- Email: [email protected]
Measurement of the transverse energy flow in nucleus-nucleus collisions at 200 GeV per nucleon
Nuclear Physics B353 (1991) 1-19 North-Holland
E EASU TRANSVERSE ENERGY I NUCLEUS-NUCLEUS COLLISIONS A 2 eV E NUCLEON HELIOS Collaboration T. AKESSON 3, S. ALMEHED6, A.L .S . ANGELISZ°, N. ARMENISE ', H. ATHERTON ;, P. AUBRY8, H.W . BARTELS4, G. BEAUDOIN 8, J.M . BEAULIEU 8, H. BEKER T, O. BENARY 18, D. BETTONI 3. `', V. BISI 19 , I . BLEVIS 21 , H. BOGGILD 3- ", W. CLELAND 12, M. CLEMEN 12 , B, COLLICK 12 , F. CORRIVEAU 7, S. DAGAN 111, K. DEDERICHS3. c, S. DELL'UOMO ", P. DEPOMMIER8, R.C .E. DEVENISH 3.d , N. DiGIACOM0 5, S. Di LIBERTO 13 , J.R . DODD 21), B. DOLGOSHEIN "", A. DRESS4. H. EN'YO T, B. ERLANDSSON 17 , M.J . ESTEN Z°, C.W . FABJAN T. P. FISCHER4 , Z. FRAENKELZ 1 , A. GAIDOT' S, F. GIBRAT-DEBU 1 S, P. GIUBELLINO", P. GLASSEL4, U. GOERLACH ;, R. HAGLUND`', L.A . HAME12, H. van HECKE, V. HEDBERG ;, R. HEIFETZ1s , A. HOLSCHER 4, B. JACAK5, G. JARLSKOG `', S. JOHANSSON 6, H. KRANER 2, V. KROH 4, F. LAMARCHE 7, C. LEROY 7, D. LISSAUER 2.18, G. LONDON 15, B. LORSTAD", A. LOUNIS8, F. MARTELLI'"', A. MARZARI-CHIESA 1`', M. MASERA 1`', M.A . MAZZONI ; , E. MAZZUCAT07, N.A . McCUBBIN 14, P. McGAUGHEYS, F. MEDDI 1;, U. MJÖRNMARK6, 17 M.T . MUCIACCIA1 , S. MURAVIEV`', M . MURRAY 1 -, M . NEUBERT 4, S. NILSSON , L. OLSEN Z , Y. OREN 18 , J.P. PANSART 15 . Y.M . PARK 12 , A. PFEIFFER 4, F. PIUZ T, V. POLYCHRONAKOSZ, G . POULARD;, M . PRICE3, D. RAHM Z, L. RAMELLO L. RICCATI 19 , G. ROMANO 1 ~', G. ROSA ;, L. SANDOR T, J. SCHUKRAFT ;, M . SEKIMOTO T, `, B. SELLDEN 17 , M. SEMAN T.f A . SHMELEVAy, V. SIDOROV 11 , S. SIMONE, Y. SIROIS 7, H . SLETTEN T, S. SMIRNOV "', W. SONDHEIM 5, H.J . SPECHT 4, I. STUMER Z, J.W . SUNIER 5, V. TCHERNIATIN "°, H.H . THODBERG 3, J. THOMPSON 12 , V. TIKHOMIROV", I. TSERRUYAZ1 , G. VASSEUR 15 , R.J . VEENHOF3.1 , R. WIGMANST. g . P. YEPES7 and W.J . WILLIS T 1 University of Bari and INFN 1-70100 Bari, Italy 2Brookhaven National Laboratory, Upton, NY 11973, USA
.3 CERN, CH-1211 Geneva 23, Switzerland 4 Unit,ersity of Heidelberg, D-6900 Heidelberg, Germany SLos Alamos National Laboratory, Los Alamos, NMR7544, USA 6 Uriit-ersity of Lund, S-223 62 Lund, Sweden "Visitor at CERN from : Visitor at CERN from : `Visitor at CERN from : d Visitor at CERN from : `Visitor at CERN from : r Visitor at CERN from : g Visitor at CERN from : h ,Angelo Della Riccia" h
University of Syracuse, Syracuse, NY 13244-1130, USA. Niels Bohr Institute, DK-2100 Copenhagen 0, Denmark. Ludwig-Maximilians-Universität, D-8000 Munich 40, Germany. Oxford University, Oxford OX1 3NP, UK . Institute of Nuclear Study, Tokyo 188, Japan. Slovak Academy of Sciences, CS-04353 Kosice, Czechoslovakia . NIKHEF-H, NL-1009 DB Amsterdam, The Netherlands . Fellow .
