Within a relativistic transport (ART) model for heavy-ion collisions, we show
that the recently observed characteristic change from out-of-plane to in-plane
elliptic flow of protons in mid-central Au+Au collisions as the incident energy
increases is consistent with the calculated results using a stiff nuclear
equation of state (K=380 MeV). We have also studied the elliptic flow of pions
and the transverse momentum dependence of both the nucleon and pion elliptic
flow in order to gain further insight about the collision dynamics.Comment: 8 pages, 2 figure

A. Poskanzer

Andrew T. Sustich

B. A. Li

Bao-An Li

Bin Zhang

C. M. Ko

G. Song

H. Appelshäuser

H. Heiselberg

H. Liu

H. Sorge

J. Barrette

J.-Y. Ollitrault

P. Danielewicz

English

arXiv

Journals published by the American Physical Society can be found at http://publish.aps.org/Within a relativistic transport model for heavy-ion collisions, we show that the recently observed characteristic change from out-of-plane to in-plane elliptic flow of protons in midcentral Au+Au collisions as the incident energy increases is consistent with the calculated results using a stiff nuclear equation of state (K = 380 MeV). We have also studied the elliptical how of pions and the transverse momentum dependence of both the nucleon and pion elliptic flow in order to gain further insight about collision dynamics

Li, Ba

Ko, Che Ming

Sustich, AT

Zhang, B.

