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Results of the ASY-EOS experiment at GSI: The symmetry energy at

supra-saturation density

P. Russotto,1 S. Gannon,2 S. Kupny,3 P. Lasko,3 L. Acosta,4, 5 M. Adamczyk,3 A. Al-Ajlan,6

M. Al-Garawi,7 S. Al-Homaidhi,6 F. Amorini,4 L. Auditore,8, 9 T. Aumann,10, 11 Y. Ayyad,12 Z. Basrak,13

J. Benlliure,12 M. Boisjoli,14 K. Boretzky,11 J. Brzychczyk,3 A. Budzanowski,15, ∗ C. Caesar,10

G. Cardella,1 P. Cammarata,16 Z. Chajecki,17 M. Chartier,2 A. Chbihi,14 M. Colonna,4 M. D. Cozma,18

B. Czech,15 E. De Filippo,1 M. Di Toro,4, 19 M. Famiano,20 I. Gasparic,10,13 L. Grassi,13 C. Guazzoni,21, 22

P. Guazzoni,21, 23 M. Heil,11 L. Heilborn,16 R. Introzzi,24 T. Isobe,25 K. Kezzar,7 M. Kis,11 A. Krasznahorkay,26

N. Kurz,11 E. La Guidara,1 G. Lanzalone,4, 27 A. Le Fevre,11 Y. Leifels,11 R. C. Lemmon,28 Q. F. Li,29

I. Lombardo,30, 31 J. Lukasik,15 W. G. Lynch,17 P. Marini,14, 16, 32 Z. Matthews,2 L. May,16 T. Minniti,1

M. Mostazo,12 A. Pagano,1 E. V. Pagano,4,19 M. Papa,1 P. Paw lowski,15 S. Pirrone,1 G. Politi,1, 19 F. Porto,4, 19

W. Reviol,33 F. Riccio,21, 22 F. Rizzo,4, 19 E. Rosato,30, 31, ∗ D. Rossi,10, 11 S. Santoro,8, 9 D. G. Sarantites,33

H. Simon,11 I. Skwirczynska,15 Z. Sosin,3, ∗ L. Stuhl,26 W. Trautmann,11 A. Trifiro,8, 9 M. Trimarchi,8, 9

M. B. Tsang,17 G. Verde,1, 34 M. Veselsky,35 M. Vigilante,30, 31 Yongjia Wang,29 A. Wieloch,3 P. Wigg,2

J. Winkelbauer,17 H. H. Wolter,36 P. Wu,2 S. Yennello,16 P. Zambon,21, 22 L. Zetta,21, 23 and M. Zoric13

1INFN-Sezione di Catania, I-95123 Catania, Italy2University of Liverpool, Physics Department, Liverpool L69 7ZE, United Kingdom

3M. Smoluchowski Institute of Physics, Jagiellonian University, Pl-30-348 Krakow, Poland4INFN-Laboratori Nazionali del Sud, I-95123 Catania, Italy

5Instituto de Fısica, Universidad Nacional Autonoma de Mexico, A.P. 20-364, Mexico 01000 D.F., Mexico6KACST, Riyadh, Saudi Arabia

7Physics Department, King Saud University, Riyadh, Saudi Arabia8INFN-Gruppo Collegato di Messina, I-98166 Messina, Italy

9Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisichee Scienze della Terra, University of Messina, I-98166 Messina, Italy10Technische Universitat Darmstadt, D-64289 Darmstadt, Germany

11GSI Helmholtzzentrum fur Schwerionenforschung GmbH, D-64291 Darmstadt, Germany12Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain

13Ruder Boskovic Institute, HR-10002 Zagreb, Croatia14GANIL, CEA et IN2P3-CNRS, F-14076 Caen, France

15H. Niewodniczanski Institute of Nuclear Physics, Pl-31342 Krakow, Poland16Department of Chemistry and Cyclotron Institute, Texas A&M University, College Station, TX-77843, USA17Department of Physics and Astronomy and NSCL, Michigan State University, East Lansing, MI-48824, USA

18IFIN-HH, Reactorului 30, 077125 Magurele-Bucharest, Romania19Dipartimento di Fisica e Astronomia-Universita, I-95123 Catania, Italy

20Western Michigan University, Kalamazoo, MI-49008, USA21INFN-Sezione di Milano, I-20133 Milano, Italy

22Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, I-20133 Milano, Italy23Dipartimento di Fisica, Universita degli Studi di Milano, I-20133 Milano, Italy

24INFN and DISAT, Politecnico di Torino, I-10129 Torino, Italy25RIKEN, Wako, Saitama 351-0198, Japan

26Institute for Nuclear Research (MTA Atomki), P.O. Box 51, H-4001 Debrecen, Hungary27Universita degli Studi di Enna ”Kore”, I-94100 Enna, Italy

28STFC Daresbury Laboratory, Warrington WA4 4AD, United Kingdom29School of Science, Huzhou University, Huzhou 313000, P.R. China

30INFN-Sezione di Napoli, I-80126 Napoli, Italy31Dipartimento di Fisica ”Ettore Pancini”, Universita di Napoli Federico II, I-80126 Napoli, Italy

32CENBGn Universite de Bordeaux, CNRS/IN2P3, F-33175 Gradignan, France33Chemistry Department, Washington University, St. Louis, MO-63130, USA

34Institut de Physique Nucleaire, IN2P3-CNRS et Universite Paris-Sud, F-91406 Orsay, France35Institute of Physics, Slovak Academy of Sciences, 84511 Bratislava 45, Slovakia

36Fakultat fur Physik, Universitat Munchen, D-85748 Garching, Germany(Dated: September 3, 2018)

Directed and elliptic flows of neutrons and light charged particles were measured for the reaction197Au+197Au at 400 MeV/nucleon incident energy within the ASY-EOS experimental campaign atthe GSI laboratory. The detection system consisted of the Large Area Neutron Detector LAND,combined with parts of the CHIMERA multidetector, of the ALADIN Time-of-flight Wall, and ofthe Washington-University Microball detector. The latter three arrays were used for the event char-acterization and reaction-plane reconstruction. In addition, an array of triple telescopes, KRATTA,

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was used for complementary measurements of the isotopic composition and flows of light chargedparticles.

From the comparison of the elliptic flow ratio of neutrons with respect to charged particles withUrQMD predictions, a value γ = 0.72 ± 0.19 is obtained for the power-law coefficient describingthe density dependence of the potential part in the parametrization of the symmetry energy. Itrepresents a new and more stringent constraint for the regime of supra-saturation density andconfirms, with a considerably smaller uncertainty, the moderately soft to linear density dependencededuced from the earlier FOPI-LAND data. The densities probed are shown to reach beyond twicesaturation.

PACS numbers: 21.65.Cd, 21.65.Ef, 25.75.Ld

I. INTRODUCTION

Differences in the collective emission properties of neu-trons and protons in neutron-rich heavy-ion reactions atintermediate bombarding energies have been proposed aspotential observables for the study of the equation ofstate of asymmetric nuclear matter [1–4]. Among them,the neutron-proton elliptic flow ratio and difference havebeen shown to be sufficiently sensitive probes of the high-density behavior of the nuclear symmetry energy [5, 6].The comparison of existing data from the FOPI-LANDexperiment [7, 8] with calculations performed with theUrQMD transport model [9–11] suggested a moderatelysoft to linear symmetry term, characterized by a coef-ficient γ = 0.9 ± 0.4 for the power-law parametrizationof the density dependence of the potential part of thesymmetry energy [5]. This result has excluded super-softscenarios but suffers from the considerable statistical un-certainty of the experimental data.

The same data set was also compared to calculationsperformed with the QMD model originally developedin Tubingen [12, 13] and a constraint compatible withthe UrQMD result was obtained [6, 14, 15]. In addi-tion, a thorough study of the parameter dependence ofthe model predictions was performed in order to devisea route towards a model-independent constraint of thehigh-density symmetry energy. It showed that presentlyacceptable limits for the choice of parameters in theisoscalar part of the transport description cause uncer-tainties comparable with but not larger than those of theexperimental FOPI-LAND data [14]. It was also foundthat different parametrizations of the isovector part ofthe equation of state, the Gogny inspired (momentumdependent, Ref. [16]) and the power law (momentum in-dependent) potential, lead to very similar predictions forthe neutron-vs-charged-particle elliptic-flow ratio or dif-ference.

To improve the statistical accuracy of the experimen-tal flow parameters for the 197Au+197Au reaction and toextend the flow measurements to other systems, the sym-metric collision systems 197Au+197Au, 96Zr+96Zr, and96Ru+96Ru at 400 MeV/nucleon incident energies have

∗deceased

been chosen for the ASY-EOS experimental campaign,conducted at the GSI laboratory in May 2011 (exper-iment S394). As in the FOPI-LAND experiment, theLarge Area Neutron Detector, LAND [17], was used forthe detection and identification of neutrons and lightcharged particles. Parts of the CHIMERA multidetec-tor [18, 19], of the ALADIN Time-of-flight Wall [20],and of the Washington-University Microball detector [21]were used for the event characterization and determina-tion of the azimuthal reaction-plane orientation. By in-cluding the KRATTA telescope array [22] with isotopicidentification of charged-particles up to atomic numberZ = 4 in the setup, additional observables as, e.g., yieldsand flows of light-charged particles and yield ratios of theisobar pairs 3H/3He or 7Li/7Be were made available forthe study of isospin effects in these reactions.

The results reported here refer exclusively to the197Au+197Au reaction whose analysis has been com-pleted. It is shown that the new data confirm the moder-ately soft to linear density dependence of the symmetryenergy deduced from the earlier FOPI-LAND data. How-ever, for technical reasons, the capabilities of the LANDdetector could not be fully exploited. This had the ef-fect that the originally intended measurement of detaileddependencies of the neutron flows on rapidity, transversemomentum, and particle type could not be fully real-ized. Uncertainties of some of the required correctionsrestricted the analysis to essentially only providing theratio of neutron over charged-particle flows, integratedover the LAND acceptance. By comparing it with theresults of UrQMD calculations adapted to the experimen-tal acceptance and analysis conditions, a new and morestringent constraint for the symmetry energy at supra-saturation densities was derived.

The technical deficiencies of the LAND timing system,the methods developed to correct for them in the anal-ysis, and the consequences for the obtained results aredescribed and explained in detail in the Appendix. Theconfidence in the validity of the main, acceptance inte-grated, result is derived from the fact that it is foundto be only weakly dependent on assumptions regardingdetails of the corrections. These uncertainties were quan-titatively assessed by varying the assumptions within welldefined intervals and by treating their effects as system-atic errors. These systematic and the statistical errors ofthe collected data set are of approximately equal magni-tude.

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The present work derives its importance also from thefact that the flow probe, at present, appears to be themost robust observable for testing the nuclear equationof state at high densities. The recent comprehensivestudy of charged particle flows for 197Au+197Au colli-sions at energies from 0.4 to 1.5 GeV/nucleon reflects aremarkable consistency in its support of a soft solutionfor the equation of state of symmetric matter, includ-ing momentum-dependent forces [23, 24]. It provides anarrower constraint than previously available [25]. Suchnarrower limits for the compressibility of symmetric nu-clear matter are very useful also with regard to the equa-tion of state of asymmetric matter. They have the effectof reducing systematic uncertainties originating from thechoice of parameters for the isoscalar sector of a transportdescription [14].

Major efforts have recently been made to reduce theapparent systematic discrepancies in the interpretationof the FOPI pion ratios [26] with increasingly complextransport calculations [27–32]. Of particular interest isthe observation that the predicted π−/π+ yield ratiosare expected to rise when the medium modifications ofpion production thresholds are explicitly considered [28].This effect may permit reproducing the experimental val-ues with choices for the symmetry energy that are lessextreme than those required in some of the earlier pionstudies [33–35]. On the other hand, the calculations ofHong and Danielewicz [27] exhibit only a small sensitiv-ity of integrated pion ratios to the stiffness of the sym-metry energy, pointing to the need for energy-differentialobservables. Further work will thus be required beforepion yields and yield ratios can be reliably applied to theinvestigation of the high-density symmetry energy.

The important role played by the nuclear symmetryenergy in nuclear structure and reactions as well as inastrophysics is the subject of several review articles [36–40]. A brief introductory review of the situation at supra-saturation densities is available in Ref. [41]. A compre-hensive list of pertinent articles has recently appeared inthe Topical Issue on Nuclear Symmetry Energy [42].