~j550-3213/91 /$03 .50 ©1991 - Elsevier Science Publishers B.V . (North-Holland)
HELIOS Collaboration / Nucleus-nucleus collisions 7111cGill Unirersit,% Montreal, P 113.4 M Canada "Unirersity of Alontreal, Montreal PQ HC? 3J7 Canada ')Lebedei - hrstitute of Physics, SU-117924 Moscow, USSR 10 hrstinite of Plrysics and Engineering, SU-115409 Moscow, USSR "histitute of Nuclear Ph®'sics, 630 090 Not~c sibirsk, USSR
' 2Urrirersi4' ofPittsburglr, Pittsburgh, PA 1-5260, USA "Unh -ersity of Rome "La Sapienza " and INFN, 1-0018-5 Rome, Italy 14Rutherford Appleton Laboratona, Didcot OXI O X, UK 'DPIWE, CEN-Saclay, E-91191 Gij-stir-Yt-cite, France l tsUnirersity ofSalerno and INFN, 144100 Salerno. Ital®v 17Uniretsity ofStockholm, S- 11346, Stock-hohn, Siveden ,'Unirersity of Tel Ark, Ramat At ,& 78, Israel Unirersity of Turin and INFX, 1-101 Turin, Italy '"Unirersity Cohtge London, London RUE 6BT, UK `1 11'eizinann Institute, 76 1 Relrorot, Israel Received 5 November 19911 The transverse energy distributions have been measured for interactions of ' 2 S nuclei with Al, Ag, W, Pt, Pb, and tI targets, at an incident energy of 200 GeV per nucleon in the pseudorapidity region -0.1 < n g g, < 5 .5. These distributions are compared with those for 16 0-W interactions in the same pseudorapidity region and with earlier measurements performed with "'0 and ' 2 S projectiles in the region -0.1 < nian < 2.9. These comparisons provide both a better understanding of the dynamics involved and improved estimates of stopping power and energy density .
1. Introduction The measurement of transverse energy produced in nucleus-nucleus collisions at high energies allows the selection of collisions yielding very dense hadronic matter. If the energy density is high enough, the hadronic matter may undergo a phase transition into a state of deconfined quarks and gluons [1]. The energy densities reached depend, among other factors, on the degree of stopping which occurs in each collision . This article presents the results of our measurements on the transverse energy (ET) with a nearly complete coverage of pseudorapidity. The maximum energy densities achieved in '60 and 32 S-W collisions have been previously estimated [2,31 from the measurement of the maximum transverse energy in the backward region and from using estimates of the relative contribution of ET in the forward region . The new measurements provide a check on the validity of these estimates . In addition, the study of the event-by-event correlation between the forward and backward transverse energies as a function of the full E T sheds light on the reaction dynamics . The dependence of the da/d ET and the d ET /dry distributions on the target and projectile is studied. Estimates of the maximum stopping and energy density reached in '6O-W and 32 S-W collisions are also obtained from the maximum value of the total transverse energy measured in the full region .
EL
ration / Nacleas- nucleus coll i ns
ee
I
31
t
The H LIO (High-Energy ton a IOn Spectrometer) detector measures the transverse energy in the backward region using r i iron /scintil ator sampling calorimeters, niu /li ui -argon calorimeter e is define for ® .1 < 'zh 2.9, whereas the forward transverse energy s ) is defined for 2.9 < l.,, < 5.5 a the "'11" r e uranium/ i til at r calorimeters have a 2 2 t the electromagnetic and a ronic sections. e li r ti analysis of the scintillator calorimeters have been described elsewhere The electromagnetic (e.m.) part U starts 3. downstream fr, target and has a 5 cm diameter hole to permit the projectile fragments to pass without interactions. This section as 1920 towers, t f them 2 2 c for larger guard areas around the periphery o its acceptance, sections in depth, 7 and 14 radiation lengths, respectively. The hadronic (had) section, just behind the e.m. section, has no hole, it as 2.5 c wide strips i the horizontal and vertical directions transverse to the beam, an it is divided i e into three sections, each about 1 .5 interaction lengths deep. e G was calibrated with electron and pion beams of momenta of 17, 5, 7 and 2 GeV/c. The calibration showed an average e/- ratio of about 1 .1 + 0.03 and a adronic energy resolution of o,/E(GeV) = 0.015 + 0.45/ ~_ E for fully contained showers. Downstream from the target, a set of three silicon ring counters (R ,, R,, and R3) [3,51 are used, as indicated below, to separate target interactions from background generated in the beam-pipe window, in the air, and in the detectors themselves .
3. The data sets During the 1987 HELIOS runs, the following numbers of triggers were collected: 15 000 O-W, 19 000 S-Al, 22 000 S-Ag, 264 000 S-W, 24 000 S-Pt, 15 000 S-Pb, and 23 000 S-U. The samples of sulphur events were filtered to remove (a) events with two simultaneous beam particles, characterized by an anomalou 3 measured total energy, (b) upstream interactions, characterized by highly correlated hits in the ring counter detectors [3], and (c) downstream interaction :, characterized by MR3 > 1.1 MR , + 10 and MR, < 40, where MR3 and MR , are the multiplicities of the most downstream and the most upstream ring detector, respectively . The oxygen sample was filtered using cuts similar to those used in ref. [2]. The remaining contamination is removed by the subtraction of spectra obtained without any target [3]. This contamination is negligible for the highest values of ET, but amounts to typically 20% for ET < 25 GeV.