Texas A&M University

RAPID COMMUNICATIONS
PHYSICAL REVIEW C, VOLUME 60, 011901Excitation function of nucleon and pion elliptic flow in relativistic heavy-ion collisions
Bao-An Li,1,* C. M. Ko,2,† Andrew T. Sustich,1,‡ and Bin Zhang2,§
1Department of Chemistry and Physics, Arkansas State University, P.O. Box 419, State University, Arkansas 72467-0419
2Cyclotron Institute and Physics Department, Texas A&M University, College Station, Texas 77843
~Received 5 April 1999; published 16 June 1999!
Within a relativistic transport model for heavy-ion collisions, we show that the recently observed charac-
teristic change from out-of-plane to in-plane elliptic flow of protons in midcentral Au1Au collisions as the
incident energy increases is consistent with the calculated results using a stiff nuclear equation of state (K
5380 MeV). We have also studied the elliptical flow of pions and the transverse momentum dependence of
both the nucleon and pion elliptic flow in order to gain further insight about collision dynamics.
@S0556-2813~99!50307-5#
PACS number~s!: 25.75.2qThe elliptic flow of hadrons in relativistic heavy-ion col-
lisions has been a subject of great interest as it may reveal
the signatures of possible quark-gluon plasma ~QGP! phase
transitions in these collisions ~see Ref. @1# for a recent re-
view!. Based on kinematical and geometrical considerations
of relativistic heavy-ion collisions, Ollitrault @2# predicted
that as the incident energy increases nucleons would change
from an out-of-plane elliptical flow to an in-plane one. Such
a transition has recently been observed in collisions of heavy
ions from the alternating gradient synchrotron ~AGS! at the
Brookhaven National Laboratory @3–5#. Data from the EOS,
E895, and E877 collaborations on the proton elliptic flow in
midcentral Au1Au collisions show that the beam energy
(E tr) at which the elliptical flow changes sign is about 4
GeV/nucleon @4,5#. Studies based on transport models have
indicated that the value for E tr depends on the nuclear equa-
tion of state ~EOS! at high densities @6,7#. Using a relativistic
Boltzmann-equation model ~BEM!, it has been found that the
experimental data can be understood if the nuclear equation
of state used in the model is stiff (K5380 MeV) for beam
energies below E tr but soft (K5210 MeV) for beam energies
above E tr @5#. Since the baryon density reached in heavy-ion
collisions at these energies increases with the beam energy,
the above study thus suggests that the nuclear equation of
state is softened at high densities. Such a softened equation
of state may imply the onset of a phase change as suggested
by lattice studies of QCD at finite temperature and zero
baryon chemical potential. However, to put this conclusion
on a firm ground requires further studies using other models.
In this Rapid Communication, we shall study the elliptical
flow in heavy-ion collisions at AGS energies using a relativ-
istic transport ~ART! model @8# and show that the experi-
mental data are consistent instead with the prediction using a
stiff EOS without invoking a softening at high densities @9#.
Furthermore, we shall show that by studying both the
nucleon and pion elliptic flow as a function of beam energy
and transverse momentum one can obtain much more infor-
*Electronic address: Bali@navajo.astate.edu
†Electronic address: Ko@comp.tamu.edu
‡Electronic address: Sustich@navajo.astate.edu
§Electronic address: Bzhang@kogroup.tamu.edu0556-2813/99/60~1!/011901~3!/$15.00 60 0119mation about the reaction dynamics and the origin of the
transition in the sign of elliptic flow.
Our study is based on the relativistic transport model
ART for heavy-ion collisions. We refer the reader to Ref. @8#
for details of the model and its applications in studying vari-
ous aspects of relativistic heavy-ion collisions from Bevalac
to AGS energies. The elliptic flow reflects the anisotropy in
the particle transverse momentum (pt) distribution at midra-
pidity, i.e., v2[^(px22py2)/pt2&, where the average is taken
over all particles of a given kind in all events @10#. In the
upper panel of Fig. 1, we compare the excitation function of
v2 for protons in midcentral Au1Au reactions obtained us-
ing the stiff ~cross!, soft ~filled square! EOS, and the cascade
FIG. 1. The excitation function of proton ~upper! and pion
~lower! elliptic flow in midcentral Au1Au reactions.©1999 The American Physical Society01-1
RAPID COMMUNICATIONS
BAO-AN LI, C. M. KO, ANDREW T. SUSTICH, AND BIN ZHANG PHYSICAL REVIEW C 60 011901~open square! with the experimental data ~open circles! of
Ref. @5#. An impact parameter of 5 fm, which is consistent
with that in the data analysis @5,11#, is used in the calcula-
tions. In agreement with other model calculations @6,7,12#,
our calculated results also show that the transition energy in
the proton elliptic flow is very sensitive to the nuclear EOS.
The value of E tr is more than 4 GeV/nucleon in the case of a
stiff EOS but decreases to below 3 GeV/nucleon for a soft
EOS. As discussed in Ref. @7#, a soft EOS, which gives a
smaller sound velocity than that of a stiff EOS, reduces the
squeeze-out contribution and thus leads to a smaller transi-
tion energy in proton elliptic flow. In the case of cascade
calculations, the absence of a repulsive potential further re-
duces the squeeze-out contribution and results in an essen-
tially in-plane flow in the beam energy range considered
here. On the other hand, the value of v2 in our calculations is
insensitive to the nuclear EOS for incident energies above
about 6 GeV/nucleon. This is different from the results of
Ref. @7#, where a distinct difference is seen between the el-
liptic flow due to a soft and a stiff EOS. Our results also
differ from that of Ref. @12# based on the ultrarelativistic
quantum molecular dynamics ~UrQMD!, in which the ellip-
tical flow in the case of a stiff EOS is much smaller than that
from the cascade model even for incident energies above 6
GeV/nucleon. However, in both our study and that from the
UrQMD the experimental data are found to be consistent
with the calculated results using the stiff EOS in this beam
energy range. These results are thus different from that of
Ref. @5#, where calculations based on the BEM show that the