II. EXPERIMENTAL DETAILS

A. Setup for S394

A schematic view of the experimental setup of theASY-EOS experiment at the GSI laboratory is shownin Fig. 1. The beam was guided in vacuum to about2 m upstream from the target. A thin plastic scintil-lator foil viewed by two photo-multipliers was used torecord the projectile arrival times and to serve as a startdetector for the time-of-flight measurement. The LargeArea Neutron Detector, LAND [17], was positioned tocover laboratory angles around 45◦ with respect to thebeam direction. A veto wall of plastic scintillators infront of LAND allowed discriminating between neutronsand charged particles. In this configuration, it was possi-

FIG. 1: (Color online) Schematic view of the experimentalsetup of the ASY-EOS experiment S394 at GSI. The chosencoordinate system is indicated, the y direction points upwardsin the laboratory. The target area with the Microball is notto scale in the main drawing but shown with a scale factorof approximately 5:1 in the lower left corner (see Sec. II B forcoverage and dimensions).

ble to measure the directed and elliptic flows of neutronsand charged particles near mid-rapidity within the sameangular acceptance. Opposite of LAND, covering a com-parable range of polar angles, the Krakow Triple Tele-scope Array, KRATTA [22], had been installed to permitflow measurements of identified charged particles underthe same experimental conditions. Results obtained withKRATTA will be published separately.

For the event characterization and for measuring theorientation of the reaction plane, three detection sys-tems had been installed. The ALADIN Time-of-Flight(AToF) Wall [20] was used to detect charged particlesand fragments in forward direction at polar angles upto θlab ≤ 7◦. Its capability of identifying large frag-ments and of characterizing events with a measurementof Zbound [20] permitted the sorting of events according toimpact parameter. Four double rings of the CHIMERAmultidetector [18, 19] carrying together 352 CsI(Tl) scin-tillators in forward direction and four rings with 50 thinCsI(Tl) elements of the Washington University Microballarray [21] surrounding the target provided sufficient cov-erage and granularity for determining the orientation ofthe reaction plane from the measured azimuthal particledistributions.

The kinematic coverage achieved with this assemblyof detection systems is illustrated in Figs. 2 and 3. InFig. 3, in particular, the enhanced particle yields in thekinematic regimes of participant and spectator emissionsare clearly visible. The product yields from the decayof the projectile spectator seen with CHIMERA and the

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FIG. 2: (Color online) Kinematic acceptance in thetransverse-velocity vs rapidity plane of the detector systemsused in the S394 experiment. The contour lines refer to thespecified values of the kinetic energy of protons in the labo-ratory, ranging from 10 MeV to 1 GeV. The indicated lowerand upper limits in energy are for protons (stopped protonsfor KRATTA and CHIMERA) and were calculated for thespecific detector thresholds and configurations. An averagevalue was chosen for the four types of detector elements ofthe Microball (labeled µBall in the figure).

AToF Wall do not exactly match because the AToF effi-ciency for hydrogen isotopes in this energy range is lowerthan that of the CHIMERA modules.

B. Detection systems

1. LAND detector

The Large Area Neutron Detector (LAND, Ref. [17]),upgraded with new TACQUILA GSI-ASIC electron-ics [43], was positioned at a distance of 5 m from thetarget. Its kinematic acceptance was similar to that ofthe forward LAND subdetector used in the FOPI/LANDexperiment [5] but slightly larger in rapidity for giventransverse momentum due to the shorter distance fromthe target. LAND consists of 10 consecutive layers of 2 x2 m2 area, together adding up to the 1-m depth of the de-tector. Each layer is formed by 20 modules of 2-m lengthwhose orientations alternate from layer to layer betweenvertical and horizontal. The modules have a 10 x 10 cm2

cross section and are built from 9 sheets of iron and 10sheets of plastic-scintillator material, all 5-mm thick, ar-ranged in alternating order and oriented parallel to theentrance plane of the detector. Two iron sheets of 2.5-mm thickness form the entrance and exit layers of eachmodule. In this design, the iron serves as a converterand the plastic scintillators as detectors for the producedionizing radiation.

As it turned out during the analysis, the standardmethod of identifying the showers generated by interact-ing neutrons in the full LAND assembly was not feasiblebecause of the timing difficulties related to the use of thenew electronic system (discussed in Sec. III A below and

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FIG. 3: (Color online) Measured invariant hit distribution for197Au+197Au collisions at 400 MeV/nucleon incident energyin the transverse-velocity vs rapidity plane for charged parti-cles detected with the three systems Microball, CHIMERA,and AToF Wall with full azimuthal coverage and for neutronsdetected with LAND. The velocities of particles detected withthe Microball are not measured and shown here with an arbi-trarily chosen homogeneous kinetic-energy distribution in theinterval 0 ≤ Ekin ≤ 100MeV . The apparent angular variationmay be influenced by ring-dependent thresholds. The arrowsindicate the rapidities of the projectile yp = 0.896 and of thec.m. system.

in the Appendix). Only 19 modules (out of 20) of the firstlayer of LAND are included in the present analysis. Thislowers the detection efficiency for neutrons and modifiesits energy dependence, effects that had to be taken intoaccount. The resulting range of polar angles that werecovered by this part of LAND was 37.7◦ ≤ θlab ≤ 56.5◦

with respect to the beam direction.A veto wall consisting of 10-cm wide and 5-mm thick

plastic-scintillator slabs covered the front face of LAND,permitting the distinction between neutral and chargedparticles. The slabs were mounted in vertical orienta-tion parallel to the modules of the first plane of LAND.Charged particles were identified on the basis of coinci-dent hits in the veto wall, matching the time and positionof the corresponding hit in LAND. However, due to in-sufficient resolution achieved in the readout of the analogsignals, the identification of the atomic number Z of therecorded charged particles on the basis of their energyloss in the veto-wall scintillators was not feasible. Thecomparative analysis was thus restricted to the collec-tive flows of neutrons with respect to that observed forall charged particles detected within the acceptance ofLAND.

2. KRATTA hodoscope

The Krakow Triple Telescope Array, KRATTA [22],was specifically designed for the experiment to measure

5

the energy, emission angles, and isotopic compositionof light charged reaction products. The 35 modules ofKRATTA were arranged in a 7x5 array and placed op-posite to LAND at a distance of 40 cm from the target.They covered 160 msr of solid angle at polar angles be-tween 24◦ and 68◦. The modules of KRATTA consistedof two, optically decoupled, CsI(Tl) crystals (thickness of2.5 cm and 12.5 cm) and three large-area, 500-µm thick,PIN photodiodes. The middle photodiode and the shortCsI(Tl) crystal read out by the diode from its front facewere operated as a single-chip telescope [44]. Very goodisotopic resolution has been obtained in the whole dy-namic range up to Z ∼ 4. The methods used for derivingit and the virtue of using digital pulse-shape recordingthroughout are described in Ref. [22].

3. CHIMERA hodoscope

Four double rings of the CHIMERA multidetector [18,19] had been transported to the GSI laboratory and in-stalled at their nominal distances from the target, cov-ering polar angles between 7◦ and 20◦. They carriedtogether 352 CsI(Tl) scintillators, 12 cm in thickness andread out with photodiodes. Each of the 8 individual ringsprovided a 2π azimuthal coverage with either 40 or 48modules per ring. For calibration purposes, 4 of the Sidetectors of the regular CHIMERA setup were installedin each ring. For these telescopes, an independent digitalpulse-shape acquisition system was used to investigateand improve the particle identification and calibrationmethods [45]. The recorded telescope data proved veryuseful for verifying the analysis schemes developed forthis experiment.

The CHIMERA rings were intended for the detectionand identification of light charged particles, primarily ex-pected to come from the mid-rapidity regime. In theanalysis, a rapidity gate y > 0.1 in the center-of-mass(c.m.) reference system was applied to exclusively selectforward-hemisphere emissions for determining the orien-tation of the reaction plane.

For the use of CHIMERA modules at the present en-ergy regime, the identification of punch-through particleswas essential. In addition, the velocity of registered par-ticles had to be reconstructed with an accuracy permit-ting the application of the rapidity gate. For particlesstopped in the CsI, this was done using the mass numberA and the deposited energy of the particles resolved inthe fast-vs-slow identification map.

For particles punching through the CsI, their atomicnumber, essentially Z = 1 or 2, was evident in the fast-vs-slow identification plots. A most probable mass numberA was assigned on the basis of the measured energy loss∆E and used to reconstruct the total kinetic energy andmomentum. The mass A = 4 was assigned to helium iso-topes. In the case of the hydrogen isotopes, A = 3 wasassigned to a Z = 1 particle if ∆Ep.t.

d < ∆E < ∆Ep.t.t ,

A = 2 was assigned if ∆Ep.t.p < ∆E < ∆Ep.t.

d , and A = 1

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FIG. 4: (Color online) Identification plot of CsI(Tl) signalsrecorded with a CHIMERA module of ring 7 (θlab ≈ 17◦)from 197Au+197Au collisions at 400 MeV/nucleon displayingthe ratio of fast-over-slow vs the slow signal components. Theloci of hydrogen and helium ions punching through the fulllength of the detector are labeled as Hpt and Hept. An ex-panded view of the area within the rectangular box is shownin the inset. Besides the punch-through groups, also the lociof mass-identified light ions are indicated there.

was assigned if ∆E < ∆Ep.t.p . Here ∆Ep.t.

x refers to thecalculated maximum energy loss ∆E deposited in theCsI(Tl) module by punch-through particles, and the sub-script x = p, d, t indicates protons, deuterons and tritons,respectively. The reconstructed total kinetic energy wasthen used to determine the velocity of the particle. Anexample of the two-dimensional maps used for the parti-cle identification and analysis is shown in Fig. 4.

4. ALADIN ToF Wall

A central square part of the ALADIN Time-of-Flight(AToF) Wall [20] with an area of approximately 1 m2 wasplaced symmetrically with respect to the beam directionat a distance of 3.7 m downstream from the target. Itwas used to detect forward emitted charged particles andfragments at polar angles smaller than 7◦, i.e. within theopening of the forward-most CHIMERA ring. The twolayers of the AToF Wall (front and rear) each consistedof 48 modules of 2.5 x 110 cm2 plastic scintillators witha thickness of 1 cm and with photo-multipliers (PMs)mounted at their upper and lower end faces. The modulesare arranged in densely packed groups of eight modules,six groups per layer, and all oriented in vertical direction.

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FIG. 5: (Color online) AToF identification plots of calibratedtime of flight vs recorded energy loss ∆E for two slats ap-proximately 30 cm and 35 cm to the right of the beam di-rection (θlab ≈ 4.7◦ and ≈ 5.4◦, respectively, at their centralparts). The groups of light elements are clearly recognized upto atomic number Z ≈ 10 as shown in the inset.

They provided the atomic numbers Z of the detectedfragments and light charged particles, as well as theirvelocities and directions of emission. The threshold wasset below the maximum of the Z = 1 distribution in thespectrum of recorded energy-loss signals. A central holeof 7.5 x 7.5 cm2 permitted the non-interacting beam topass undetected through the AToF Wall.

The atomic number Z of light fragments is individuallyresolved on the basis of the measured time and energyloss up to approximately Z = 10, as illustrated in Fig. 5.The unusually high background appearing in these mapsis attributed to interactions of the ions with air duringtheir flight path to the detector. Heavier fragments areidentified with a resolution of ∆Z ≈ 2 (FWHM) on thebasis of the Z calibrations generated in earlier exper-iments with the AToF Wall [20, 46]. The time-of-flightresolution varies with Z, smoothly decreasing from 300 ps(standard deviation) for lithium fragments to about 100ps for fragments with Z > 10. The AToF timing signalswere used to generate a reaction trigger. The minimumrequirement was 3 recorded tracks in the front-wall and3 recorded tracks in the rear-wall modules. The front-and rear-wall tracks are usually pairwise correlated andproduced by the same particles. The central group ofeight modules containing the central opening was not in-cluded in the trigger circuit. These trigger requirementshad the effect of suppressing collisions producing mod-erate excitations. However, the forward position of thewall and the long passage of the beam through air hadthe effect of still producing unwanted trigger signals gen-

erated by reactions on non-target material. The methodschosen to efficiently eliminate such events in the analysisare explained below.

5. Microball

The target was surrounded by an array of fifty 3.6-mm to 5.6-mm thick CsI(Tl) elements of the WashingtonUniversity Microball (so-called Reaction Microball [21]).This array had 4 azimuthally symmetric rings, subtendedthe range of polar angles between 60◦ and 147◦ in thelaboratory and, thus, was essentially sensitive to back-ward emissions in the c.m. frame of the reaction. Theazimuthal distributions of modules recording a hit abovethreshold provided a measure of the orientation of thereaction plane as seen in the rear hemisphere. The smalldiameter of the array of only about 10 cm offered a nearlynegligible solid-angle for reactions occurring downstreamfrom the target, a property that was used for suppressingbackground reactions in the analysis.

C. Beams and targets

With beam intensities of about 105 pps and targets of1-2% interaction probability, about 5·106 events were col-lected for each of the systems 197Au+197Au, 96Zr+96Zr,and 96Ru+96Ru. Additional runs were performed with-out a target to measure the background from the inter-action of projectile ions with non-target material. The3.7 m column of air between the target and the AToFWall represents by itself an additional target with a the-oretical interaction probability of about 6% for 197Auprojectiles.

