimental and UrQMD+SMM collisions including event number (, ) prior and after applying the cuts.

Figure 1:
Figure 2:
Figure 3:
Figure 4:
Figure 5:
Figure 6:
p+C p+C He+Li, C p+Ta
4.2 GeV/c 10 GeV/c
5882 16509 6147 2342
891 2890 786 1141
20000 60000 23000 7230
1428 4858 10435 6333
exp. 0.633 0.638 0.662 0.642
mod. 0.657 0.658 0.670 0.702
(MeV/c) 125.2 7.2 85.7 5.8 80.9 16.2 76.1 5.3
(MeV/c) 116.2 4.9 94.3 3.7 86.2 1.9 79.8 1.9
(MeV/c) -21.6 11.1 -16.1 5.4 -19.7 4.8 -18.8 4.8
(MeV/c) -19.0 7.9 -15.9 3.9 -17.2 1.8 -18.1 1.9
Table 1:
4.2 GeV/c 5882 20000
891 1428 -0.053 0.020 -0.052 0.013
p+C
10 GeV/c 16509 60000
2890 4858 -0.071 0.013 -0.072 0.008
6147 23000
He+Li, C -0.051 0.019 -0.052 0.007
786 10435
2342 7230
p+Ta -0.071 0.016 -0.072 0.007
1141 6333
Table 2:
Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
""
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
   
Add comment
Cancel
Loading ...
316072
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description