experimental data suggest a softening of the EOS from a stiff
one at low beam energies to a softer one at higher energies.
Since different model calculations lead to different depen-
dence of the proton elliptical flow on the nuclear EOS, it is
thus not possible at present to draw conclusions from com-
parisons of the theoretical results with the experimental data.
To test these theoretical models, simultaneous studies of
other experimental observables will be useful.
Since pions are abundantly produced in high energy
heavy-ion collisions, their elliptical flow is expected to pro-
vide further insight about collision dynamics. In the lower
panel of Fig. 1, we show our predictions for the excitation
function of the pion elliptic flow. All three charge states of
the pion are included in the analysis. Effects due to the dif-
ferent charges will be discussed in the next paragraph. It is
shown that pions also show a transition from out-of-plane to
in-plane elliptic flow as the beam energy increases. However,
both the magnitude of pion elliptic flow and the transition
energy at which it changes sign are significantly smaller than
those for nucleons. This can be qualitatively understood from
the collision dynamics. For nucleons, the sign and magnitude
of elliptic flow depends on both transverse expansion time of
participant nuclear matter and the passage time of the two
colliding nuclei. The latter reflects the time scale for the
spectators to be effective in preventing the participant had-
rons from developing an in-plane flow, thus enhancing the
squeeze-out contribution to the elliptical flow. For pions,
however, the shadowing effect due to spectator nucleons is
less important as a result of the time delay in their produc-
tion, i.e., a significant number of pions are emitted later in01190the reaction from the decay of both baryon and meson reso-
nances after the spectator nucleons have already moved
away. Therefore, both the magnitude of squeeze-out contri-
bution and the transition energy in the pion elliptic flow are
significantly smaller than those of nucleons. The study of the
excitation function of both nucleon and pion flow is useful in
understanding the origin of the transition from out-of-plane
to in-plane elliptic flow.
In Fig. 2, we show the pt dependence of nucleon and pion
elliptic flow in a midcentral collision of Au1Au at a beam
momentum of 6 GeV/c . They are obtained from the ART
model with a soft nuclear EOS. For protons, the elliptic flow
increases approximately quardratically at low pt and then
increases linearly at high pt , as expected from the nucleon
azimuthal angle distributions @1,13,14#. For pions, their v2
value is larger than that for protons at low pt but becomes
similar at high pt . Again, one can understand this result
from the reaction dynamics. Low pt pions are more likely
produced later in the reaction, and they are thus less likely to
be shadowed by spectator nucleons and have thus a larger
in-plane flow compared to low pt protons. On the other hand,
high pt pions are mainly produced early in the reaction and
thus freeze out together with high pt nucleons, leading then
to a similar elliptic flow, which approaches that of the hy-
drodynamical limit @14#. It is interesting to mention that the
observed pt dependence of v2 for nucleons and pions is re-
markably similar to that found at both Bevalac/SIS @13,15#
and SPS energies @16#, indicating the similarity of the colli-
sion dynamics at these different energies. We note that nega-
tive pions have higher in-plane flow than the positive ones as
a result of the Coulomb potential from protons, i.e., negative
pions are attracted to while positive ones are repelled away
from the reaction plane by protons.
In summary, using a relativistic transport model we have
found that the transition from out-of-plane to in-plane elliptic
flow in midcentral Au1Au collisions as the beam energy
increases is consistent with a stiff nuclear EOS without in-
FIG. 2. The transverse momentum dependence of nucleon and
pion elliptic flow in the reaction of Au1Au at pbeam /A56 GeV/c
and an impact parameter of 4 fm using a soft nuclear equation of
state.1-2
RAPID COMMUNICATIONS
EXCITATION FUNCTION OF NUCLEON AND PION . . . PHYSICAL REVIEW C 60 011901voking a phase transition. This result is consistent with that
from the UrQMD model but different from that from the
BEM. To help disentangle these different predictions, we
have also shown the excitation function of the pion elliptic
flow and the transverse momentum dependence of both the
nucleon and pion elliptic flow, which are expected to reveal01190interesting information about both the reaction dynamics and
the origin of the observed change in the sign of elliptic flow.
This work was supported in part by NSF Grant No. PHY-
9870038, the Robert A. Welch foundation under Grant
A-1358, and the Texas Advanced Research Program.@1# J.-Y. Ollitrault, Nucl. Phys. A638, 195c ~1998!.
@2# J.-Y. Ollitrault, Phys. Rev. D 46, 229 ~1992!; 48, 1132 ~1993!.
@3# J. Barrette et al., E877 Collaboration, Phys. Rev. C 55, 1420
~1997!; 56, 2336 ~1997!.
@4# H. Liu et al., E895 Collaboration, Nucl. Phys. A638, 451c
~1998!.
@5# C. Pinkenburg et al., E895 Collaboration, nucl-ex/9903010.
@6# H. Sorge, Phys. Rev. Lett. 78, 2309 ~1997!.
@7# P. Danielewicz et al., Phys. Rev. Lett. 81, 2438 ~1998!.
@8# B. A. Li and C. M. Ko, Phys. Rev. C 52, 2037 ~1995!; 53, R22
~1996!; 54, 3283 ~1996!; 54, 844 ~1996!; Nucl. Phys. A601,
457 ~1996!; Phys. Rev. C 58, R1382 ~1998!; G. Song, B. A. Li,
and C. M. Ko, Nucl. Phys. A646, 481 ~1999!.
@9# B. A. Li, C. M. Ko, A. Sustich, and B. Zhang, in Proceedingsof the Relativistic Heavy-Ion Mini-Symposium at the APS Cen-
tennial, Atlanta, Georgia, 1999, edited by R. Seto ~World Sci-
entific, Singapore, in press!.
@10# A. Poskanzer and S. A. Voloshin, Phys. Rev. C 58, 1671
~1998!.
@11# R. A. Lacey ~private communication!.
@12# S. Soff, S. A. Bass, M. Bleicher, H. Sto¨cker, and W. Greiner,
nucl-th/9903061.
@13# P. Danielewicz, Phys. Rev. C 51, 716 ~1995!.
@14# H. Heiselberg and A.-M. Levy, Phys. Rev. C 59, 2716 ~1999!.
@15# B. A. Li, Phys. Lett. B 300, 14 ~1993!; Nucl. Phys. A570, 797
~1994!.
@16# H. Appelsha¨user et al., NA49 Collaboration, Phys. Rev. Lett.
80, 4136 ~1998!.1-3