Measurements with iron shadow bars in front ofLAND, with and without a target, were used to deter-mine the background of scattered neutrons not directlyoriginating from the target. The shadow bars consisted ofseveral pieces of iron, together representing a block of 60cm in thickness and shaped to precisely cover the solid-angle acceptance of the LAND detector as seen from thetarget position. Results obtained with the 96Zr and 96Rubeams and targets will not be presented here.

III. DATA ANALYSIS

The analysis of the experimental data has been per-formed within the FairRoot software framework primar-ily developed for the use with the future FAIR detec-tors [47]. The FairRoot framework contains a completesimulation of the ASY-EOS detector setup and geome-try and of the data analysis schemes. Theoretical calcu-lations can be performed within the same software en-vironment and filtered in order to adapt them to theexperimental acceptance and analysis conditions.

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FIG. 6: (Color online) Experimental correlation of the maxi-mum atomic number, Zmax, of the fragments within an eventand the quantity Zbound as deduced from the fragments de-tected with the AToF Wall. The dots represent the meanvalues of Zmax over the intervals of Zbound indicated by thehorizontal error bars.

A. LAND timing

A major difficulty arose from the fact that the newTACQUILA GSI-ASIC electronics [43] of the LAND de-tector did not permit the recognition of the very low-energy γ-ray signals in the LAND modules. The abso-lute time calibration, therefore, had to be obtained froma spectra comparison with data of the FOPI-LAND ex-periment. Furthermore, the digital timing informationwas found to be frequently, with approximately 30% -40% probability, affected by ±25 ns time jumps, arisingfrom errors in counting the number of 25-ns clock cyclesoccurring between the start and stop signals in a timemeasurement. These uncertainties were identified andcorrected with procedures that are described in detail inthe Appendix. Where possible, recourse was taken bycomparing with or adjusting to existing data from previ-ous FOPI and FOPI-LAND experiments.

The goal pursued in the present analysis consistedin applying the evident corrections and in quantifyingthe uncertainties associated with correction steps thatcould not be unambiguously determined. For the time-resolved differential data, the main uncertainty arisesfrom the so-called second correction step, devised forwrongly recorded hits not recognized in the first correc-tion step (see Appendix). In addition to recovering thecorrect times of the intended class of hits, it has the sideeffect of misplacing an unknown number of valid hits inthe time spectra. This causes a mixing of the flow proper-ties within the affected time intervals. The problem wasinvestigated by applying the second correction to ran-domly chosen fractions of the selected group of candidatehits and by comparing the consequences with data sets

1

10

210

CHIMERA multiplicity0 5 10 15 20 25 30 35 40 45

boun

dA

TO

F Z

0

10

20

30

40

50

60

70

80

CHIMERA multiplicity0 5 10 15 20 25 30 35 40 45

boun

dA

TO

F Z

0

10

20

30

40

50

60

70

80

FIG. 7: (Color online) Experimental correlation of the quan-tity Zbound as deduced from the fragments detected with theAToF Wall with the charged-particle multiplicity measuredwith CHIMERA. Events within the hatched area were ex-cluded from the analysis; the high-intensity group near mul-tiplicity 27 with Zbound ≈ 0 is caused by central collisions;the symbols represent the mean Zbound of the remaining dis-tribution as a function of the CHIMERA multiplicity.

obtained in FOPI measurements [48]. It will be shownthat the mixing affects the deduced flow parameters but,to a much smaller extent, the flow ratios. Its contribu-tion to the systematic error of the power-law exponent γamounts to ∆γ = ±0.05.

This particular correction and the mixing that it causesplay only a minor role for the acceptance-integrated re-sults obtained after integrating over the full time spec-tra. Timing errors have no consequence here as long asthey do not lead beyond the limits of the integration in-terval. A remaining source of uncertainty is the precisechoice of the low-energy thresholds as it should matchtheir counterparts in the calculations. For charged par-ticles, the threshold energy is given by the requirementto pass through the veto wall and to reach the first scin-tillator plane of LAND, for protons about 60 MeV. Itis thus independent of the time measurement, providedthe hit is within the accepted time interval. For neu-trons, the low-energy threshold is defined by the chosenintegration limit at long times-of-flight. Timing errorsare effective here. To minimize the overall uncertainty,the integration limit was placed at times-of-flight muchlonger than expected for charged particles and into a low-intensity region less affected by the timing corrections(see Appendix). Its nominal value corresponded to 30MeV kinetic energy for nucleons. The level of remaininguncertainties was determined by varying the integrationlimit within a wide interval and by comparing with calcu-lations performed with corresponding energy thresholdsfor neutrons. As observed in the differential case, theflow ratios are only mildly affected because uncertaintiescancel. The observed variation of ∆γ = ±0.07 repre-

8

sents the overall systematic error arising from the LANDtiming properties.

B. Impact parameter determination

For selecting according to impact parameter, globalvariables were constructed from the CHIMERA andAToF data. They included

Zbound =N∑

i=1

Zi with Zi ≥ 2 (1)

and the ratio of transverse to longitudinal charge,

ZRAT = 10 · Ztrans/Zlong (2)

with an arbitrarily chosen scale factor 10 and with

Ztrans =

N∑

i=1

Zisin2(θi), Zlong =

N∑

i=1

Zicos2(θi) (3)

where θi is the polar angle of the ith particle in the labo-ratory reference system. Zbound is close to the charge ofthe primary spectator system and monotonically corre-lated with the impact parameter, while ZRAT increaseswith the centrality of the reaction. The choice of thesevariables as impact parameter selectors has been guidedby performing UrQMD calculations for given impact pa-rameter ranges and filtering the simulated reaction eventsfor angular acceptance, detection thresholds, and resolu-tion of the detectors.

For constructing Zbound, fragments recorded withCHIMERA and the AToF Wall were used where not oth-erwise indicated. Larger fragments (Z > 4) are exclu-sively expected at very forward angles, well within thekinematic acceptance of θlab ≤ 7◦ of the AToF Wall (cf.Figs. 4, 5). The evolution of the largest atomic num-ber, Zmax, observed in an event as a function of Zbound,here from AToF alone, is shown in Fig. 6. The relativebehavior of these two observables resembles closely thatknown from earlier results reported by the ALADIN Col-laboration for the 197Au+197Au reaction [20, 49]. Onlyfor large Zbound is a difference observed, as 〈Zmax〉 doesnot reach up as close to the projectile Z as it did in theALADIN experiments with different trigger conditions.The trigger chosen for the present experiment suppressedthe most peripheral events with a small multiplicity ofcharged particles and a corresponding Zmax near Z = 79.

The expected anti-correlation of Zbound as determinedfrom AToF alone, rising with impact parameter b andthe multiplicity of charged particles measured with theCHIMERA rings at intermediate angles is observed aswell (Fig. 7). The group of events with both, smallZbound and small multiplicities detected with CHIMERA(hatched area in the figure) is interpreted as containingnearly undeflected heavy projectile fragments that havepassed undetected through the central hole of the AToF

0.2 0.4 0.6 0.8 10

20

40

60

80

BO

UN

DZ

ZRAT

Au+Au (exp)UrQMD

(a)0.2 0.4 0.6 0.8 1

0

20

40

60

80

Au+EF (exp)

ZRAT

BO

UN

DZ

(b) 10

20

30

40

50

60

0 5 100

500

1000

/db

(arb

. uni

ts)

σd

b (fm)

Au+Au (UrQMD)

BOUNDZ

ZRAT

(c)0.2 0.4 0.6 0.8 1

0

20

40

60

80Au+Au (UrQMD)

ZRAT

BO

UN

DZ

(d)0

5

10

15

20

25

30

35

FIG. 8: (Color online) Top row: Inclusive Zbound vs ZRATcorrelation for data sets taken with (a) and without (b) a tar-get foil in place (EF stands for Empty Frame). Bottom row:UrQMD calculations for the correlation of Zbound vs ZRATfor 197Au+197Au collisions at 400 MeV/nucleon and impactparameter b < 10.0 fm, filtered to match the experimentalconditions (d), and for impact-parameter distributions dσ/dbobtained under various conditions (c). The unbiased distri-bution for the full reaction for b < 10.0 fm is given by theblack (solid) histogram while the blue, green, and red linesshow impact parameter distributions obtained when selectingvery central, semi-central, and peripheral event classes, re-spectively, by gating either on Zbound (dashed) or on ZRAT(dotted, see Table I). The dashed horizontal lines in panel (a)represent the corresponding gates for the Zbound selection.The line of Zbound centroids as a function of ZRAT of theUrQMD distribution of panel (d) is drawn into the experi-mental distribution (panel (a)).

Wall. Such events are expected from very peripheral197Au+197Au collisions as well as from the interactionof the beam with N or O nuclei of the air downstream ofthe target. The class of events within the hatched regionwas not further considered in the analysis.

The correlation of Zbound with ZRAT , as obtainedfrom the combined CHIMERA and AToF data for197Au+197Au collisions at 400 MeV/nucleon, are pre-sented in Fig. 8 (a). The two impact-parameter sensi-tive quantities are globally anti-correlated as expected:Zbound grows while ZRAT drops with increasing impactparameter. For orientation, ZRAT = 0.15 is obtained forparticles detected at the forward limit of the CHIMERAacceptance θlab = 7◦, ZRAT = 1.3 for particles detectedat the largest angle θlab = 20◦, and ZRAT ≈ 0.7 fora homogeneous distribution within the CHIMERA ac-ceptance. The observed distribution is compatible withthese limits. Values smaller than ZRAT = 0.15 are sup-pressed by the trigger condition of four or more charged

9

particles detected with CHIMERA and two or more hitsrecorded by the Microball by which peripheral collisionsare suppressed. In addition, the adopted condition re-quiring an anti-correlation of the preferential azimuthaldirections of these particles observed with CHIMERAand with the Microball was applied (see Sec. III D). Avery similar pattern is observed for the result of UrQMDcalculations, performed for the range of impact parame-ters b < 10.0 fm (Fig. 8 (d)). The centroid line deducedfrom the simulations follows the experimental distribu-tion shown in panel (a) rather well.

The correlation observed when the target foil is re-moved is shown in panel (b) of Fig. 8. The yields arenormalized with respect to the integrated beam intensity,so that the much lower intensity of background reactionsbecomes evident. They display a similar anti-correlation,however much less pronounced and extending mainlyover the range typical for the more peripheral collisionsin the 197Au+197Au case. The observed concentration ofbackground events at large Zbound > 40 also coincideswith the expectation for collisions of 197Au beam parti-cles with predominantly 14N encountered downstream ofthe target location [50]. The initially high yield of AToFtrigger signals from 197Au+air collisions is reduced tothe apparent low level by applying the conditions on themultiplicity and azimuthal orientation of Microball hitswithin the event.

class, b interval Zbound ZRATmin max < b > min max < b >

very central, < 3.0 fm 0 18 2.56 0.615 2.0 2.51semi-c, 3.0 − 7.5 fm 18 45 6.18 0.245 0.615 5.71peripheral, > 7.5 fm 45 8.74 0.245 8.76central, < 7.5 fm 0 45 5.69 0.245 2.0 5.27FOPI, 3.35 − 6.0 fm 19 33 5.00 0.365 0.585 4.69

TABLE I: Selection gates used to define the indicated fiveclasses of centrality. Their names and the nominal rangesof impact parameter b are given in the first column (semi-cstands for semi-central). The gate required for the compari-son with FOPI data (Sec. IV A) is given in the bottom row.The following columns list the minimum and maximum val-ues of the gating intervals used and the corresponding meanvalues of the impact parameter b as given by the UrQMD cal-culations for the two sorting variables Zbound (columns 2-4)and ZRAT (columns 5-7). No upper gate of Zbound and nolower gate of ZRAT was applied when selecting peripheralevents.

For the actual impact-parameter selections within therange of interest b < 7.5 fm, the global observables Zbound

and ZRAT were used. The intervals chosen to selectvery central, semi-central and peripheral event classesare listed in Table I together with the mean impactparameters expected for these classes according to theUrQMD calculations. The condition on multiplicity spec-ified above provided no additional restriction within thisrange of central and semi-central collisions (cf. Fig. 8(a)). The quality of the resolution that can be expected,according to the UrQMD model, is illustrated in panel

(c) of Fig. 8. The examples of very central, semi-centraland peripheral selections with nominal impact-parameterintervals of b < 3 fm, 3 < b < 7.5 fm, and b > 7.5 fm,respectively, are displayed. The expected smoothing ofthe boundaries of the actually selected intervals is aboutequal for the Zbound and ZRAT observables. The inter-val chosen for generating the acceptance-integrated flowratio in the final analysis is a nominal b < 7.5 fm, listedas central class in the table. As the calculations show,the actual distribution can be expected to contain nearlyall events with b < 6 fm and, with decreasing probabil-ity, a selection of events with impact parameters up tob ≈ 10 fm.