HELIOS Colhibortition / Nuclells-11"clel's colli-violls
4
lysis
t
is calculated by a weighted sum of the The forward transverse energy E"' T energies found in individual towers of the e.m.section and in individual strips of ft"T the ha&oWc section of ULAC: E T mE TF"(e .m.)+ETf )"(had) [6] . The erra. contribution to ET'"' is straightforward :
E," (e .m .) .
where si is the sine of the polar angle of the ith tower, measuring energy Ei. is complicated by the lateral spread of the The hadronic contribution to E~" T showers due to the projectile fragments. To understand this effect, we have studied the shower profiles produced by sulphur ions and protons interacting at the centre of the hadronic section of ULAC. The average shower profiles for protons and sulphur ions are quite similar (fig . 1). The two central strips are excluded from the determination of ET", limiting the pseudorapidity acceptance to 77 < 5 .5, but the measured energies in these strips are used, event-by-event, to correct for leakage into neighbouring strips of the energy deposited by nuclear fragments. To correct approximately for this leakage, the hadronic contribution to ET' is experimen-
a)
b)
C(U21 0 .8
0 .8 0 .6 0 .4
flu
0 .2
0
w
2
4
6
Strip number
8
10
0 .2
0
2
4
6
8
10
Strip number
Fig . 1 . The energy of the neigl*ouring strips compared with the central strip in the ULAC as a function of strip number : (a) for incident 32 S at 200 GeV per nucleon, (b) for incident 200 GeV protons . For a strip, the energy is summed for the three hadronic sections .
DELI®S Collaboration / Nucleus-nescleus collisiot:s
5
tally defined as E"I(had)
= 2[
Xi(E.,, -,Bi E.,,,) +
Yj(E,.~
where Xi (Y) is the sine of the polar angle of the geometric centre of the ith x-strip ( jth y-strip), E., , (EY) is the energy measured in that strip, and ßi (j3) is the fraction of the energy of the central energy slab energy E, r,, (E,. ) in the ith ( j th) strip as determined in fig. 1 . Assuming azimuthal symmetry, the factor -r/2 corrects for the effect of the cartesian readout of the hadronic section of ULAC. The correspondence between the experimental definition of ET' and the true one has been investigated in a Monte Carlo simulation. We used an event generator [2], to which was added the fragment simulation of ref. [7] in order to determine the sensitivity of E T to projectile fragments, to the particle mix, and to 104
103
0
10
w
b
10-1 10-4 1 0
100
200
300
400
500
ET IGeVI
per Fig. 2. Transverse-energy differential cross section, dur/d ET , in the full region for 200 GeV nucleon 32 S on AI, Ag, W, Pt, Pb, and U collisions.
HE1.IOS Collaboration / Nucleus-nucleus collisions
6
the momentum distributions. The converted energy is defined as the kinetic energy of the baryons and the total energy of all oth-: particles including the antibaryons . The calorimeter simulation included the response to different particles (e 1 70, the " energy leakage (affecting the energy scale), and the resolution (affecting the shape). The evaluation of the systematic uncertainty included that already evaluated for the backward direction C7.1%) [2] as well as the errors in the evaluation of the forward E T, which were due to the following : subtraction of leakage of fragment energy (2%), calibration (2%), particle composition (3%), and e/-7r ratio (3%). The combined systematic uncertainty on the ET" scale is 5.0%. Our data TABLE 1
The transverse-energy differential cross section dQ/d ET in the full region for 200 GeV per nucleon 32 S-Al collisions ET [GeV]
