We study the energy dependence of collective (hydrodynamic-like) nuclear
matter flow in 400-1970 A MeV Ni+Au and 1000-1970 A MeV Ni+Cu reactions. The
flow increases with energy, reaches a maximum, and then gradually decreases at
higher energies. A way of comparing the energy dependence of flow values for
different projectile-target mass combinations is introduced, which demonstrates
a common scaling behaviour among flow values from different systems.Comment: 12 pages, 3 figures. Submitted to Physical Review Letter

A. D. Chacon

A. Insolia

A. Lang

A. S. Hirsch

A. Scott

B. Blättel

B. Srivastava

Bao-An Li

C. McParland

C. Tuvé

D. Beavis

D. Cebra

D. Keane

D. L. Olson

E. L. Hjort

F. Bieser

F. P. Brady

G. Rai

G. V. Russo

H. G. Ritter

H. H. Gutbrod

H. H. Wieman

H. S. Matis

H. Ströbele

H. Å. Gustafsson

J. A. Hauger

J. Aichelin

J. B. Elliott

J. C. Kintner

J. Chance

J. L. Romero

J. Poitou

J. Rasmussen

J. Romanski

J. W. Harris

K. G. R. Doss

K. Wolf

M. A. Lisa

M. D. Partlan

M. Gilkes

M. Justice

M. McMahan

M. Partlan

M. Tincknell

N. T. Porile

P. Danielewicz

P. Warren

R. E. Renfordt

R. Potenza

R. Scharenberg

S. Albergo

S. Costa

S. Wang

T. J. M. Symons

T. Wienold

V. Koch

W. Bauer

Y. Choi

Y. Shao

Z. Caccia

Physical Review Letters

English

arXiv

Crossref

The Energy Dependence of Flow in Ni Induced Collisions from
                    
                      400

Chance, J.

Albergo, S.

Bieser, F.

Brady, F. P.

Caccia, Z.

Cebra, D.

Chacon, A. D.

Choi, Y.

Costa, S.

Elliott, J. B.

Gilkes, M.

Hauger, J. A.

Hirsch, A. S.

Hjort, E. L.

Insolia, A.

Justice, M.

Keane, D.

Kintner, J. C.

Lisa, M. A.

Matis, H. S.

McMahan, M.

McParland, C.

Olson, D. L.

Partlan, M. D.

Porile, N. T.

Potenza, R.

Rai, G.

Rasmussen, J.

Ritter, H. G.

Romanski, J.

Romero, J. L.

Russo, G. V.

Scharenberg, R.

Scott, A.

Shao, Y.

Srivastava, B.

Symons, T. J. M.

Tincknell, M.

Tuv��, C.

Wang, S.

Warren, P.

Wieman, H. H.

Wienold, T.

Wolf, K.

OAKTrust Digital Repository (Texas A&M Univ)