C. Reaction plane orientation

For the experimental estimates of the azimuthal orien-tation of the impact-parameter vector, both CHIMERAand AToF data were used. In the CHIMERA analysis, aQ-vector [51] was calculated as

~QCHI =

N∑

i=1

Zi~βt,iγi, (4)

with the transverse-velocity vectors ~βt,i and with N ≥ 4,i.e. by requiring at least four identified particles recordedby CHIMERA. An important factor in the Q-vector def-inition is the weight factor ω = +1(−1) for emissionsin the forward (backward) hemisphere in the c.m. sys-tem. It is omitted here because emissions in the forwardhemisphere are exclusively selected with the condition

on rapidity yc.m. > 0.1. The vector ~QCHI represents aZ- and transverse-velocity-weighted, i.e. approximatelytransverse-momentum-weighted, direction in the planeperpendicular to the beam direction.

In the AToF analysis, a second vector ~QAToF has beendetermined from the recorded positions of the interac-tion of detected fragments with the Time-of-Flight Wall.The horizontal coordinates were determined with the un-certainty given by the slat widths of 2.5 cm. It reducesto 1.25 cm if the fragment was identified in both layersas observed in most cases. The vertical coordinate wasdetermined from the measured difference of the top andbottom time signals, and a resolution of typically about±2 cm was obtained. The distance to the beam axis,under the assumption of approximately beam velocity,is proportional to the transverse velocity of the detectedparticle or fragment. The resulting azimuthal vector wasweighted with the atomic number Z of the fragment and~QAToF was obtained by summing over all individual vec-tors within an event. Also here, the weight factor ω canbe omitted as the AToF acceptance of θlab ≤ 7◦ stronglyfavors projectile fragments. A time-of-flight gate select-ing forward emissions in the c.m. frame was used in ad-dition.

The resolution obtained with these two quantities isoverall comparable but depends somewhat on the impact

10

180− 90− 0 90 180180−

90−

0

90

180(a)

(de

g)C

HI

φ

0

1

2

3

4

5

6

7

8

180− 90− 0 90 180180−

90−

0

90

180

(b)

(de

g)C

HI

φ

0

0.5

1

1.5

2

2.5

3

3.5

180− 90− 0 90 180

50

100

150

200

(deg)AToF

φ - CHI

φ

Au+Au(c)

Au+EF

Yie

ld

FIG. 9: (Color online) Bi-dimensional representations of thedifference of the azimuthal reaction-plane orientations indi-vidually obtained from CHIMERA and the AToF Wall, underthe condition that the CHIMERA and Microball orientationsare within the adopted anti-correlation gate, and shown formeasurements with (a) and without (b) a gold foil in the tar-get frame. Panel (c) shows yield curves for these two cases,Au+Au and Au+EF (EF stands for empty frame), normal-ized with respect to the integrated beam intensity.

parameter. Peripheral collisions associated with smallmultiplicities in the CHIMERA part of the recordedevent may be more easily characterized with the heavyfragments seen in AToF while more central collisionsleading to high CHIMERA multiplicities may produceonly few light fragments within the acceptance of theAToF Wall. As it turned out, in the impact parame-ter range of interest, central with b ≤ 7.5 fm, only about10% of the events permitted the calculation of a Q-vectorfrom AToF hits alone. Because the AToF geometry is notazimuthally symmetric, the resulting inclusive Q-vectordistributions are not fully isotropic.

With the Microball data, the reaction-plane orienta-tion was estimated by summing over the azimuthal di-

rections of the recorded hits. A vector ~QµBall has beencalculated as

~QµBall =

N∑

i=1

rit, (5)

-180 -90 0 90 1800

500

(a)

1000

1500

2000peripheral

-180 -90 0 90 1800

(b)

1000

2000

semi-central

-180 -90 0 90 1800

(c)

50

100

150very-central

0 45 90 135 1800

(d)

1000

2000

3000

0.97≈ χ

0 45 90 135 1800

(e)

2000

4000

6000

1.58≈ χ

0 45 90 135 1800

(f)50

100

150

200 1.25≈ χ

(deg)RP

φ (deg)RP

φ (deg)RP

φ

(deg)RP

φ∆ (deg)RP

φ∆ (deg)RP

φ∆

Cou

nts

Cou

nts

FIG. 10: Top row: Inclusive distributions of the angle ΦRP

representing the reaction-plane orientation obtained with theQ-vector method from the combined CHIMERA and AToFdata for peripheral (panel (a)), semi-central (b), and verycentral (c) impact-parameter intervals (see Table I for theirdefinitions).Bottom row: Distributions of the difference of orientations ofthe sub-event reaction planes for the same three event classes,peripheral (d), semi-central (e), and very central (f), obtainedwith the mixing technique of Refs. [53, 54] and by using theweight Zβtγ (see text and Table II). The corresponding valuesof the reaction plane dispersion parameter χ are indicated.

where rit is the azimuthal unit vector in the direction ofthe location of the detector module that recorded the ith

hit. A minimum multiplicity of N ≥ 2 was imposed. Inthis case, the weight factor ω has been omitted becausethe rapidity of the detected particles was not determinedeven though the Microball acceptance of θlab ≥ 60◦ canbe expected to select mainly backward emissions. As

shown below, the orientation of ~QµBall was indeed foundto be opposite to those of the CHIMERA and AToF Q-vectors.

The three Q-vectors are strongly correlated. The de-gree of coincidence of the azimuthal orientations of the

vectors ~QCHI and ~QAToF for the class of events contain-

ing a valid ~QAToF is shown in Fig. 9. The individualreaction-plane orientations obtained from the CHIMERAand AToF Wall data are evidently very similar. With thetarget foil removed (panel (b)), the coincidence of ori-entations is no longer present; the correlation pattern isdominated by the slightly reduced acceptance of AToF inthe region near 0◦. The resulting distributions of the dif-ference ΦCHI−ΦAToF is shown in the bottom panel. Theazimuthal angle Φ that is used here and in Figs. 10, 11is defined in accordance with the chosen coordinate sys-tem (Fig. 1), with Φ = 0◦ coinciding with the x andΦ = 90◦ with the y direction. The applied condition re-quiring that the CHIMERA and Microball orientationsare within the adopted anti-correlation gate of ±90◦ sup-presses unwanted background, as discussed in Sec. III Din more detail.

The inclusive reaction-plane distributions, as given

11

by the combined Q-vectors obtained by summing overrecorded hits in CHIMERA and AToF for three choicesof impact-parameter windows, are shown in the top rowof Fig. 10. The observed flatness indicates that the par-ticle angular distributions have not been biased by vari-ations of the detector efficiencies, by properties of theevent triggering or by other azimuthal asymmetries inthe experiment.

Several different methods of estimating the reaction-plane orientation were applied to the data in order toidentify possible systematic uncertainties related to it.They are all based on the Q-vector method of Ref. [51]but differ in the kinematic quantities used as weights forsumming over the included particles and fragments. Be-sides the product Zβtγ (cf. Eq. 4), equal weights for allparticles and the atomic number Z alone of each particlewere also used as weights for summing over the azimuthaldirections of the recorded hits either in both CHIMERAand AToF or in CHIMERA alone. It was, in addition, in-vestigated to what extent the result varies with the valueof the rapidity gate chosen for selecting the forward hemi-sphere in the c.m. reference frame.

detectors and chosen weight yc.m. > 0.1 yc.m. > 0.2CHIMERA alone, equal weight 1.39 1.30

CHIMERA+AToF, equal weight 1.45 1.37CHIMERA alone, Z 1.51 1.42

CHIMERA+AToF, Z 1.58 1.50CHIMERA alone, Zβtγ 1.52 1.42

CHIMERA+AToF, Zβtγ 1.59 1.49

TABLE II: Resolution parameter χ obtained for the estima-tion of the reaction-plane orientation with different choicesfor the Q-vector construction for the case of semi-central197Au+197Au collisions. The first column indicates the con-sidered detector systems and weights, the second and thirdcolumns show χ for two values of the rapidity gate chosen forCHIMERA hits.

The criterion chosen for this investigation was theachieved resolution of the reaction-plane orientation. Itdetermines the necessary corrections and the uncertaintyassociated with the obtained flow parameters [52]. Itwas evaluated with the sub-event mixing technique asdescribed in Refs. [53, 54] and quantified through theresolution parameter χ. This parameter is inversely pro-portional to the width of the difference distribution ofsub-event orientations, assumed to be Gaussian in thepresent case (cf. Ref. [52]). Examples of difference dis-tributions obtained for selected intervals of impact pa-rameter are given in the bottom row of Fig. 10, includingthe corresponding results for χ. The resolution param-eters obtained with the studied choices of weights anddetector systems are listed in Table II for the class ofsemi-central events. The best resolution, indicated by thelargest value for χ, has been achieved using the productZβtγ as the weight and by summing over the recordedhits with yc.m. > 0.1 in both CHIMERA and AToF. Allthe results shown in the following sections were obtainedwith this choice. It is interesting to note, however, that

180− 90− 0 90 180180−

90−

0

90

180

(de

g)B

all

µφ

(deg)CHI

φ

Au+Au

(a)180− 90− 0 90 180180−

90−

0

90

180

(deg)CHI

φ

Au+EF

(b)50

100

150

200

250

300

350

0 45 90 135 1800

5

10

15

(deg)Ballµ

φ - CHI

φ

Au+AuAu+EF

(c)

Yie

ld/B

P (

arb.

uni

ts)

0 5 10 15 20

10

210

310

410

510

LAND multiplicity

(d)

>90 degBallµ

φ- CHI

φ

FIG. 11: (Color online) Top row: Correlation between theQ-vector orientations determined with CHIMERA (abscissa)and with the Microball (ordinate) for data sets taken with(panel (a)) and without (panel (b)) a target foil in place (EFstands for Empty Frame).Bottom row: Difference of the Q-vector orientations forAu+Au and for Au+EF data (panel (c)), normalized withrespect to the integrated beam intensity (BP stands for beamparticles), and the raw hit multiplicities (panel (d)) regis-tered with LAND for Au+Au (solid line) and for Au+EFdata sets (dotted). The hatched area in panel (c) indicates therange of events rejected by the required anti-correlation of theCHIMERA and Microball Q-vector orientations (Sec. III D).

other choices for the weighting factors lead to very com-parable results (Table II).

The correction factors resulting from the so determineddispersion of the reconstructed reaction plane were ob-tained according to Ref. [53, 54]. Resolution parame-ters χ in the range of 1.2 to 1.6 (Fig. 10) correspondto attenuation factors 〈cos(n∆φ)〉 of approximately 0.8to 0.9 for n = 1, i.e. for the case of directed flow, andto ≈ 0.5 to 0.65 for the elliptic flow (n = 2). Theirinverse values represent the correction factors to be ap-plied to the Fourier coefficients describing the measuredazimuthal anisotropies. The validity of the method usedfor determining the reaction-plane orientation and its ex-perimental dispersion were confirmed by a comparison ofcollective flows obtained from the KRATTA and fromFOPI data [48] for the same reaction. Excellent agree-ment is obtained for directed and elliptic flows of hydro-gen and helium isotopes within the common acceptanceof the two experiments [55].

12

D. Background corrections

For rejecting background reactions due to the interac-tion of Au projectiles with non-target material, the corre-lation of the Q-vector orientations as given by CHIMERAand by the Microball detectors was used. Figure 11 showsthe correlation between their azimuthal directions, ΦCHI

and ΦµBall, for 197Au+197Au reactions (panel (a)) and197Au+Empty Frame (panel (b)) data, normalized rela-tive to each other with respect to the integrated beamintensities. The strong anti-correlation for on-target re-actions is evident. It is expected because forward-emittedparticles were selected with CHIMERA (yc.m. > 0.1) andthe Microball covers mainly the backward hemisphere inthe c.m. frame.

In runs with empty target frames, the recorded yieldsare low and only a weak positive correlation is observed.The distribution of differences between the two Q-vectororientations, normalized with respect to the integratedbeam intensity, is presented in panel (c). To minimize thecontributions of non-target collisions in the data analy-sis, an anti-correlation of the CHIMERA and MicroballQ-vector orientations was required. The applied condi-tion |ΦCHI − ΦµBall| > 90◦ led to a relative weight ofbackground reactions of less than 20%. It underlines theimportance of the Microball data for identifying and re-jecting off-target reactions.

Panel (d) of Fig. 11 shows the LAND raw multiplicity(number of modules hit per event), normalized with re-spect to the integrated beam intensity, for 197Au+197Auand 197Au+Empty Frame data and after applying theCHIMERA-Microball anti-correlation condition. Thecontribution from non-target backgrounds in the kine-matic region of LAND is weak, starting with less than20% at unit multiplicity to much less than 1% at multi-plicity 10. In the final analysis, normalized yields of theremaining non-target background events were subtractedfrom the corresponding 197Au+197Au data sets.

IV. EXPERIMENTAL RESULTS

Azimuthal distributions of neutrons and light chargedparticles measured with LAND with respect to the re-action plane determined with the CHIMERA and AToFdetectors, as described in the previous section, were ex-tracted for 197Au+197Au reactions from data collectedwith and without a target and without and with theshadow bar in front of LAND. After subtracting the mea-sured and normalized background yields, the obtaineddistributions were fitted with the Fourier expansion

f(∆φ) ∝ 1 + 2v1cos(∆φ) + 2v2cos(2∆φ) (6)

to determine the coefficients describing the observed di-rected (v1) and elliptic (v2) flows. ∆φ represents the az-imuthal angle of the momentum vector of an emitted par-ticle with respect to the determined reaction plane [52].