Bin half-width [GeV]
do-/d ET [mb/GeV]
Error [mb/GeV]
36 .5
2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4
9.94 x 10' () 9.07 x 10 + " 9.13 x 10' ° 9.27 x 10"' 8.62 x 10 +° 8.75 x 10 + " 7.07 x 10 + ° 6.87 x 10" ) 6.75 x 10 +° 5 .41x10+° 5 .65 x 10' () 5 .69 x 10+" 4.96 x 10'() 4.81 x 10+" 4.74 x 10'() 4.50x10"' 3.97 x 10+" 3.74 x 10 +" 2.98 x 10+ ° 2.94 x l0'" 2.41 x 10 +" 1.76 x 10 +° 1.92 x 10 +° 1.44 x I0,() 1.02 x 10 +() 5.31 x 10 - ' 4.90 x lo -, 3.99 x 10 -1 2.40 x 10 - 1 1 .15 x 10 - ' 6.07 x 10 -2 2.92x10 - '1 .23 x 10 -2 4.08 x 10 -3
4.68 x 10 - ' 4.52 x 10 - ' 4.44 x 10 - ' 4.35 x 10 - ' 4.16 x 10 - ' 4.12 x 10 - ' 3.77 x 10 - ' 3.71 x 10 - ' 3.57 x 10 - ' 3.26x10 - ' 3.20 x 10 - ' 3.16 x 10 - ' 2.87 x 10 - ' 2.79 x 10 - ' 2.70 x 10 - ' 2.61x10 - ' 2.45 x 10 - ' 2.38 x 10 - ' 2.11 x 10 -1 2.07 x 10 -1 1.87 x 10 - ' 1.72 x 10 -1 1.72 x 10 -1 1 .49 x 10 - 1 1.24 x 10 -1 8.87 x 10 -2 8.66 x 10-2 8.99 x 10 -2 7.43 x 10-2 4.19 x 10 -7.83 x 10 -3 6.21x10 - ; 4.74 x 10 - ; 3.71 x 10 - ;
41.4 46.2 51.1 56.0 60.8 65.7 70.6 75.4 80.3 85.2 90.0 94.9 99.8 104.6 109.5
114.4 119.2 124.1 129.0 133.8 138.7 143 .6 148.4 153.3 158.2 163.0 167.9 172.8 177 .6 182 .5 187.4 i92.2 197.1
HELIOS Collaboration / Ntcletts-nucleus collisions
on the almost symmetrical system 32 S- 2'AL were use to check r evaluation ETack ET°`~ relative to as a function of ET, and was found to e consistent with. the expectation . To compute the pseudorapidity density of E T, a pseudorapidi st be attributed to each channel of ULAC . There is a unique pseudorapidi for each tower of the e.m. section, but each strip of the hadronic section covers a rather large range of pseudorapidity . The Nlonte Carlo calculation shows that the pseudorapidity is correctly measured, on the average, if we give each strip the pseudorapidity of its centre minus 0.31. An effective pseudorapidity resolution of 0.~ in most of ULAC and of 0.4 near q = 5.5 is attained .
TABLE 2
The transverse-energy differential cross section do,/d ET in the full region for 200 GeV per nucleon 32 S-Ag collisions ET [GeV]
Bin half-width [GeV]
4 .7 14 .1 23 .5 38 .1 51 .7 61 .1 79 .9 108 .2 127 .0 145 .8 164 .6 174 .0 183 .4 192 .8 202 .2 211 .6 221 .0 230-4 239 .8 249 .2 258 .6 268 .1 277 .5 286 .9 296 .3 305 .7 315 .1 324 .5 333 .9 343 .3 352 .7 362 .1
4.7 4 .7 4.7 9 .4 4.7 4 .7 14.1 14 .1 4.7 14 .1 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7
da/d ET [mb/GeV]
Error [mb/GeV]
x x x x x x x x x x x x x x x x x x x x x x x x x x
2.58 x 10 +2 6.59 x 10 + ' 3.07 x 10 +0 1 .95 x 10 + " 2.69 x 10 +° 2.50 x 10 +° 1 .17 x 10 +° 8.78 x 10 - ' 1.49 x 10 +° 7.80 x 10 - ' 8.83 x 10 - ' 9.89 x 10 - ' 1.10 x 10+ ° 2.08 x 10 - ' 2.08 x 10' 2.08 x 10' 1.96 x 10 - ' 1 .92 x 10 - ' 1.83 x 10 - ' 1.76 x 10 - ' 1 .72 x 10 - ' 1.67 x 10 - ' 1 .42 x 10 - '
3 .30 8 .22 2 .36 1 .54 8 .91 9 .53 4 .83 2 .76 6 .02 4 .40 3 .64 4 .31 4 .65 4 .15 4 .15 4 .14 3 .65 3 .51 3 .17 2 .97
2 .72 2 .66 1 .92 1 .65 9 .89 5 .40 3 .48 x 1 .78 x 7.33 x 2 .33 x 8.69 x 1 .33 x
10 +10 + ' 10 + ' 10 + ' 10 +° 10 ' + 10 +° 10 +(' 10 +° 10 +° I0+ ° 10 + " 10 +° 10 +° 10 +(' 10 + " 10 +° 10 +° 10 +° 10 +° 10 + " 10 +0 10 +° 10+ () 10 - ' 10 - ' 10 - ' 10 - ' 10 -2 10 -2 10 - ; 10 -3
1.31 x 10 -1 1.01 x 10 - ' 7.43 x 10-2 2.24 1 .58 9.88 4.01 2 .25 9.41
x k x x x x
10-2 iÛ -2
10 --'` 10 --3 10 - ; 10 -4
8
L.1~~~ C~~lhal~c~atat~rara
,~ a~laac°Ic'ate-raatc°la.~aa~+ ~°~~lllslc~aa~ r,a~t ~ 3