Excitation function of nucleon and pion elliptic flow in relativistic heavy-ion collisions

Crossref

Physical Review C

OAKTrust Digital Repository (Texas A&M Univ)

RAPID COMMUNICATIONSPHYSICAL REVIEW C, VOLUME 60, 011901Excitation function of nucleon and pion elliptic flow in relativistic heavy-ion collisionsBao-An Li,1,* C. M. Ko,2,† Andrew T. Sustich,1,‡ and Bin Zhang2,§1Department of Chemistry and Physics, Arkansas State University, P.O. Box 419, State University, Arkansas 72467-04192Cyclotron Institute and Physics Department, Texas A&M University, College Station, Texas 77843~Received 5 April 1999; published 16 June 1999!Within a relativistic transport model for heavy-ion collisions, we show that the recently observed charac-teristic change from out-of-plane to in-plane elliptic flow of protons in midcentral Au1Au collisions as theincident energy increases is consistent with the calculated results using a stiff nuclear equation of state (K5380 MeV). We have also studied the elliptical flow of pions and the transverse momentum dependence ofboth the nucleon and pion elliptic flow in order to gain further insight about collision dynamics.@S0556-2813~99!50307-5#PACS number~s!: 25.75.2qThe elliptic flow of hadrons in relativistic heavy-ion col-lisions has been a subject of great interest as it may revealthe signatures of possible quark-gluon plasma ~QGP! phasetransitions in these collisions ~see Ref. @1# for a recent re-view!. Based on kinematical and geometrical considerationsof relativistic heavy-ion collisions, Ollitrault @2# predictedthat as the incident energy increases nucleons would changefrom an out-of-plane elliptical flow to an in-plane one. Sucha transition has recently been observed in collisions of heavyions from the alternating gradient synchrotron ~AGS! at theBrookhaven National Laboratory @3–5#. Data from the EOS,E895, and E877 collaborations on the proton elliptic flow inmidcentral Au1Au collisions show that the beam energy(E tr) at which the elliptical flow changes sign is about 4GeV/nucleon @4,5#. Studies based on transport models haveindicated that the value for E tr depends on the nuclear equa-tion of state ~EOS! at high densities @6,7#. Using a relativisticBoltzmann-equation model ~BEM!, it has been found that theexperimental data can be understood if the nuclear equationof state used in the model is stiff (K5380 MeV) for beamenergies below E tr but soft (K5210 MeV) for beam energiesabove E tr @5#. Since the baryon density reached in heavy-ioncollisions at these energies increases with the beam energy,the above study thus suggests that the nuclear equation ofstate is softened at high densities. Such a softened equationof state may imply the onset of a phase change as suggestedby lattice studies of QCD at finite temperature and zerobaryon chemical potential. However, to put this conclusionon a firm ground requires further studies using other models.In this Rapid Communication, we shall study the ellipticalflow in heavy-ion collisions at AGS energies using a relativ-istic transport ~ART! model @8# and show that the experi-mental data are consistent instead with the prediction using astiff EOS without invoking a softening at high densities @9#.Furthermore, we shall show that by studying both thenucleon and pion elliptic flow as a function of beam energyand transverse momentum one can obtain much more infor-*Electronic address: Bali@navajo.astate.edu†Electronic address: Ko@comp.tamu.edu‡Electronic address: Sustich@navajo.astate.edu§Electronic address: Bzhang@kogroup.tamu.edu0556-2813/99/60~1!/011901~3!/$15.00 60 0119mation about the reaction dynamics and the origin of thetransition in the sign of elliptic flow.Our study is based on the relativistic transport modelART for heavy-ion collisions. We refer the reader to Ref. @8#for details of the model and its applications in studying vari-ous aspects of relativistic heavy-ion collisions from Bevalacto AGS energies. The elliptic flow reflects the anisotropy inthe particle transverse momentum (pt) distribution at midra-pidity, i.e., v2[^(px22py2)/pt2&, where the average is takenover all particles of a given kind in all events @10#. In theupper panel of Fig. 1, we compare the excitation function ofv2 for protons in midcentral Au1Au reactions obtained us-ing the stiff ~cross!, soft ~filled square! EOS, and the cascadeFIG. 