0.3 0.4 0.5 0.6

1v

-0.3

-0.2

-0.1

0

0.1

0.2

0.340% 60%71% 80%86% 93%100% FOPI

proj/y

laby

0.3 0.4 0.5 0.6

2v

-0.2

-0.15

-0.1

-0.05

0

FIG. 12: (Color online) Measured directed (top panel) and el-liptic flows (bottom panel) of charged particles as determinedwith different timing corrections in comparison with FOPIresults (filled triangles, from [48]) for the same 197Au+197Aureaction at 400 MeV/nucleon in the interval of impact param-eters 3.35 ≤ b ≤ 6 fm. The percentages of cases to which theso-called second step of the timing corrections was appliedare given in the legend (see text). The solid and dashed blacklines indicate the limits 40% and 100%, respectively, of thestudied probability interval.

Due to insufficient resolution, charge identification withthe ∆E-vs-time-of-flight technique has not been possiblewith LAND in the present experiment. Therefore, onlyresults for neutrons and for all recorded charged particlesare presented in the following.

A. Timing corrections

The timing information of particles detected withLAND in these data sets had been corrected as describedin Sec. III A and in the Appendix. One of the unknownparameters appearing in this procedure was the num-ber of particles misplaced or wrongly corrected in theso-called second step. Therefore, a series of analysis runswas performed in which the percentage of particles sub-jected to it was reduced from 100% to 40% in steps of in-creasing width. The resulting flow parameters are shownin Fig. 12 as a function of the reduced rapidity ylab/yproj.It is observed that the influence of the second correctionis negligible at rapidities ylab/yproj ≈ 0.4 but significantat lower and higher rapidities. At a reduced rapidityylab/yproj = 0.4, the acceptance of LAND in this experi-ment selects transverse momenta of approximately 0.3 to

13

0.5 GeV/c/nucleon for which the discussed effect is, ap-parently, less severe. As expected for a mixing betweentime intervals, the modifications at low and high rapidi-ties occur in opposite directions for both the directed andelliptic flows.

For the data selected for this purpose, an interval ofnominal impact parameters 3.35 ≤ b ≤ 6 fm was chosenbecause corresponding flow data had been made availableby the FOPI Collaboration [48]. It is contained withinthe semi-central event class and its parameters are listedin the bottom line of Table I. The comparison is notmeant to identify a “best” percentage at which the prob-lem will largely disappear. It only shows that the 100%application of the second step does not necessarily leadto improved flow values, consistent with the observationmade for the time spectra discussed in the Appendix. Italso suggests an application with 40% as a useful lowerlimit. Variations within this interval of 40% to 100% areconsidered as suitable for quantifying the contribution ofthe mixing and the underlying timing uncertainty to thesystematic error of the measurement. It applies mainlyto the flow parameters deduced as a function of rapidityor of transverse momentum. The effect is of minor im-portance for the acceptance-integrated flow ratios basedon time-integrated particle yields.

B. Collective flow

Flow parameters obtained after correcting for the dis-persion of the reaction plane are shown in Fig. 13 as afunction of the transverse momentum per particle pt/A.They are integrated over the rapidity range covered bythe LAND acceptance which increases with pt/A fromylab/yproj ≈ 0.3 to 0.7 (cf. Fig. 1 of Ref. [5]). The ob-served yield of particles decreases rapidly with increasingtransverse momentum, so that the low-intensity regionsat high pt are more strongly affected by occasionally mis-placed particles originating from the regions of high yieldat lower pt. For this reason, the analysis is restricted totransverse momenta pt/A ≤ 0.7 GeV/c. The selectedrange of nominal impact parameter is b ≤ 7.5 fm (centralevent class), and a fraction of 80% is chosen for the appli-cation of the second correction step discussed above, com-patible with the comparison of elliptic-flow results shownin Fig. 12. The coefficient v1 rises from negative valuesfor small pt/A to small positive values at pt/A > 0.6,reflecting the correlation of transverse momentum withrapidity caused by the acceptance of LAND. The coeffi-cient v2 is small at small pt/A and assumes values belowv2 = −0.1 at larger pt/A, indicating the strength of par-ticle squeeze-out in the directions perpendicular to thereaction plane.

0.2 0.3 0.4 0.5 0.6 0.7

1v

-0.4

-0.3

-0.2

-0.1

0

0.1

Neut (stiff)Ch (stiff)Neut (soft)Ch (soft)Neut (Exp)Ch (Exp)

/A (GeV/c)t

p0.2 0.3 0.4 0.5 0.6 0.7

2v

-0.15

-0.1

-0.05

0

FIG. 13: (Color online) Measured flow parameters v1 (toppanel) and v2 (bottom panel) for the central event class(b < 7.5 fm) in 197Au+197Au collisions at 400 MeV/nucleonfor neutrons (filled circles) and charged particles (filled trian-gles) as a function of the transverse momentum pt/A. TheUrQMD predictions for neutrons and charged particles ob-tained with a stiff (γ=1.5, red solid and dotted lines, re-spectively) and a soft (γ=0.5, blue dashed and dash-dottedlines, respectively) density dependence of the symmetry termhave been filtered to correspond to the geometrical acceptanceof the experiment. The experimental data are corrected forthe dispersion of the reaction-plane orientation. Where notshown, the statistical errors are smaller than the size of thesymbols.

V. INTERPRETATION WITH URQMD

As in the earlier FOPI-LAND study [5], the ultrarela-tivistic QMD (UrQMD) model of the group of Li and Ble-icher [9–11] has been employed to deduce the density de-pendence of the nuclear symmetry energy. Even thoughalternative parametrizations have recently become avail-able [56, 57], the version employed in the FOPI-LANDstudy was used again, so as to permit a direct comparisonof the density dependences obtained from the two exper-iments. The differences are, furthermore, not very large.In the study presented by Wang et al. using a varietyof Skyrme forces a very comparable stiffness parameterL = 89 ± 23 MeV was obtained, differing from the orig-inal result L = 83 ± 26 MeV by only a few MeV [5, 57].The parameter

L = 3ρ0∂Esym

∂ρ|ρ=ρ0

(7)

is proportional to the slope of the symmetry energy atsaturation (see, e.g., Ref. [38]).

14

The UrQMD model was originally developed to studyparticle production at high energy [58]. By introducinga nuclear mean field with momentum dependent forces,it has been adapted to the study of intermediate energyheavy-ion collisions [59]. The chosen equation of state issoft. The updated Pauli-blocking scheme, introduced toprovide a more precise description of experimental ob-servables at lower energies, is described in Ref. [60]. Dif-ferent options for the dependence on isospin asymmetrywere implemented. Two of them are used here, expressedas a power-law dependence of the potential part of thesymmetry energy on the nuclear density ρ according to

Esym = Epotsym+Ekin

sym = 22 MeV(ρ/ρ0)γ+12 MeV(ρ/ρ0)2/3

(8)with γ = 0.5 and γ = 1.5 corresponding to a soft and astiff density dependence.

The UrQMD predictions for these two choices areshown in Fig. 13 in comparison with the experimentaldata, for both neutrons and charged particles. A filter-ing procedure was used to adapt the results to the exper-imental conditions. They qualitatively follow the exper-imental flow values, even though the predicted squeeze-out is less pronounced than that observed. A significantsensitivity with respect to the stiffness of the symmetryenergy is visible for the elliptic flow of neutrons. By com-paring it to the strength of the charged-particle flow inthe form of flow ratios or differences, this sensitivity isexpected to be preserved, even in the presence of a globalover- or underprediction of the elliptic flows [5, 6].

The slight underprediction is known to be related tothe so-called FP1 parametrization for the momentum de-pendence of the elastic nucleon-nucleon cross sections inthe default version of the UrQMD model that was usedhere. UrQMD studies of the reaction dynamics at inter-mediate energies have shown that the in-medium modifi-cation of the elastic nucleon-nucleon cross-sections is animportant ingredient for realistic descriptions, and vari-ous parametrizations have been tested [56]. In the previ-ous FOPI-LAND study, additional calculations were per-formed with the FP2 parametrization, causing the ellipticflow parameter v2 to be slightly overpredicted. The ab-solute values of v2 obtained with FP1 and FP2 differ by≈ 40% for this reaction [60, 61]. The calculated ratiosretain, nevertheless, the sensitivity of the elliptic flow tothe stiffness of the symmetry energy and depend onlyweakly on the chosen parametrization for the in-mediumcross sections [5].

The systematic study of the residual model depen-dence of transport descriptions of the elliptic flow ratiosand differences by Cozma et al. [14] has, in addition,demonstrated that the Tubingen QMD transport modelused there leads to equivalent results regarding the de-duced stiffness of the symmetry energy. In particular,also the impact of including or neglecting the momen-tum dependence of the symmetry potential was investi-gated with different parametrizations. Important inputquantities identified by this study were the isoscalar com-pressibility and the width of the nucleon wave function

employed in the calculations. Narrower constraints forthese quantities will reduce the theoretical uncertainties.A quantitative study of the model differences betweenthe UrQMD and the Tubingen versions was performedby Wang et al. [57]. Expressed in terms of the centralvalue obtained for the slope parameter L, an uncertaintyof ∆L ≈ 10 MeV may be ascribed to the observed modeldependence of the UrQMD versus the Tubingen-QMDanalyses.

Besides the momentum-dependence of the symmetrypotential [16, 62–66], attention has to be paid to therecent observation of short-range correlations [67, 68],leading to larger tails of the momentum distributions insymmetric matter than in pure neutron matter and toa reduction of the kinetic part in the parametrization ofthe symmetry energy [69–71]. It will be interesting to in-corporate these correlations in transport models and toexplore their consequences [72, 73]. However, in a firststudy [29], the effect for elliptic-flow ratios was found tobe negligibly small for the case of a mildly soft to lineardensity dependence of the symmetry energy that is sup-ported by the present data. It is, nevertheless, evidentthat the improvement of current theoretical descriptionsis an important goal for the future. Reducing theoret-ical uncertainties and enhancing their consistency [74],will permit tighter constraints for the high-density de-pendence of the symmetry energy.

The UrQMD transport program is stopped at a col-lision time of 150 fm/c and a conventional phase-spacecoalescence model with two parameters is used to con-struct clusters. Nucleons with relative momenta smallerthan P0 and relative distances smaller than R0 are con-sidered as belonging to the same cluster. The valuesP0 = 0.275 GeV/c and R0 = 3.0 fm have been adoptedas standard parameters. With these values the overalldependence of cluster yields on Z is rather well repro-duced but the yields of Z = 2 particles are underpre-dicted [5]. In the comparison with the FOPI data set usedfor Fig. 12, after normalization with respect to Z = 1,an underprediction by a factor 1.4 was observed. Theyields of deuterons and tritons in central collisions arealso underestimated by similar factors.

Constraints for the symmetry energy were determinedby comparing the ratios of the elliptic flows of neutronsand charged particles (ch), vn2 /v

ch2 , with the correspond-

ing UrQMD predictions for the soft and stiff assump-tions. Because hydrogen isotopes could not be selected,as done in the FOPI-LAND study [5], a test was per-formed for confirming the equivalence of results obtainedwhen including all recorded charged particles in the anal-ysis. For this purpose, the data of the FOPI-LANDexperiment were analyzed with and without the condi-tion Z = 1 applied in the charged-particle selection andwith the limitation pt/A ≤ 0.7 GeV/c of the integrationinterval in transverse momentum. The correspondingpower-law coefficients γ were determined by comparingwith UrQMD calculations performed with the same con-ditions. In addition, the effect of enhancing the weight

15

0.3 0.4 0.5 0.6 0.70.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

/A (GeV/c)t

p

ch 2/vn 2v

stiff

soft

0.10±=0.75γ

FIG. 14: (Color online) Elliptic flow ratio of neutrons overall charged particles for central (b < 7.5 fm) collisions of197Au+197Au at 400 MeV/nucleon as a function of the trans-verse momentum per nucleon pt/A, evaluated with a frac-tion of 80% for the second step of timing corrections (seeSec. IV A). The black squares represent the experimentaldata, the green triangles and purple circles represent theUrQMD predictions for stiff (γ = 1.5) and soft (γ = 0.5)power-law exponents of the potential term, respectively. Thesolid line is the result of a linear interpolation between thepredictions, weighted according to the experimental errors ofthe included four bins in pt/A, and leading to the indicatedγ = 0.75 ± 0.10.

of the Z = 2 contribution to the calculated Z-integratedflow was tested. Since good agreement was obtained withan enhancement factor 1.4, corresponding to the observedunderprediction, it was used as default option in the anal-ysis. Overall, the changes observed in these tests for thecentral values were less than ∆γ = 0.05, accompaniedhowever by the larger statistical error of the FOPI-LANDdata set.