/d ~~- in flee full region `i e crans`°erse¢cnergy differential cross section for 2(i0 GeV per nucleon ?`S-V~ collisions E~ [Ge`']
13in half-®vidt [GeV]
da~/d ~~- [ b/GeV]
32,9
4.7
1 .25 x 10+'
136.4
4,7
42,3 51,7 61 .1 70.5 79.9 59,4 95.5 105.2 117.E i 27 .0 145.8
164.E 174.0 183.4 192 .8 202.2 211.E 221.0 230,4 239.5 249,2 258,6 265.1 277, i 256.9
29b .3 305 . 7 315 .1
324 .5 333,9 343 .3 352.7 362.1
371 .5 38(1 .9
390,3
399,7 409.1 415.5 427,9
437 .4 446 .8
456,2
~rror [ b/GeV]
4.7 4,7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4, 7
1 .58 x 1 .13 x 1.00 x 1 .06 x 8.97 X 5 .63 x 7.10 x 6.02 x 7.11 x 7 .66 x
4.7
7.38 x 10 +"
1.75 x 1 .45 x 1 .45 x 1 .32 x 1 .24 x 1 .OU x 9,91 x 8 .68 x 7.87 x 6.82 x 4.75 x 3.68 x 3.25 x
4.7 4.7 4.7 4.7 4.7 4.7 4 .7 4, 7 4.7 4, 7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7
6.76 x 10 +" 6.19 x 10 +° 5.98 x 10 +" 6.18 x 10 +" 6A6 x 10 ~ ° 5 .14x10 1 " 4.61 x 10 +° 4.67 x 10 +" S .IO x 10 +" 4.98 x 10 +" 4 .93 x 10 +° 4.99 x 10 +" 4 .96 x 10 +" 4.81 x 10 +" 4.66 x 10 +" 4.32 x 10 +" 4.06 x 10 + " 3.70 x 10 +" 3.14 x 10 + " 2.46 x 10 +° 1 .79 x 10 + " 1 .18 ~: IOY" 7.95 x 10 - ' 4.73 x 10 - ' 2 .79 x 10 - ° 1 .34 x 10 - ' 6.12 x 10 - 2 .84 x 10 --' 1 .28 x 10 --'
3.15 x 10 -' 3.02 x 10 - ' 2.96 x 10 - ° 3.02 x 10 -' 3.00 x 10 -' 1.11x10 - ' 7.95 x 10 - ' 7.93 x 10 - -' 7.11 x 10 --' 7.02 x l 0-6.97 x 10 -7.02 x 10 -7.05 x 10 -' 6 .90 x 10 6.77 x 10 6.49 x 10 - -' 6.32 x 10 -2 4.17 x 10 3.85 x 10 --' 2 .71 x 10 - ~ 2.32 x 10 --' 1 .33 x 10 - ~ 1 .08 x 10 - ' 8.32 x 10 --' 6.38 x 10 - ; 4.38 x 10 2,93 x 10 2.03 x 10 - ; 1 .38 x 10 --~
4.7
l .49 x 10 - ; 5 .80 x 10 - `'
8,65 x 10 - ~ 3.36 x 10 - ~
4.7 4.7
10 + ° 10 + ' 10 +' 10 +' 10 +" 10 Y ° 10 +" 10 +° 10 +" 10 +"
6.78 x 10 +"
3.48 x 10 - ;
10+° 10 +" 10+" 10 +" 10 +" 10 +" 10 t" 10 -' 10 - ' 10 - ' 10 -' 10 -' 10 -'
7.47 x 10 - ;
S colla ration / Nucleas-nucleits colfisions
5.
Its
5.1 . TARGET DEPENDENCE
The differential cross sections da/dET in the full region are presented as function of ET in fig. 2 and in tables 1-6 for collisions of -32 S with various targe nuclei at an incident energy of 200 GeV per nucleon. For all targets, the distributions have the shape that was previously observed for incident oxygen a sulphur beams in the backward region [2,3]: a plateau (shorter for the A] target) followed by a steeply falling tail .
TABLE 4 The transverse-energy differential cross section dar/dE T in the full region for 200 GeV per nucleon ;2S-Pt collisions ET [GeV]
Bin half-width [GeV]
da/d ET [mb/GeV]
Error [rnb/GeV]
319 61 .1 814 117.6 145.8 1710 2012 221.0 230.4 2348 2442 258.6 268.1 277.5 286.9 296.3 305.7 315.1 3215 333.9 343.3 3517 362.1 371.5 3819 390.3 399.7 4011 418.5 427.9 437.4 46 .8
14.1 14.1 14.1 14.1 14.1 14.1 14.1 4.7 17 4.7 4.7 17 47 4.7 47 17 17 17 4.7 17 17 4.7 17 47 17 4.7 17 17 17 4.7 17 17
1 .39 X 10' 8 .23 X 10+°' 9.31 X 10"' 9.29 X 10" ) 6.30 x 10' ( ' 6.40 X 10"' 6.81 x 10+ 1) 5.93 X 10' 5.93 X 10' 5.30 x 10 +" 4.53 X 10` 5.43 X 10"' 5.51 x 10+ 1) 4.86 X 10+" 5.27 X 10'° 5.25 X 10 " 4.66 X 10+() 5 .26 x 10+(' 4.71 X 10' 3.72 X 10 + " 3 .61 X 10 +) 2.85 X 10' 2.07 x 10+ 11
7.63 X 10 - " 1.77 X 10 -e 1 .54 X 10" ) 1 .35 X 10 - 'e 1 .10 X 10l le 1 .03 X 10' 1 .05 X lo', 3.38 X 10+ 1 3.38 X 10- ' 3.19 X 10- 1 2.95 X 10 -1 3.23 X 10 -1 3.26 X 10 - ' 3.06 X 10 - ' 3.19 x 10 - ' 3.18 x 10 - 1 3.00 X 10' 3.19 x 10 - ' 3 .02 X 10' 2.68 X 10 - ' 2 .64 X 10 - 1 1 .05 X 10' 8 .89 X 10 -'7.12 X 10 -2 5.68 X 10-'4.10 X 10-2 2.91 X 10 ` 2.34 X 10 - 2 1 .29 X 10-, 3.46 X 10 -3 2.57 X 10 -3 1 .57 X lß - '