arXiv:nucl-ex/9607008v2  23 Jul 1996The energy dependence of flow in Ni induced collisionsfrom 400 to 1970A MeVJ. Chance(1), S. Albergo(2), F. Bieser(4), F. P. Brady(1), Z. Caccia(2), D. Cebra(1,4),A. D. Chacon(6), Y. Choi(5)∗, S. Costa(2), J. B. Elliott(5), M. Gilkes(3)†, J. A. Hauger(5),A. S. Hirsch(5), E. L. Hjort(5), A. Insolia(2), M. Justice(3), D. Keane(3), J. C. Kintner(1)‡,M. A. Lisa(4), H. S. Matis(4), M. McMahan(4), C. McParland(4), D. L. Olson(4),M. D. Partlan(1)§, N. T. Porile(5), R. Potenza(2), G. Rai(4), J. Rasmussen(4), H. G. Ritter(4),J. Romanski(2)∗∗, J. L. Romero(1), G. V. Russo(2), R. Scharenberg(5), A. Scott(3)††,Y. Shao(3)‡‡, B. Srivastava(5), T. J. M. Symons(4), M. Tincknell(5), C. Tuve´(2), S. Wang(3),P. Warren(5), H. H. Wieman(4), T. Wienold(4), K. Wolf(6)(1) University of California, Davis, California 95616(2) Universita´ di Catania & INFN-Sezione di Catania, Catania, Italy, 95129(3) Kent State University, Kent, Ohio 44242(4) Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720(5) Purdue University, West Lafayette, Indiana 47907-1396(6) Texas A&M University, College Station, Texas 77843(The EOS Collaboration)AbstractWe study the energy dependence of collective (hydrodynamic-like) nuclearmatter flow in 400-1970 A MeV Ni+Au and 1000-1970 A MeV Ni+Cu reac-tions. The flow increases with energy, reaches a maximum, and then graduallydecreases at higher energies. A way of comparing the energy dependence offlow values for different projectile-target mass combinations is introduced,which demonstrates a common scaling behaviour among flow values from dif-1fererent systems.PACS numbers: 25.70.Pq, 25.75.LdTypeset using REVTEX2The study of nuclear matter over a wide range of temperatures and densities and thedetermination of the Equation of State (EOS) of nuclear matter continue to be of consid-erable interest [1]. Lacking the possibility of comprehensive studies of nuclear matter inbulk (as in neutron stars), one resorts to the study of transient, finite systems provided bynucleus-nucleus collisions (over a wide range of energy). It is now clear that the extractionof EOS information from nuclear collisions requires a comprehensive set of measurements ofcollision observables, which can be compared to realistic microscopic calculations involvingthe nuclear matter variables.At GeV per nucleon energies, where the collision velocity exceeds that of nuclear sound,the collisions produce densities several times higher than ground state densities and exhibitcompression-induced flow of nuclear matter [1]. However, it was not until the analysis ofevents from the 4π Plastic Ball/Wall [2] and Streamer Chamber [3] detector systems at theBevalac that the matter flow characteristics could be studied and quantified for a range ofsystems and energies. More recently, at the Bevalac at LBNL, the EOS Collaboration carriedout a comprehensive set of measurements over a wide range of energies, and projectile-target combinations [4]. Similar studies are underway at GSI in Darmstadt and, with lighterprojectiles, by the DIOGENE Collaboration at Saclay [5]. EOS Collaboration data has beenused to study flow for the Au+Au system at lab energies ranging from 250 to 1150A MeV[6]. Particle flow for protons, deuterons and alpha particles has been determined, using thetransverse momentum method [7]. The flow is found to increase with particle mass A, andwith energy up to projectile energies of 1150A MeV where it tends to level out at valuesclose to the Plastic Ball data [8].Here we present analyses of recent EOS Ni + Au data with energies between 400 and1970A MeV and EOS Ni+ Cu data at energies of 1000, 1500 and 1970A MeV. This studywith the Ni beam allows the use of higher energy per nucleon projectiles, and so extends theenergy of our flow measurements beyond the 1150A MeV limit of the EOS Au + Au data[6]. We also present a comparison of the flow values with predictions of a BUU model fromBauer et al. [9], and introduce a scaled flow which allows the comparison of flow data from a3variety of projectile-target mass systems. In total, the data (supported by the calculations)provide the strongest evidence yet that, with increasing energy, flow reaches a maximumnear 1000A MeV, and then declines.The EOS Collaboration detector systems have been described in Refs. 4 and 6. Thedata presented here were obtained using the EOS Time Projection Chamber [10], situatedin the magnetic field of the HISS Magnet. The TPC provides fairly unambiguous particleidentification, as well as a measurement