A. Differential data

The ratio vn2 /vch2 obtained from the present data for

the class of central (b < 7.5 fm) collisions as a function ofthe transverse momentum per nucleon pt/A is shown inFig. 14. The chosen fraction for the second step of timingcorrections (see Sec. IV A) is 80%, compatible with thecomparison with FOPI data presented in Fig. 12. Underthis assumption, the best description of the neutron-vs-charged-particle elliptic flow is obtained with a power-law coefficient γ = 0.75 ± 0.10 where ∆γ = 0.10 is thestatistical uncertainty returned by the fit routine. It re-sults from linearly interpolating between the predictionsfor the soft, γ = 0.5, and the stiff, γ = 1.5, predictionsof the model within the range of transverse momentum0.3 ≤ pt/A ≤ 0.7 GeV/c.

The dependence of the resulting γ on the choice madefor the second timing correction in the data analysis isshown in Fig. 15. Under the assumption that the second

40 50 60 70 80 90 1000.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

fraction (%)

γ

0.15±=0.75γ

FIG. 15: Potential-term coefficient γ deduced by interpolat-ing between the UrQMD predictions shown in Fig. 14 as afunction of the fraction chosen for the second step of timingcorrections (see Sec. IV A).

correction should be applied to at least 40% of the cor-responding particles, the 1-σ error margins are confinedwithin the interval γ = 0.75 ± 0.15 as apparent from thefigure. The larger error ∆γ = 0.15 is expected to in-clude the systematic uncertainty caused by the existenceof misplaced hits, not identified in the first step and onlypartly included in the second step of the timing correc-tion scheme of the analysis.

B. Acceptance-integrated flow ratio

The new constraint deduced in the preceding sectionis slightly lower but still within the uncertainty intervalof the previous value γ = 0.9 ± 0.4 deduced from theFOPI-LAND data and the same UrQMD model [5]. Theerror is significantly reduced by a factor of more thantwo. To confirm the validity of the obtained result andto minimize complications arising from the time-of-flightmeasurement with LAND, an acceptance-integrated flowratio was determined by integrating over the full thitspectrum shown in Fig. 21 in the Appendix. It includesall recorded particles irrespective of their actual locationwithin this spectrum. The corresponding UrQMD calcu-lations were integrated over the full acceptance of LANDas given by the covered interval of laboratory angles. Thethresholds and the energy and particle-type dependentdetection efficiency of the effectively used first plane ofthe LAND detector behind the veto wall were taken intoaccount (Fig. 16). The efficiency calculations were car-ried out with Geant3 within the FairRoot software frame-work [47].

The still remaining uncertainty arising from this pro-cedure is connected with the choice of the upper limitof the time-of-flight interval which determines the lowerthreshold of the neutron energy. For protons to passthrough the veto wall and to be detected in a LANDmodule, a minimum energy of about 60 MeV is required

16

/A (MeV)kinE0 100 200 300 400 500

effic

ienc

y (%

)

0

10

20

30

40

50

60

70

80

90

100

Li7

He4

He3

tdpn

FIG. 16: (Color online) Detection probability of the first planeof the LAND detector, preceded by the veto wall, for neu-trons (dots), protons (filled squares), deuterons (filled trian-gles), tritons (filled tip-down triangles), 3He (open circles),4He (open squares), and 7Li (open triangles) as a function ofthe particle kinetic energy per nucleon Ekin/A.

while neutrons with lower energies may still be detected(Fig. 16). The magnitude of this effect has been assessedby varying the upper limit of time-of-flight integrationbetween 60 and 90 ns, resulting in a slight variation ofthe obtained flow ratio and the exponent γ. The UrQMDcalculations were performed for this purpose with kinetic-energy thresholds that corresponded to the chosen in-tegration limit for neutrons and the physical lower de-tection thresholds for charged particles. Acceptance-integrated elliptic-flow values were then determined fromthe azimuthal anisotropy of the obtained yields and thelinear interpolation between the predictions was used todetermine the corresponding exponents γ.

The results for the measured and calculatedacceptance-integrated flow ratios and the resulting γ areshown in Fig. 17. A small monotonic variation of γ withthe assumption regarding the upper limit of the ToF in-terval is evident. The 1-σ error margins are confined tothe interval γ = 0.77± 0.17. It overlaps with the intervalobtained by varying the fraction of hits included in thesecond correction step (Fig. 15). This is not unexpectedas the two methods are both aiming at quantifying theremaining consequences of not recognized simultaneoustiming errors of the two signals from a paddle. The vari-ation of the maximum of the ToF interval, in addition,includes the effect of a possible smearing of the energythreshold for neutrons and charged particles by the 25-nstime jumps.

C. Final corrections

Up to this point, the effects of charge-changing pro-cesses, nuclear or instrumental, have been ignored in theanalysis. The largest effects of this kind are caused bymisidentifications of charged particles as neutrons, be-

60 65 70 75 80 85 90

0.6

0.7

0.8

0.9

1

soft

stiff

ch 2/vn 2v data

60 65 70 75 80 85 90

0.4

0.6

0.8

1

1.2

Maximum ToF (ns)

0.17±=0.77γ

γFIG. 17: (Color online) Measured elliptic-flow ratio for central(b < 7.5 fm) collisions of 197Au+197Au at 400 MeV/nucleon incomparison with stiff and soft UrQMD predictions (top panel)and deduced symmetry term coefficient γ (bottom panel) as afunction of the upper limit of the time-of-flight interval usedto obtain time integrated results. The dashed horizontal linesmark the upper and lower limits of the 1-σ statistical errormargin ∆γ = ±0.10 within the time interval 60 < ToF <90 ns.

cause of a missing veto signal, and of neutrons as chargedparticles because of a neutron-induced reaction in a vetopanel that produces a signal. Nuclear charge-exchangereactions with cross sections on the level of millibarn areless important in comparison (see, e.g., Refs. [75, 76]).Furthermore, protons converted into neutrons in the vetowall may still have left a signal there while neutrons con-verted to protons are included in the measured, rathersmall, efficiency for neutron detection of the thin vetopaddles (see below). Misidentifications reduce the differ-ence between the measured flow patterns and thus causea small increase of the apparent flow ratio. The resultingsymmetry-term coefficient appears stiffer than withoutthese effects.

Calculations within the R3BRoot simulation frame-work [47] have been performed with different assump-tions regarding the detector response and particle recog-nition. In particular, the particle-dependent detectionthresholds have been taken into account (Fig. 16). Theobtained reduction of the power-law exponent γ variedbetween ∆γ = −0.03 and -0.07, with the lower and up-per boundaries being obtained with the most extremeassumptions.

The magnitude of the required correction is, qualita-

17

0

20

40

60

80

0 0.5 1 1.5 2

ρ/ρ0

Esy

m

(M

eV)

n/ch flowBrownZhangHIC Sn+SnIASFOPI-LANDASY-EOS

FIG. 18: (Color online) Constraints deduced for the densitydependence of the symmetry energy from the present data incomparison with the FOPI-LAND result of Ref. [5] as a func-tion of the reduced density ρ/ρ0. The low-density results ofRefs. [78–81] as reported in Ref. [82] are given by the symbols,the grey area (HIC), and the dashed contour (IAS). For clar-ity, the FOPI-LAND and ASY-EOS results are not displayedin the interval 0.3 < ρ/ρ0 < 1.0.

tively, easily understood. A 1-mm gap between veto pad-dles causes an inefficiency of approximately 1%. It maycause the equivalent amount of charged particles to ap-pear as neutrons in the analysis. As charged particlesby nature, they have a five-fold higher probability forbeing detected in the first layer of LAND. By takinginto account the known yield ratio of charged particlesover neutrons of approximately 2/3 and the measuredflow ratio of vn2 /v

ch2 = 0.72 (Fig. 17), a corrected ra-

tio vn2 /vch2 = 0.71 is obtained. With the sensitivity of

the flow ratio as represented in the figure, the correctionamounts to ∆γ = −0.05. It represents an upper limit forthis particular effect because the veto paddles are alignedwith respect to the elements of the first plane of LANDand not all particles passing through the veto gaps arerecorded. As an analysis detail, we note here that in test-ing the coincidence of timing signals in the veto wall andfirst plane of LAND the possibility of undetected ±25 nsdisplacements of one of the signals was taken into account(errors in the positions derived from the time signals haveall been corrected, see Appendix). Other processes ex-ist but are less important. The detection probability forneutrons in the 5-mm veto paddles is below 1% (cf. Fig. 1of Ref. [17]) and the coincidence requirement of a match-ing hit in the first module of LAND further reduces theprobability of misidentifications of this kind. In the sim-ulations, all these effects are included.

The adopted reduction ∆γ = −0.05 ± 0.02 leads to afinal result for the power-law coefficient γ = 0.72 ± 0.19.

The quoted uncertainty is obtained by a linear addi-tion of the systematic error of the correction and the∆γ = −0.17 uncertainty resulting from the comparisonof the acceptance-integrated flow ratio with the UrQMDcalculations (Fig. 17). The possibility of charge misiden-tifications considered here has not been taken into ac-count in the FOPI-LAND analysis. There, its magni-tude appears small in comparison with the uncertainty∆γ = ±0.4 of this earlier result. It was also not includedyet in presentations of preliminary ASY-EOS results atconferences [77].

The obtained constraint for the density dependence ofthe symmetry energy is shown in Fig. 18 in compari-son with the FOPI-LAND result of Ref. [5] as a functionof the reduced density ρ/ρ0. The new result confirmsthe former and has a considerably smaller uncertainty.Judging from the purely statistical error of ∆γ = ±0.10(Fig. 15), even smaller errors can be expected from futuremeasurements.

For reference, the low-density behavior of the symme-try energy from Refs. [78–81] as reported in Ref. [82]is included in the figure. The present parametrizationis found compatible also with these results from nuclearstructure studies and from reactions at lower bombard-ing energy. The corresponding slope parameter describ-ing the variation of the symmetry energy with density atsaturation is L = 72±13 MeV. Judging from the analysiswork done with the FOPI-LAND data, one may expectthat the analysis of the present data with the TubingenQMD [6, 14] will lead to a similar or possibly slightlylarger value for the parameter L [15, 57, 83].

The sharp value Esym(ρ0) = 34 MeV is a consequenceof the chosen parametrization (Eq. 8). Using valueslower than the default Epot

sym(ρ0) = 22 MeV, as occa-sionally done in other UrQMD studies [56, 84], is likelyto lower the result for L. Values of the symmetry en-ergy at saturation in the interval between 30 MeV and32 MeV seem to be favored by a majority of terrestrialexperiments and astrophysical observations as shown inrecent compilations [85, 86]. Motivated by these re-sults, the present UrQMD analysis has, in addition, beperformed with Epot

sym(ρ0) = 19 MeV, corresponding toEsym(ρ0) = 31 MeV. The obtained power-law coefficientγ = 0.68 ± 0.19 is lower by ∆γ = 0.04 and the corre-sponding slope parameter L = 63 ± 11 MeV is lower by9 MeV, changes that both remain within the error mar-gins of these quantities. It is to be noted, however, thatthe precise results of Brown [80] and Zhang and Chen [81]are no longer met with this alternative parametrizationof the symmetry energy.

VI. DENSITY PROBED

Calculations predict that central densities of two tothree times the saturation density may be reached in197Au+197Au collisions at 400 to 1000 MeV/nucleon ontime scales of ≈ 10 − 20 fm/c [87]. The resulting pres-

18

sure produces a collective outward motion of the com-pressed material whose strength, differentiating betweenneutrons and protons, is influenced by the symmetry en-ergy in asymmetric systems [25]. It is to be expected, onthe other hand, that the observed transverse momentaof emitted particles and their azimuthal variation appar-ent as elliptic flow carry information acquired during thefull reaction history. The tests performed with the FOPI-LAND flow data and varying parameters for the potentialpart of the symmetry energy in the UrQMD had alreadyindicated that densities above and below saturation con-tribute to the observed flow patterns [5].

A force-weighted density has been defined by Le Fevreet al. in their recent study of the equation of state ofsymmetric matter, based on FOPI elliptic-flow data andIQMD calculations [24]. For 197Au+197Au collisions at400 MeV/nucleon, its broad maximum extends over den-sities 0.8 < ρ/ρ0 < 1.6. Liu et al. report in their studyof pion production in the same reaction that the rela-tive sensitivity of the π−/π+ yield ratios to the sym-metry energy is distributed over a density range of ap-proximately 0.7 < ρ/ρ0 < 1.8 with a maximum nearρ/ρ0 ≈ 1.2 [88]. These more quantitative studies, withpartly different methods, consistently support the as-sumption that supra-saturation densities up to nearlytwice saturation are probed at this energy with collec-tive flows and meson production, not exclusively but withmajor effects produced above saturation.