1 .34 x 10 -4)
8 .63 X 10- ' 4 .56 X 10- 1 2 .35 X 10- ' 1 .56 X 10- 1 4.83 X 10 -2 1.42 X 10 -2 8.12 X 10 -3 3. 1.4 X 10 - -3
-allon / Nucleus -- nucklo cafli's 'MR t 3 dtr/dEf in the full region for The ttmovevse-enetg~, 200 GeV pet nucleon 12S-Pb collisions
f-mvidth
412 511 10,2 .7 162.2 221,2 231 1 .0 M7 27M4 2W 3%7 3145 3244 3342 349 .0 350) 3617 3745 38&4 3W 40&0 AM 4217 4414
19 4.9 117 117 117 117 117 01) 19 19 19 19 it) 4.19 4.9 4.9 19 19 4.9 19 19 19 4.9 4.9 19 19 4.9 19 4.9 19 18
WeVI las X au I= X 1"
VA I X
I
.
lui
~ 41
S33 X Io , 6m4 X lo" , 7.(lh X 10 ' 5. Î9 X 10 610 X Io -,, 6ag X Io "I 5.40 X 10 , 'l 5cq X 1(1+I 9 5.73 X lo' , S. ',s X Io -,, 523 X lu - " 5.57 X 10"' SAU X lu -Il 4.95 X lo' , 539 X Io", 37 X 10 4AI X 10"' 435 X 10"' ,.60 X Io 2.79 X 10 L79 X Ur' 1.29 X 10"' smi X Io -, 3 .34 X 10 134 X 10 -5.20 X 10 - 2 2.30 X 10 -2 93(1 X I o-
1 .4.1
1
n-40
a n-0
wo I n -40 sm s X Io -, SA7 X 10 177 X 10 421 X 10 -1 7.64 X 10 -1 7M3 X 10 -1 Til X Io -, M X 10 -1 2AS X 10 -1 2AO X 10 -1 237 X 10 -1 2A7 X 10-1 2A6 X 10 -1 231 X 10-1 2A5 X 10- 1 2AI X 10-1 213 X 10 - 1 2.17 X 10 1 .97 X Ur' 113 X 10 -1 1.38 X 10 - 1 121 X Io -, 4M2 X 10- 1 141 x 10-2 136 X 10-2 9m5 X 10-2 W x 10-3 9.30 X 10-3 I
iaximum Ques of ET obtained in the full region (from ET 21-' 190 GeV Or o E-, ~ 470 GeV Or 32 S-U) are subtan6ally larger than the values Ou 31 in the back-waTd region 94 GeV and = 339 GeV, respectively) . The E T sured with full coverage, relative to that in the backward region, increases sistently more for average central collisions (defined as the value of ET for \%hich da/d is half the plateau value) than for the high-ET tail. For example, i S-W Collisio 200 GeVner nucleon, the extension from the backward to the ses ET for average central collisions from 198 to 327 Ge eV in the tail (fig . 3). The ET distributions for 200 GeV per W targets are compared in fig. 3 with the predictions of the IS 3).05 193 event generators. FRITIOF uses independent
~ä~~~ ~
r r~ ~l
37 .6 51®7 61 .1 70 .5 79. 98.8 117.E 136.4 155 .2 164.E 174. 183 .4 192 .8 2 2 .2
211 .E 221 .0 230.4 239.8 249 .2 258 .6 268 .1 277 .5 285 .9 296.3 305 .7 315 .1 324.5 333.9 343.3 352.7 362 .1 371 .5 38 .9 3 3 399.7 4 1 -118.5 427.9 -i37.4 6,8 -156,2 5,6 475, 4
9 .4 4a7 4 .7 4 .7 4 .7 14 .1 4.7 14.1 4.7 4.7 4.7 4 .7 4 .7 ~1 .7 4 .7 4 .7 4.7 4.7 4.7 4.7 4.7 4 .7 4 .7 4 .7 -1 .7 4.7 4 .7 -1.7 4.7 4.7 4.7 4.7 4 .7
"tp~~~~4~~,~~~~p
~~ ~
9.72 1. 6 .81H .36 4 .62
°~ee~~~
~~~~~b~~~~~~~
~
~ 11~~~
x 1
x x x x 6.20 x 4 .12 x 3 .82 x 9.24 x
1 1 1
°aa 10°~a
l0 `a" 1 T aa 10'~~ 1 ° ~a -~~ 5 .5x1 °~a 5.95 x 1 6.83 x 10" r` - ~a 3.36 x 1 5.68 x 10°~ a 6. x !0°~r~ °aa 5 .49 x 10 `"a 5 .77x 1 5 .&5 x 1®' aa 4 .99 x 10 -aa 5 .92 x 1 ` aa S .D7 x 10 - ~a 5 .55 x 10 -6a 5.52 x 10 -aa 5.79 x 10` p `~ 5 .88 x 1 -~a ae 5 .47 x 10` -Fa 4 .43 x 10 T ar~ -# .92 x 1 4 x 10 -aa +°a 3 .57 x 10 - ar, 2.62 x 1
-c'a
4.7 -1,7 .H .7
2.11x1 x l -~ 1. ..ct 1 .18 x 1 6.82x 1 -° -~.43 x 10- c _c 2 .~r1x1 1,73x 1 -° 8 . a x H~~ -= ~,33 x 10 - T .13 x 10 -
~ .7 -H .7
~.59x 10~~
4 .7 4 .7 -1 .7
4 .7 -1.7 407
6.3~9 x 1 6.6P' x D ° 4 .91 x 10 r~ 3. x 10' r ~ 2. . x 1 °E~ 3.07 x D 0 °
2.95
2.29 x 10` r 2 .34x 2.25 x 2 .3~3 x x 1. 2.05 x 4.45 x 4.D6~ x
10~ ar 10 ~ cr ~ ° ~r fr DO° cP D0~° DO" c 10° a D0_ a 10" a DO- a DO` H ¬H- a DO - ~' D0_ a