of momentum, for particles of charge up to Z =6. Particle ID is ambiguous for rigidities above 2.4 GeV/c. Thus, some misidentificationwill occur and its effect is represented in the uncertainties. The target is just upstreamfrom the TPC and this results in a large and nearly seamless acceptance. Laser beamcalibrations provide a check of the corrections for B field inhomogeneities, and measurementsof drift velocity. Simulations have been performed to study the geometrical acceptance ofthe detector and to provide acceptance corrections.In the present experiment, the thickness of the Au target was 730 mg/cm2 correspond-ing to about 1% interaction probability. The trigger was provided by a scintillator justdownstream from the target. The MUSIC (Multiple Sampling Ionization Chamber) detec-tor, downstream from the TPC, provided an on-line check on the threshold charge of theheaviest fragment allowed by the trigger. For this analysis, data for a wide range of impactparameters were taken. We used charged particle multiplicity as a measure of the collisioncentrality, and have adopted the Plastic Ball [8] convention by dividing the events into fivemultiplicity bins with bin M1 corresponding to the most peripheral and bin M5 having themost central events. For the Ni+Au 400, 600, 1000 and 1970A MeV the numbers of eventsanalyzed were 32k, 26k, 33k and 26k respectively. The Ni + Cu 1000, 1500 and 1970 AMeV analyses were done on recently analyzed data sets of respectively, 35k, 19k and 48kevents. For each event, the reaction plane was determined using the transverse momentaof the particles, as proposed by Danielewicz and Odyniec [7]. The plane is determined bythe vector ~Q =∑i wi~pti and the incident beam direction. Here ~pti is the transverse mo-mentum of particle i, and wi is a weighting factor defined to maximize the contribution of4high rapidity particles to the ~Q vector determination. Normally, for symmetric collisions ofequal A, wi is taken to increase linearly with rapidity up to wi = ±1 at |y′cm| = δ and to beconstant at ±1 for |y′cm| ≥ δ. Using the sub-event method of Ref. 7 we found the optimalreaction plane determination to be made with δ ≃ 0.7. We also found that varying δ by0.1 results in only a 1% change in the flow values. For the asymmetric 58Ni + 197Au, thenucleon-nucleon and nucleus-nucleus center of mass frames are different. There is thereforesome ambiguity as to which reference frame to use for determining the weighting factors.We went through an iterative procedure as follows: We start out in the nucleus-nucleus cmframe, do the ~Q weighting in that frame, and then project the ~pt of each particle onto thereaction plane. We refer to this projection as px for each particle in the event. Plottingthe 〈px/A〉 (henceforth referred to as p˜x) vs. rapidity for all events at a given energy thenyields the typical S-shaped curves. These S curves do not cross the p˜x = 0 axis at yc = 0where yc here refers to the rapidity in the chosen frame, in this case the nucleus-nucleus cmframe. We next look at p˜x vs. lab rapidity and note where the curve crosses the p˜x = 0axis. This crossing rapidity defines the velocity of the new frame in which we do the nextweighting. A couple of iterations yields a stable crossing value of y. Finally, we need tocorrect p˜x for the fact that we project onto an imperfectly known reaction plane. For thiswe use the sub-event method of Ref. 7. These corrections increase the p˜x values from 10%(for the more central Ni+ Au events) to 20% (for the more peripheral Ni+ Cu events).Figure 1 shows the S-shaped plots of p˜x vs. y′ for the four Ni + Au systems and formultiplicity bin M4. Here, for the moment, we include only protons, for which we haveunambiguous particle identification. Following the Plastic Ball analysis we define the flow,F , as the slope (dp˜x/dy′)p˜x=0 at the zero crossing (generally around y′ = 0.35). The slope iscalculated from a linear fit to the data. Similar F values are obtained using a cubic fit. Theimperfect asymmetry of the S-curve with respect to the p˜x = 0 axis is due to both the loweracceptance in the lower rapidities, as well as reflecting transverse momentum conservationin the asymmetric collision: The larger number of (mainly target) particles (both spectator5and participant) at low rapidity, is balanced at higher rapidity, by fewer particles havinglarger average pt values. From the geometrical acceptance studies we found that acceptancecorrections on the flow values are on the order of 5% for the lower energy Ni + Au 