For the present purpose, a detailed analysis of the colli-son processes has been performed with the Tubingen ver-sion [14] of the QMD model (TuQMD). The sensitivity tothe various density regimes probed in heavy-ion collisionswas studied quantitatively by examining their impact onthe variation of elliptical-flow-ratio observables with thetwo choices of a mildly stiff and a soft parametrizationfor the density-dependent asymmetric-matter equationof state (asy-EoS). To that end, the density-dependentquantity DEFR (Difference of Elliptic-Flow Ratio)

DEFR(n,Y )(ρ) =vn2vY2

(x = −1, ρ) −vn2vY2

(x = 1, ρ) (9)

has been determined using the TuQMD transport model.Here Y labels a particle or a group of particle species andx the asy-EoS stiffness resulting from the momentum-dependent one-body potential introduced by Das et

al. [16]. The density-dependent elliptic-flow ratios(EFR) in this expression are calculated with a modifiedsymmetry potential

Vsym(x, ρ) =

{

V Gognysym (x, ρ) ρ ≤ ρ

V Gognysym (0, ρ) ρ > ρ

(10)

with x = ±1 according to Eq. 9. The difference of thex = ±1 potentials is tested only at densities up to theparticular ρ, the argument of DEFR. This choice leadsto DEFR(n,Y )(0) = 0 and to the proper stiff-soft split-ting for large values of the density ρ. Values at inter-mediate densities are a measure of the impact on ellip-tic flow observables of regions of density lower than that

chosen for the argument. The derivative of DEFR withrespect to density provides thus the sensitivity density ofthe elliptic flow ratio observable under consideration asa function of the nuclear matter density.

0.0

0.25

0.5

0.75

Sen

sitiv

ity0.0 0.5 1.0 1.5 2.0 2.5 3.0

/ 0

n/pn/Hn/ch

0.0

0.25

0.5

DE

FR(n

,ch)

FIG. 19: Density dependence of the difference of the ellipticflow ratio (DEFR) of neutrons over charged particles, definedby Eq. 9, for 197Au+197Au collisions at 400 MeV/nucleon ob-tained with the TuQMD transport model [14] and the FOPI-LAND acceptance filter (upper panel) and the correspondingsensitivity density (lower panel, solid line) together with sen-sitivity densities obtained from elliptic-flow ratios of neutronsover all hydrogen isotopes (dashed) and neutrons over protons(dash-dotted).

In the upper panel of Fig. 19, the density dependence ofDEFR(n,Y ) for the choice Y =all charged particles (ch) ispresented. It is seen that DEFR increases monotonicallyup to density values in the neighborhood of 2.5 ρ0, closeto the maximum density probed by nucleons in heavy-ion collisions at 400 MeV/nucleon incident energy. Therelative sensitivity of the elliptic flow ratio of neutronsover charged particles to the various density regions ispresented in the lower panel of Fig. 19, together with thesame quantity for the neutron-over-proton and neutron-over-hydrogen flow ratios. It is readily observed that themaximum sensitivity of the neutron/proton EFR liesin the 1.4 to 1.5 ρ0 region. It is lowered to 1.0 to 1.1ρ0 for the choices that involve light complex particles.The probed regions of nuclear density are thus consid-erably higher than the densities around or below 0.7 ρ0probed with nuclear structure observables [80–82]. Evenlower densities in the vicinity of ρ0/3 have very recentlybeen reported as the region of sensitivity probed with thedipole polarizability of 208Pb [89].

The moderately different density regions probed byEFR observables involving protons and, respectively,

19

light complex particles are expected to lead to slightlydifferent extracted values for the asy-EoS stiffness. Pre-liminary results, employing existing experimental FOPI-LAND data for vn2 /v

p2 and vn2 /v

H2 and the TuQMD trans-

port model, suggest this to be the case [90]. A slightlystiffer asy-EoS is favored by the latter observable, a dif-ference that will be enhanced if one corrects for the factthat transport models coupled with phase-space coales-cence algorithms tend to underpredict light cluster mul-tiplicities by factors ranging up to 2-3. Deuterons andtritons are of particular interest here. This result sug-gests that, at higher densities, the asy-EoS density de-pendence is somewhat softer than at saturation. It maythus be feasible to extract constraints for the parametersof the higher order terms of the Taylor expansion of thesymmetry energy in density around the saturation point,in particular the curvature parameter Ksym. Informa-tion regarding the curvature is of high interest as, e.g.,the inclusion of exchange terms in microscopic modelscause a stiffening [91] while considering the momentumtails caused by short-range correlations may cause a soft-ening [73] of the predictions for the symmetry energy inthe density regime near and above saturation.

It is, therefore, of extreme importance for future ex-periments to be able to extract a clean separate protonsignal. Additionally, theoretical models that allow for anindependent adjustment of the slope and curvature pa-rameters of the symmetry energy term will be required tobe able to push the extracted constraints for the asy-EoSdensity dependence into the 2ρ0 region.

VII. CONCLUSION AND OUTLOOK

From the measurement of the elliptic flows of neutronsand light charged particles in the reaction 197Au+197Auat 400 MeV/nucleon incident energy a new, more strin-gent constraint for the nuclear symmetry energy at supra-saturation density has been deduced. From the compari-son of the elliptic flow ratio of neutrons over charged par-ticles with UrQMD predictions, a value γ = 0.72 ± 0.19is obtained for the power-law coefficient of the potentialpart in the parametrization of the model. It confirms themoderately soft to linear density dependence of the sym-metry energy deduced previously from the FOPI-LANDdata. The densities probed were shown to reach beyondtwice saturation.

The effects of deficiencies of the LAND timing elec-tronics have been studied in detail and their effectsassessed by systematically varying correction parame-ters over their intervals of uncertainty. An acceptance-integrated flow ratio for neutrons over charged particleshas been generated by integrating over the time-of-flightspectra. It is largely insensitive to timing uncertaintiesbut still subject to a systematic error caused by an in-strumental smearing of detection thresholds. Their ef-fect contributes to the total error ∆γ = ±0.19 of theacceptance-integrated result that includes a statistical er-

ror ∆γ = ±0.10.

The slope parameter that corresponds to the obtainedparametrization of the symmetry energy is L = 72 ±13 MeV. As densities near and beyond saturation are effi-ciently probed with the present observable, one may con-vert this result into a symmetry pressure p0 = ρ0L/3 =3.8 ± 0.7 MeVfm−3 (with ρ0 = 0.16 fm−3), equivalent to6.1±1.1 ·1032 Pa. It represents the pressure in pure neu-tron matter at saturation because the pressure in sym-metric matter vanishes at this density. The pressure inneutron-star matter with asymmetries δ = (ρn − ρp)/ρless than unity should be lower. The estimate devel-oped in Sec. 9.1 of Ref. [38], based on β-equilibrium,yields a proton fraction xp = (1 − δ)/2 of about 5%for Esym = 34 MeV (cf. Eq. 8) and saturation den-sity. With the corresponding asymmetry δ = 0.90, thepressure of the asymmetric baryonic matter is reduced to3.1 MeVfm−3. Adding the contribution of the degenerateelectrons yields a value of 3.4 MeVfm−3 for the pressurein neutron-star matter at saturation density. The sameor very similar values are obtained with the expressionspresented in Refs. [86, 92]. Compared to the results ofSteiner et al. [93], they are located within the upper halfof the 95%-confidence interval obtained by these authorsfrom neutron-star observations.

While interpretations in this direction may still appearspeculative at present and in need of further study, theyreveal the potential of pressure measurements in nuclearreactions. As far as the modeling of nuclear reactions isconcerned, it will be important to improve the descrip-tion of the nuclear interaction in transport models [74], toreduce the parameter ranges also in the isoscalar sector,to improve the algorithms used for clusterization, as wellas going beyond the mean-field picture, including short-range correlations. The latter have recently been investi-gated in nuclei [67, 68] and their consequences for trans-port descriptions of intermediate-energy heavy-ion reac-tions are of high interest and need to be investigated [72].Moreover, it will be quite important to compare the ex-perimental data with the predictions of several trans-port models, of both Boltzmann-Vlasov and molecular-dynamics type [94], in order to pursue the work towardsa model-independent constraint of the high-density sym-metry energy initiated in Ref. [14].

The results of the present experiment, together withthe theoretical study of the density probed, may also beseen as a strong encouragement for extending the mea-surement of neutron and charged particle flows to otherreaction systems and energies. The presented calcula-tions suggest that the curvature parameter Ksym canbe addressed experimentally if higher precision and el-emental and isotopic resolution for charged particles canbe achieved. Future experiments will, therefore, benefitfrom the improved calorimetric capabilities of the Neu-LAND detector presently constructed as part of the R3Bexperimental setup [95] and from the availability of ra-dioactive ion beams for reaction studies at FAIR.

20

Acknowledgments

The authors are indebted to the Accelerator De-partment and the Target Laboratory of the GSIHelmholtzzentrum for providing high-quality beams andtargets. We are particularly grateful to the LaboratoriNazionali del Sud for making parts of the CHIMERAmultidetector available for the experiment. We thankW. Reisdorf and the FOPI Collaboration for providingspecifically selected data sets from their experiments andfor continuing support of the project. The contributionsof R. Bassini and C. Boiano during the preparatory phaseare gratefully acknowledged.

This work has been supported by the European Unionunder Contract No. FP7-25431 (Hadron-Physics2), byINFN (Istituto Nazionale di Fisica Nucleare) experi-ments EXOCHIM and NEWCHIM, by the National Nat-ural Science Foundation of China under Grant Nos.11375062, 11547312, and 11505057, by the HungarianOTKA Foundation No. K106035, by the Polish Min-istry of Science and Higher Education under GrantNo. DPN/N108/GSI/2009, by the Foundation for Pol-ish Science - MPD program, co-financed by the Euro-pean Union within the European Regional DevelopmentFund, by the Polish National Science Center (NCN),Contract Nos. UMO-2013/10/M/ST2/00624 and UMO-2013/09/B/ST2/04064, by the Slovak Scientific GrantAgency under Contract 2/0121/14, by the UK Scienceand Technology Facilities Council (STFC) under GrantsNos. ST/G008833/1, ST/I003398/1, and STBA00019,by the US Department of Energy under Grants Nos.DE-FG02-93ER40773 and de-sc0004835, by the USA Na-tional Science Foundation Grant No. PHY-1102511, andby the Robert A. Welch Foundation through Grant A-1266.

VIII. APPENDIX: CORRECTION OF LAND

TIMING

In the TACQUILA electronic board [43], the time mea-surement of a recorded hit is performed by registeringthe time of the start signal (tac) inside a 25-ns clock-cycle window, the time of the common stop signal insideits 25-ns clock-cycle window (so-called t17) and the num-ber nc of cycles occurring between the start and stopcycles. The returned calibrated time information tcal isthen given by

tcal = tac + 25nc − t17 (ns). (11)

The resolution of the timing system is of the order of10 ps (rms) [43].

Examples of the observed correlations between t17 (inchannels) and the so measured tcal (in ns) for the twophotomultipliers (PM’s) of a paddle of the first plane ofLAND are shown in panels (a) and (b) of Fig. 20. Ide-ally, no correlation should be visible as the distribution

of the stop signals inside the clock cycle window shouldbe completely random. Unexpectedly, however, a strongcorrelation is observed; preferences exist, primarily, forhigh t17 values at smaller times tcal but also for low t17values at larger times. This behavior by itself impliesan improper functioning of the TACQUILA board. It isevidence of incorrect determinations of nc, depending onwhere the t17 signal appears within the clock cycle. Inaddition, it was found that the probability of wrong nc

countings was rate dependent; it increased with increas-ing frequency of hits recorded in the LAND modules.This behavior, as discovered during the data taking wasconfirmed with bench tests performed after the experi-ment and ultimately corrected by replacing parts of theTACQUILA electronic readout system.

As a consequence, the region marked as A1 inFig. 20 (a) must be considered as overpopulated becauseof a wrong counting of the number nc of clock cycles;the returned nc is likely to be one-unit smaller than thetrue value, causing an offset of -25 ns of the calibratedtime tcal. With smaller probability, counting errors largerthan one cycle were observed as well. It follows that anymeasured time in LAND is not necessarily but possiblywrong by ±25 ns or, with decreasing probability, evenmultiples of it.

The described malfunctions clearly affect the measure-ments of the hit position Ytime along the vertically ori-ented paddles, derived from the difference, and of thearrival time thit at the paddle, derived from the sum ofthe two signals recorded for a hit. The two quantities aregiven by

Ytime = tcal 1 − tcal 2 (12)

thit = (tcal 1 + tcal 2)/2 (13)

where the indices 1 and 2 refer to the two PM’s of a givenpaddle; the signals tcal 1 and tcal 2 are, at this stage, notyet synchronized, i.e. not yet corrected for time offsetsgenerated by, e.g., differences of the cable lengths of thetwo PM’s. The position Ytime is, therefore, still given inunits of nanoseconds and not necessarily centered withrespect to the paddle length.