4.14x 4.05 x 3.85 x 4.D9 x 3.92 x 4. x 4. x 4 .D0 x -1 .D4 x DO -° 3.9 x 1 - a 3 .59 x 10- a 3.78 x 10 " ~ 1 .53 x 10" ~ t' 1. x 10c 1. x 10~ 1 .1Ox10~~ 9 . ' ~ ~ 10 - t' 8. x HO~ r 6 .ZZx 10~~ 2 ~0 x DO 1 .~#1x10 -® 1 .5~5, x 1C~~ d 1 .E0 x DO" m 7.55 x D
-D, 3~ D~~
12
HELIOS Collabortition / Nucleus-nucleus collisions -0.1
0
100
200
300
ET AT
400
500
Fig. 3. The differential cross section duld ET for 32 S-W collisions at 200 GeV per nucleon in the full (A) . forward (v), and backward W regions. The predictions for FRITIOF (continuous line) and IRIS Washed line) are shown for the backward and full regions . Also shown is the IRIS prediction (dashed line) for the forward region . The horizontal error bars indicate the systematic error of 717i on the ET scale. nucleon-nucleon interactions, whilst IRIS is based on colour exchange, with the dual parton model [91 as the starting point. Both models use the Lund fragmenta-
tion model [10] . The ET in the forward rapidity region is somewhat overestimated in the tail of the distribution by the IRIS generator. In the full and backward regions, and for both projectiles, the models reproduce the plateau in a satisfactory
fashion, but fall short, by about 15%, of describing the extent of the tail . This may
be due to an underestimation of the stopping power and/or to cascading in the target nucleus, not included in the models .
The target mass dependence of E"n"" can be fitted to the form A"" [2,3]. The T value of a varies with the pseudorapidity window and decreases from a = 0.5 in
the back-ward
region [3](0.48 ± 0.02 and 0.53 ± 0.04 for '6 0 at 60 and 200 GeV per 32 nucleon, respectively, and 0.53 ± 0.05 for S at 200 GeV per nucleon), to a = 0.39 32 + ON (W S at 200 GeV) in the full region . The latter value is closer to a = -L 3 expected from naive scaling with target nucleus thickness, and was also reported
0
HELIOS Collaboration / Aluclens-nuclens colfi_%
the WA80 and NA35 [111 experiments. The rise of E~"' interpreted as a sign of "partial stopping", since, in the case of full s Ecentral would cease to rise beyond a certain size of the target. T Full stopping, however, is observed at lower energies, e.g. at BNL in collisi VsNN = 5 GeV, already in medium-size nuclear targets [121. 5.2. FORWARD VERSUS BACKWAR
TRANSVERSE ENERGY DEPOSITI
Fig. 4 shows a contour plot of the event-by-event differe I c Ss sect ETback versus for S-W collisions . The most probable Ell is proportional to ETf" T ntral , ETback up to a value close to ET where the sulphur nucleus fully overlaps the ET target . Beyond this, ETfo' appears to be saturated and is independent of ETback This saturation can be interpreted in several ways: for example, (a) after full overlap, the number of participating projectile nucleons no longer increases, while that for the target continues to increase ; the backward rapidity shift occurring when more target nucleons are participating forces ETfo'IET to decrease, so that Efo' is approximately independent of ETback at large enough E-r, T, or (b) the production mechanism for ETf" is independent of the production mechanism for
i i
2P.-
UJ
320 280 240 200 160 120 80 40 0
40
80
12O
160
200
Forward/backward contour plot
240
28
320 OTI-,11ft (GeV1
Fig . 4. Contour plot of the differential cross section d2or/(dEfa`IEIV I ) for the production of E-F in the backward region, and of E T in the forward region at 200 GeV per nucleon . Successive contours are separated by a factor 1 /e. The IRIS prediction for one contour is shown as a dashed line .