400Aand 600A MeV systems . Flow value corrections above 600A MeV are negligible since thedetector has full acceptance for the region where the fitting is performed.In Figure 2 the extracted values of the slope, F (for protons), at y′(px = 0) are plottedvs. projectile kinetic energy per nucleon and compared to the flow predicted by a basic BUUmodel [9]. This model does not include composite particle formation so the comparison iswith the experimental proton F values. With the inclusion of bound protons (from d, t,etc.) the trend of the F values, as a function of energy, is similar. It should be notedthat the BUU model used here does not include momentum dependent interactions. It isexpected that adding these will increase the predicted BUU flow values, bringing them tobetter agreement with the data. The hard EOS BUU flow values appear to reach theirmaximum at a lower energy than the soft EOS. In this aspect the hard EOS BUU is closerto the energy dependence of the data. However, neither case gives quantitatively the energydependence, and work on this aspect continues [11]. The main point here is that the BUUmodel does predict a rise and fall of flow. The energy dependence in Fig. 2 is consistentwith the EOS Au + Au proton flow data of Partlan et al. [6] and the Plastic Ball data [8]which show the flow beginning to plateau above 800A MeV.We have studied other flow observables: the maximum value of p˜x, the maximum valueof F , regardless of the corresponding y value, and the sum∑p˜x, summed over all valuesfor y′ > y′(p˜x = 0). All of these observables give a flow energy dependence consistent withthat for F . We have also analyzed the data using the reaction plane independent flow signalquantity [12] proposed by the FOPI group. In addition we have examined the flow angledependence on multiplicity for the 4 energies. Both the flow angle and the FOPI signal showan energy dependence (rise and fall) similar to that of F in Fig. 2.It can be argued that flow should be determined from the laboratory rapidity, y, ratherthan from reduced rapidity, y′ = y/ybeam. Then flow becomes Fy = dp˜x/dy = F/yp where6yp is the projectile beam rapidity in the lab frame. Plotting Fy vs. energy we find that therise of flow is reduced while the decline becomes more significant.The rise and fall of flow is explicable or at least qualitatively reasonable. As energyincreases, the nucleon-nucleon cross sections become more forward peaked. The meantransverse momentum at first rises rapidly with energy and then is almost constant abovepz ≃ 2 GeV/c. Thus, flow as a manifestation of multiple scattering effects should eventuallyfall as pz continues to increase.It is of great interest to compare the flow values for a wide range of data. To allow fordifferent projectile-target (A1, A2) mass combinations, we divide the flow value by (A1/31 +A1/32 ) and call FS = F/(A1/31 + A1/32 ) the scaled flow. In recent calculations of flow [13], theauthors use an F/A1/3 scaling for symmetric systems, and argue that, for a given energy,the flow should scale with collision (compression) time. This suggested the (A1/31 + A1/32 )−1scaling used here. Figure 3 shows a plot of FS vs. energy per nucleon of the projectile. Weinclude here data from the EOS experiment (solid points), along with values derived fromother experiments [8,14–16] for a variety of energies and mass combinations. As closely aspossible the data selected correspond to Plastic Ball multiplicity bins M3 and M4 or to anequivalent range of impact parameters. For the EOS and Plastic Ball data all the isotopes ofZ = 1 and 2 are included, except for [16] where the data is for Z=1 and multiplicity bin M3.The Streamer Chamber data [14,15] normally include all protons, whether free or bound inclusters. Generally the flow values using all isotopes of Z = 1 and 2 are 10 − 20% largerthan those for protons. In Fig. 3 the scaled flow values, FS, follow, within the uncertainties,a common trend with an initial steep rise and then an indication of a gradual decline. ThePlastic Ball data are quoted with fairly small statistical uncertainties, ≃ 4−7%, about twicethe size of the data points in Fig. 3. For the Ar + Pb [14] and Ar + KCl [15] StreamerChamber data, we estimated the flow and statistical uncertainties from the p˜x vs. y dataplots, for the appropriate multiplicity ranges. Our estimated uncertainties for these flowvalues are in the range of 15-23%. The 1800A MeV Ar +KCl Streamer Chamber data, asanalyzed in Ref. 7, produce a very large flow and scaled flow value (Fs ≃ 93 MeV/c per7nucleon which is off the plot scale and not included in Fig. 3).In summary, we have determined the nucleon flow for Ni induced collisions over anenergy range of 400 to 1970A MeV. For these Ni systems flow, F , as measured by thechange with rapidity of the average transverse momentum, rises with energy, and thendeclines. Comparison of our flow results with flow data from other mass systems is madeby introducing a scaled flow, FS = F/(A1/31 + A1/32 ) which exhibits a nearly universal flowenergy dependence.ACKNOWLEDGMENTSWe are pleased to acknowledge the support of the National Science Foundation (GrantNo. PHY-9123301), the Department of Energy (Contracts/grants DE-AC03-76SF00098,DE-FG02-89ER40531, DE-FG02-88ER40408, DE-FG02-88ER40412, DE-FG05-88ER40437)and Associated Western Universities; and the assistance of the Bevalac Operations SupportGroups.∗ Present address: Sung Kwun Kwan University, Suwon, Rep. of Korea, 440-746† Present address: State University of New York, Stonybrook, NY 11794‡ Present address: Lawrence University, Appleton, WI 54912§ Present address: Nuclear Science Division, LBNL, Berkeley, CA 94720∗∗ Present address: The Svedberg Laboratory, University of Uppsala, S751-21 Sweden†† Present address: Physics Department, College of Wooster, Wooster, OH 44691‡‡ Present address: Crump Institute for Biological Imaging, UCLA, Los Angeles, CA 917768REFERENCES[1] A recent conference on this topic has been held. Please see the Nuclear Equation ofState, Vol. 216 of NATO Advanced Study Institute, Series B: Physics, edited by W.Greiner and H. Sto¨cker (Plenum, New York, 1989).[2] H. A˚. Gustafsson et al., Phys. Rev. Lett. 52, 1590 (1984).[3] R. E. Renfordt et al., Phys. Rev. Lett. 53, 763 (1984); H. Stro¨bele et al., Phys. Rev. C27, 1349 (1983).[4] S. Costa (for the EOS Collaboration), Proceedings of the 23rd International WinterMeeting on Nuclear Physics at Bormio, Italy, January 23-30 (1994).[5] J. Gosset et al., ibid. Ref. 1, p. 87; J. Poitou et al., Nucl. Phys. A 536, 767 (1992).[6] M. Partlan et al. (the EOS Collaboration), Phys. Rev. Lett. 75, 2100 (1995).[7] P. Danielewicz and G. Odyniec, Phys. Lett. 157B, 146 (1985).[8] H. H. Gutbrod, A. M. Poskanzer and H.-G. Ritter, Reports on Progress in Physics 52,1267 (1989), and references therein.[9] W. Bauer, Phys. Rev. Lett. 61, 2534 (1988); Bao-An Li and W. Bauer, Phys. Rev. C44, 2095 (1991); W. Bauer, C. K. Gelbke, and S. Pratt, Ann. Rev. Nucl. Sci. 42, 77(1992).[10] G. Rai et al., IEEE Trans. Nucl. Sci. 37, 56 (1990).[11] J. Chance, Ph.D. Dissertation, UC Davis, 1996.[12] T. Wienold et al., GSI-Preprint-94-74.[13] A. Lang, B. Bla¨ttel, W. Cassing, V. Koch, U. Mosel and K. Weber, Zeitschrift fu¨rPhysik A 340, 287 (1991).[14] D. Beavis et al., Phys. Rev. C 45, 299 (1992).9[15] D. Beavis, S. Y. Chu, S. Y. Fung, W. Gorn, D. Keane, Y. M. Liu, G.Van Dalen, M.Vient, Phys. Rev. C 33, 1113, (1986).[16] J.W. Harris et al., Nucl. Phys. A 471, 241C (1987); K.G.R. Doss et al., Phys. Rev.Lett. 59, 2720 (1987).10FIGURESNi400 A MeV Ni600 A MeVNi1000 A MeV Ni1970 A MeVy’y’0.25 0.5 0.75 1.00.0 0.25 0.5 0.75 1.0-50050100150-50050100150p x(MeV/c)˜FIG. 1. S curves for the four Ni + Au energies, using protons only in multiplicity bin M4. p˜xis the average of the x component of the momentum (see text). y′ is the rapidity in the lab framescaled by the rapidity of the beam.Ni+Au200300400500Ni+Cu2002503003500 500 1000 1500 2000 2500FIG. 2. Proton flow as a function of beam energy per nucleon in multiplicity bin M4. The toppanel is for Ni + Au EOS data. The solid symbols are the flow values from the graphs in Fig. 1while the open symbols are for soft and hard equation of state BUU Ni + Au calculations withan equivalent impact parameter distribution. The bottom panel consists of flow values determinedfrom Ni+ Cu EOS data.11FIG. 3. Scaled flow values vs. beam energy per nucleon for different projectile-target systemsfor Plastic Ball multiplicity bins 3+4. In the EOS and Plastic Ball data all isotopes of Z=1,2 areincluded. For the Streamer Chamber all free and bound protons are included. To improve thedistinction between data points at the same beam energy, some of the beam energy values havebeen staggered around by as much as 20 MeV.12

The Energy Dependence of Flow in Ni Induced Collisions from 400 A to 1970 A MeV

The energy dependence of flow in Ni induced collisions from 400 to 1970A
  MeV

The energy dependence of flow in Ni induced collisions from 400 to 1970A MeV

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