1. The excitation function of proton ~upper! and pion~lower! elliptic flow in midcentral Au1Au reactions.©1999 The American Physical Society01-1RAPID COMMUNICATIONSBAO-AN LI, C. M. KO, ANDREW T. SUSTICH, AND BIN ZHANG PHYSICAL REVIEW C 60 011901~open square! with the experimental data ~open circles! ofRef. @5#. An impact parameter of 5 fm, which is consistentwith that in the data analysis @5,11#, is used in the calcula-tions. In agreement with other model calculations @6,7,12#,our calculated results also show that the transition energy inthe proton elliptic flow is very sensitive to the nuclear EOS.The value of E tr is more than 4 GeV/nucleon in the case of astiff EOS but decreases to below 3 GeV/nucleon for a softEOS. As discussed in Ref. @7#, a soft EOS, which gives asmaller sound velocity than that of a stiff EOS, reduces thesqueeze-out contribution and thus leads to a smaller transi-tion energy in proton elliptic flow. In the case of cascadecalculations, the absence of a repulsive potential further re-duces the squeeze-out contribution and results in an essen-tially in-plane flow in the beam energy range consideredhere. On the other hand, the value of v2 in our calculations isinsensitive to the nuclear EOS for incident energies aboveabout 6 GeV/nucleon. This is different from the results ofRef. @7#, where a distinct difference is seen between the el-liptic flow due to a soft and a stiff EOS. Our results alsodiffer from that of Ref. @12# based on the ultrarelativisticquantum molecular dynamics ~UrQMD!, in which the ellip-tical flow in the case of a stiff EOS is much smaller than thatfrom the cascade model even for incident energies above 6GeV/nucleon. However, in both our study and that from theUrQMD the experimental data are found to be consistentwith the calculated results using the stiff EOS in this beamenergy range. These results are thus different from that ofRef. @5#, where calculations based on the BEM show that theexperimental data suggest a softening of the EOS from a stiffone at low beam energies to a softer one at higher energies.Since different model calculations lead to different depen-dence of the proton elliptical flow on the nuclear EOS, it isthus not possible at present to draw conclusions from com-parisons of the theoretical results with the experimental data.To test these theoretical models, simultaneous studies ofother experimental observables will be useful.Since pions are abundantly produced in high energyheavy-ion collisions, their elliptical flow is expected to pro-vide further insight about collision dynamics. In the lowerpanel of Fig. 1, we show our predictions for the excitationfunction of the pion elliptic flow. All three charge states ofthe pion are included in the analysis. Effects due to the dif-ferent charges will be discussed in the next paragraph. It isshown that pions also show a transition from out-of-plane toin-plane elliptic flow as the beam energy increases. However,both the magnitude of pion elliptic flow and the transitionenergy at which it changes sign are significantly smaller thanthose for nucleons. This can be qualitatively understood fromthe collision dynamics. For nucleons, the sign and magnitudeof elliptic flow depends on both transverse expansion time ofparticipant nuclear matter and the passage time of the twocolliding nuclei. The latter reflects the time scale for thespectators to be effective in preventing the participant had-rons from developing an in-plane flow, thus enhancing thesqueeze-out contribution to the elliptical flow. For pions,however, the shadowing effect due to spectator nucleons isless important as a result of the time delay in their produc-tion, i.e., a significant number of pions are emitted later in01190the reaction from the decay of both baryon and meson reso-nances after the spectator nucleons have already movedaway. Therefore, both the magnitude of squeeze-out contri-bution and the transition energy in the pion elliptic flow aresignificantly smaller than those of nucleons. The study of theexcitation function of both nucleon and pion flow is useful inunderstanding the origin of the transition from out-of-planeto