In the case of malfunctions, the time differences maybe sufficiently large, so that the deduced hit position fallsoutside the physical length of the paddle. This can beeasily corrected by adding or subtracting 25 ns to thetime difference. It will move the hit to its correct positioninside the paddle. To recover the correct arrival timesthit is not equally feasible in this case. It would requirethe knowledge of whether the wrong position of Ytime

is caused by erroneous +25 ns in one or -25 ns in theother of the two signals coming from a paddle. The twopossibilities correspond to thit values that differ by 25 ns.Moreover, it is also possible that both time measurementsare affected by the same ±25 ns time jump. In that case,the position Ytime is correct but the returned arrival timethit is erroneous by ±25 ns. Because the expected range

21

640 660 680 700 720 7400

1

2

3

4310×

A1A2

(a)t1

7_1

(arb

. uni

ts)

0

10

20

30

40

50

60

640 660 680 700 720 7400

1

2

3

4310× tcal_1 (ns)

tcal_2 (ns)

B1B2

(b)

t17_

2 (a

rb. u

nits

)

0

10

20

30

40

50

60

100− 50− 0 50 100

50−

0

50

(cm)ampY

2UU

D

(c)

(ns

)tim

eY

0102030405060708090

100− 50− 0 50 100

50−

0

50 (d)

(cm)ampY

(ns

)tim

eY

0102030405060708090

100− 50− 0 50 100

50−

0

50

(cm)ampY

(e)

(ns

)tim

eY

0102030405060708090

FIG. 20: (Color online) Panels (a) and (b): Observed corre-lations of t17 vs calibrated time tcal for the two signals tcal 1

and tcal 2 of a module of the first plane of LAND. Panels (c)and (d): Observed correlations of the position signals Ytime

vs Yamp deduced from the time and amplitude information ofthese signals, respectively, before (c) and after (d) the firstcorrection step. Panel (e): the same correlation after the cor-rection step 1stbis. The significance of the marked regions inpanels (a) through (c) is explained in the text.

of arrival times at LAND exceeds 25 ns, an easy and

straightforward procedure for recovering the correct timeinformation does not exist.

It has, nevertheless, been possible to develop a cor-rection scheme for recovering the correct times withhigh probability and for determining the consequencesof remaining uncertainties for the finally determinedsymmetry-term coefficient. This was achieved with thehelp of correction parameters whose effects can be as-sessed on a quantitative level. The scheme divides intotwo parts.

The first correction step starts from the observed cor-relation of the position measurement Ytime with the posi-tion Yamp obtained from the amplitudes of the normalizedPM signals. The uncorrected correlation (Fig. 20 (c))shows clearly separated regions of unphysical positionsYtime, marked with U (up), D (down), and 2U (twice up),in addition to the strongest group of coinciding positionmeasurements. The distribution of uncorrected positionsYtime for a typical module of the first plane of LAND isshown in the top panel of Fig. 21 and the correspondingthit distribution is shown in the bottom panel of the samefigure (“no corr”, full line in black). The two side groupswith wrong Ytime positions are weak (< 10%) comparedto the main group but significant. The probability fordouble time jumps in the same direction is below 1%and essentially negligible. The 25-ns repetitions of struc-tures in thit are clearly visible in Fig. 21 (bottom panel),in particular, the repeated appearance of narrow artifi-cial peaks generated by the electronics. These structureswere removed before other corrections were applied.

In the attempt to correct the wrong positions, the cho-sen scheme takes into account the value of t17 relativeto the returned time as shown in panels (a) and (b) ofFig. 20. In the example of a hit belonging to the region’U’ in panel (c), tcal 1 may be located in what is definedas the “good” region, i.e. in the interval between 640 nsand 720 ns but outside the gates ’A1’ and ’A2’ in panel(a), and tcal 2 may be located in region ’B1’ of panel (b).In this case, it is obviously more probable that tcal 2 isincorrect, i.e. that the number of clock cycles is wrong byone unit, and 25 ns are thus added to its value. Instead,if tcal 1 is located in region ’A2’ and tcal 2 in the “good”region, i.e outside the gates ’B1’ and ’B2’ in panel (b),25 ns are subtracted from tcal 1. Corresponding correc-tions are applied to hits belonging to regions marked as’D’ and ’2U’ in Fig. 20 (c) as well as to a region ’2D’when it appeared in other cases. This part of the correc-tion scheme is summarized in Table III and marked as1st step in the last column. Note that three possibilitiesexist for correcting the rare double jumps, depending onwhere the hits are found to be located. The superscripts“+” and “-” used in the table indicate regions analogousto the four regions ’A1’, ’A2’, ’B1’, and ’B2’ marked inpanels (a) and (b) of Fig. 20 but located further out byanother +25 ns or -25 ns from the central part of thespectrum.

Panel (d) of Fig. 20 shows the Ytime-vs-Yamp correla-tion after this first correction step. The corresponding

22

(ns)timeY-60 -40 -20 0 20 40 60

Yie

ld (

arb.

uni

ts)

1

10

210

310

(ns)hitt620 640 660 680 700 720

Yie

ld (

arb.

uni

ts)

210

310

410

0t

no corr

corrst1 corr bisst1 corrnd2

bad peaks

FIG. 21: (Color online) Hit distributions for a module of thefirst plane of LAND as a function of the position Ytime (toppanel) and of the arrival time thit (bottom panel). Black solidlines denote the uncorrected distributions, the colored linesrepresent the distributions after the 1st (red, small dots), the1stbis (green, thick dots), and the 2nd (blue, thick dashed)corrections. “Bad peaks” refers to artificial sharp peaks at25 ns intervals (filled purple areas) generated by the electronicreadout.

Ytime and thit distributions are shown in Fig. 21 (in red).It is evident that not all the wrong positions have disap-peared because some hits do not fulfill the assumptionsmade in devising the first step of the correction scheme(of the order of 2%, cf. Fig. 21, top panel). In thatcase, an additional correction called 1stbis is applied. Atthis step, the location of the hit pattern in the t17-vs-tcal maps (Fig. 20 (a) and (b)) is ignored and the correctYtime is recovered by either adding 25 ns to one or by sub-tracting 25 ns from the other of the two time signals tcal 1and tcal 2 of that hit. The choice made between these twopossibilities was based upon which of them had appearedwith the higher probability when the 1st correction stephad been applied to the same paddle. Panel (e) of Fig. 20shows the Ytime-vs-Yamp correlation after this correction:now all the positions deduced from time signals are cor-rect. They coincide with the positions deduced from theamplitudes and are within the physical length of the pad-dle (Fig. 21, top, in green, coinciding with blue).

At this stage, cases in which both time measure-ments are affected by the same time jump have not beentouched. They remain correct regarding their positionsYtime but the problem of their erroneous arrival timesthit is not solved yet. For that purpose, an additional

panel (c) panel (a) panel (b) tcal 1 tcal 2 correctionU A2 -25 ns 1st

U B1 +25 ns 1st

D A1 +25 ns 1st

D B2 -25 ns 1st

2U A2 B1 -25 ns +25 ns 1st

2U A2+ -50 ns 1st

2U B1− +50 ns 1st

2D A1 B2 +25 ns -25 ns 1st

2D A1− +50 ns 1st

2D B2+ -50 ns 1st

good A1 B1 +25 ns +25 ns 2nd

good A2 B2 -25 ns -25 ns 2nd

TABLE III: The first three columns indicate the regions re-ferred to in the listed panels of Fig. 20 while the next twocolumns specify the actions taken on tcal 1, tcal 2, or both.The last column indicates the number of the correction stepas given in the text.

vel (cm/ns)18 19 20 21 22 23 24 25

Nor

m. Y

ield

0

0.05

0.1

0.15

0.2

FOPI-LAND=706.1 ns0t=707.6 ns0t=709.1 ns0t

FIG. 22: (Color online) High velocity tail of normalized ve-locity spectra for several assumptions on the time-zero valuet0 in comparison with the corresponding spectrum measuredin the FOPI-LAND experiment.

correction step has been conceived. It is based on the as-sumption that the coincident location of the two signalsof a hit in either regions ’A1’ and ’B1’ or in ’A2’ and ’B2’of their respective t17-vs-tcal maps is a strong indicationof a simultaneous jump. The correction step consists ofeither adding or subtracting 25 ns to both values tcal 1and tcal 2 of that hit, so that they fall into the centralregions of their maps. It is marked as 2nd step in the lastcolumn of Table III. It simply changes the arrival timesthit by 25 ns but leaves the position Ytime and its corre-lation with Yamp unaffected. The so obtained final thitdistribution is shown in Fig. 21 (bottom panel, in blue).

It is evident that the second correction step falselymodifies correctly measured cases of long or short timeswith time signals tcal 1 and tcal 2 accidentally falling intothe marked regions. Its effect is particularly large in theinterval 640 ns to 660 ns of the thit spectrum where itcauses a depression (Fig. 21, bottom panel). The ge-

23

ometric mean between the yields before and after thiscorrection would approximately represent a smooth timespectrum that would seem more probable. This level canbe reached if only about 80% of the hits near the centerdown to about 50% towards the edges of this region areactually moved in the second step while the rest of theselected candidates is left at their original arrival times inthe 640 ns to 660 ns interval. However, as it is not knownwhich of the hits should be moved and which should beleft at their time positions, a correction of this kind isnot properly feasible. It will smoothen the time spec-trum but, because of the necessarily random selection,an inevitable mixing of hits between the affected timeintervals will occur.

This situation was addressed by considering the frac-tion of randomly selected hits whose arrival times areactually modified in step 2 as an unknown correction pa-rameter. The time spectrum in Fig. 21 (bottom panel)and the comparison of flow results as a function of thisfraction with FOPI results (Fig. 12 in Sec. IV A) sug-gest a value of at least 40%. Apart from that, it remainsunknown and its significance for the differential flow ra-tios must be assessed. The result, a systematic variationof ∆γ = 0.05 as a function of this fraction, is shown inFig. 15 and discussed in Sec. V A. For the acceptance-integrated analysis based on time-integrated data sets(Sec. V B), the present corrections are of minor impor-tance because very few hits are actually moved across theboundaries of the integration interval.

Due to the logarithmic gain chosen for the newTACQUILA electronic board, the signals of low-energygamma rays fell below threshold with the effect thatthe calibration of the time spectra could not be basedon a measured gamma peak. The location of the zero-time-of-flight point t0 was, therefore, determined froma comparison of velocity spectra, generated with vari-ous assumptions on t0, with the well calibrated spectrumavailable from the FOPI-LAND experiment. The high-velocity part of the spectrum was found to exhibit themost distinctive variation as a function of the choice fort0 (Fig. 22). The presence of artificial peaks at arrivaltimes thit ≈ 677 and 702 ns (Fig. 21, bottom panel)limited the useful range to velocities vel > 18 cm/nsor Ekin > 230 MeV for nucleons. The rapid variationof the velocity spectrum with the choice of t0 permit-ted its determination with an uncertainty of the order of1 ns (Fig. 22). Its location at thit = 707.6 ns is markedin the spectrum of arrival times thit. As the displayed

times are measured with respect to a delayed commonstop signal, finite time-of-flight values are to the left oft0. Photons would appear at thit = 691 ns, indicat-ing that the yield at larger thit represents the level ofbackground and of hits that are still misplaced. Theinterval 18 ≤ vel < 25 cm/ns used for the compari-son corresponds to 680 ≤ thit < 688 ns, a region onlymildly affected by corrections. The same is true for themain group of recorded hits with arrival times betweenthit = 669 and 685 ns, corresponding to flight times be-tween 23 and 39 ns and to kinetic energies of 100 to400 MeV for nucleons (note that artificial peaks are re-moved).

The correction effects are stronger for arrival times be-tween thit = 642 and 663 ns, expected for nucleons withapproximately 30 to 70 MeV kinetic energy. The timespectrum in that region is strongly modified by the sec-ond correction step moving particles from this region intothe main group centered at thit = 680 ns (Fig. 21, bot-tom panel). The threshold energy of 60 MeV for pro-tons to pass through the veto wall and to be detectedin a LAND module is located within the affected region(thit = 659 ns). The same is true for the thresholds ofdeuterons and tritons, located at smaller energy per nu-cleon and correspondingly longer times-of-flight.

In order to be independent of the applied corrections,the acceptance-integrated result was obtained by inte-grating the time spectra up to thit = 640 ns, i.e. be-yond the critical regions. The maximum time-of-flight of67.5 ns defines a threshold of 30 MeV for neutrons. Itis lower than the physical thresholds for charged parti-cles, a condition that was equally applied in the UrQMDsimulations. Only double time jumps and backgroundevents, apart from the neutrons below threshold, cancontribute to the low-intensity region at thit < 640 ns.Possible systematic effects related to these effects wereinvestigated by varying the integration limit between617 < thit < 648 ns, i.e. flight times between 60 and90 ns, and by correspondingly adjusting the neutron-energy threshold in the calculations. The resulting vari-ation of γ is small as shown in Fig. 17.

It is once more noted here that the timing correctionsare applied to all particles independently of whether theyare charged or neutral. This has obviously reduced theirinfluence on the flow ratios that are used as the principalobservables, in agreement with the results of the testsperformed.

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