in-plane elliptic flow.In Fig. 2, we show the pt dependence of nucleon and pionelliptic flow in a midcentral collision of Au1Au at a beammomentum of 6 GeV/c . They are obtained from the ARTmodel with a soft nuclear EOS. For protons, the elliptic flowincreases approximately quardratically at low pt and thenincreases linearly at high pt , as expected from the nucleonazimuthal angle distributions @1,13,14#. For pions, their v2value is larger than that for protons at low pt but becomessimilar at high pt . Again, one can understand this resultfrom the reaction dynamics. Low pt pions are more likelyproduced later in the reaction, and they are thus less likely tobe shadowed by spectator nucleons and have thus a largerin-plane flow compared to low pt protons. On the other hand,high pt pions are mainly produced early in the reaction andthus freeze out together with high pt nucleons, leading thento a similar elliptic flow, which approaches that of the hy-drodynamical limit @14#. It is interesting to mention that theobserved pt dependence of v2 for nucleons and pions is re-markably similar to that found at both Bevalac/SIS @13,15#and SPS energies @16#, indicating the similarity of the colli-sion dynamics at these different energies. We note that nega-tive pions have higher in-plane flow than the positive ones asa result of the Coulomb potential from protons, i.e., negativepions are attracted to while positive ones are repelled awayfrom the reaction plane by protons.In summary, using a relativistic transport model we havefound that the transition from out-of-plane to in-plane ellipticflow in midcentral Au1Au collisions as the beam energyincreases is consistent with a stiff nuclear EOS without in-FIG. 2. The transverse momentum dependence of nucleon andpion elliptic flow in the reaction of Au1Au at pbeam /A56 GeV/cand an impact parameter of 4 fm using a soft nuclear equation ofstate.1-2RAPID COMMUNICATIONSEXCITATION FUNCTION OF NUCLEON AND PION . . . PHYSICAL REVIEW C 60 011901voking a phase transition. This result is consistent with thatfrom the UrQMD model but different from that from theBEM. To help disentangle these different predictions, wehave also shown the excitation function of the pion ellipticflow and the transverse momentum dependence of both thenucleon and pion elliptic flow, which are expected to reveal01190interesting information about both the reaction dynamics andthe origin of the observed change in the sign of elliptic flow.This work was supported in part by NSF Grant No. PHY-9870038, the Robert A. Welch foundation under GrantA-1358, and the Texas Advanced Research Program.@1# J.-Y. Ollitrault, Nucl. Phys. A638, 195c ~1998!.@2# J.-Y. Ollitrault, Phys. Rev. D 46, 229 ~1992!; 48, 1132 ~1993!.@3# J. Barrette et al., E877 Collaboration, Phys. Rev. C 55, 1420~1997!; 56, 2336 ~1997!.@4# H. Liu et al., E895 Collaboration, Nucl. Phys. A638, 451c~1998!.@5# C. Pinkenburg et al., E895 Collaboration, nucl-ex/9903010.@6# H. Sorge, Phys. Rev. Lett. 78, 2309 ~1997!.@7# P. Danielewicz et al., Phys. Rev. Lett. 81, 2438 ~1998!.@8# B. A. Li and C. M. Ko, Phys. Rev. C 52, 2037 ~1995!; 53, R22~1996!; 54, 3283 ~1996!; 54, 844 ~1996!; Nucl. Phys. A601,457 ~1996!; Phys. Rev. C 58, R1382 ~1998!; G. Song, B. A. Li,and C. M. Ko, Nucl. Phys. A646, 481 ~1999!.@9# B. A. Li, C. M. Ko, A. Sustich, and B. Zhang, in Proceedingsof the Relativistic Heavy-Ion Mini-Symposium at the APS Cen-tennial, Atlanta, Georgia, 1999, edited by R. Seto ~World Sci-entific, Singapore, in press!.@10# A. Poskanzer and S. A. Voloshin, Phys. Rev. C 58, 1671~1998!.@11# R. A. Lacey ~private communication!.@12# S. Soff, S. A. Bass, M. Bleicher, H. Sto¨cker, and W. Greiner,nucl-th/9903061.@13# P. Danielewicz, Phys. Rev. C 51, 716 ~1995!.@14# H. Heiselberg and A.-M. Levy, Phys. Rev. C 59, 2716 ~1999!.@15# B. A. Li, Phys. Lett. B 300, 14 ~1993!; Nucl. Phys. A570, 797~1994!.@16# H. Appelsha¨user et al., NA49 Collaboration, Phys. Rev. Lett.80, 4136 ~1998!.1-3

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Excitation function of nucleon and pion elliptic flow in relativistic
  heavy-ion collisions

Excitation function of nucleon and pion elliptic flow in relativistic heavy-ion collisions

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