HELIOS Collaborinion J1
1
A'ucleus -nuclcus collisions
S prediction for one of the contours is shown; e overshoot in is apparent an there is less saturation i the prediction . Perhaps this is a consequence of an underestimate of stopping and/or cascading. T of the -fr"' distribution to be considerne would expect the tails of r,/ ably steeper than those of back, an fig. 3 shows that this is indeed the case . The /E~l" is determined only saturation of E" means that the width of the tail o y the event-to-event fluctuations n E~" and is independent of the S- geornet . The widths of the contours of fig. reflect the magnitude of the event-to-event fluctuations of" versus E back . Analysis of the contours shows that for central collisions the r. .s. width of the event-to-event fluctuations in ET " is 12-15 GeV, or about 10%. The contour widths do not depend strongly on the transverse ° '°'`
k
[I .1] .
~tom
TABLE 7 The transverse-energy differential cross section da/d E-1- in the full region for 200 GeV per nucleon "'O-W collisions E T [GeV]
Bin half-width [GeV]
do-/d ET [mb/GeV]
Error [mb/GeV]
124 .6 129 .3 134 .0 138 .7 143 .4 148 .1 152 .8 157 .5 162 .2 166.9 171 .6 176.4 181 .1 185 .8 190.5 195 .2 199 .9
2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2.4
6.92X10 + " 1 .05 X 10" 9.71 X 10 + ` 1 9.34 X 10 +° 1 .04 X 10" 8.58 X 10 +° 8.97 X 10 +° 7.05 X I0+()
2.31X10 +° 1 .00 X 10 +° 9.67 X 10 9.48 X 10 1 .00 X 10 +° 9.10 X 10 -, 9.31 X 10 - ' 8.25 X 10 -1 8.69 X 10 -1 7.91X10 -1 8.25 X 10 -1 7.48 X 10 -1 7.95 X 10 -1 6.88X10 -1 7.57 X 10 -1 6.64 X 10 -1 6.48 X 10 -1 4.67 X 10 - 1 4.45 X 10 -1 4.22 X 10 -1 1 .42 X 10 -1 1 .29 X 10 -1 1 .13 X 10 -1 8 .23 X 10-2 7 .30 X 10-2
204 .6 209 .3 214 .0 218 .7 223 .4 218 .1 232 .8 '37 .5 242.2 246 .9 2_>1 .6 256.3 265.7 270.4
2.4 2.4 2.4 2.4 2.4 2 .4
7.82 X 10 +° 6.47X10 +° 7.05 X 10 +° 5 .79 X 10 +° 6.56 X 10 +° 4.91X10 +° 5 .96 X 10 +° 4.60 X 10 +° 4.40 X 10 +° 2 .29 X I0+() 2 .09 X 1 .89 X 1 .07 X 8 .96 X 6 .86 X 3 .68 X 2 .92 X 1 .27 X 7 .16 X 3 .55 X 3 .51 X 1 .03 X 3 .38 X
10+ ()
10 + " 10 + " 10 - ' 10 -° 10 - 1 10 - 1 10 - ' 10 -2 10 -2 10-2 10 -2 10 --'
4 .78 3 .58 2 .51 2 .48 5 .93 3 .38
X X X X X X
10 -2 10 -10 -2 1()-2 10 -3 10 - ;
S Collaboration / Nucletes- uclens collQsions
energy; the fluctuations about 1 eV.
T r``
or peripheral collisions (low, values of
'r
5.3. PROJECTILE DEPENDENCE
Comparison with the data taken with incident 16 illustrate the e e e ET production on projectile mass. The ET differential cross section for collisions is given in table 7 and compared with that for 32S_W collisions in fig. 5. 32S '6G The increase of ET for over is 62% for average central collisions an 55% in the tail. An estimate of the maximum stopping fraction S can be obtained from the ratio S(ET) --- ET/ETa''. We determine Ea"a'' by distributing the available energy according to our measured d ET/d r7 for the highest ET [141 [where Eavail = VFS m(Np + Nt) is the available centre-of-mass energy, with s = 2 x 2 x NP x , x GeV2 ; NP and Nt are the number of participating projectile and target nucleons, respectively, and m is the nucleon mass]. The values of S for ET such that da/d ET reaches 10-4 times the plateau value in the full region are reported in 104 103 102 10
w E
W
10-1 10-2 10-3 'In-4
0
100
200
300
ET (GeV)
400
Fig. 5. Comparison between the ET distributions over the full region for 16Oat 2 GeV per nucleon.
500
and ~?S-
(A)
_~~~~ ~t)~~a7~)i))CJlld)13
1()
°ihc~
r
ä~tl(°~('1tS--l11Q(°~('dl " (°t)~~ISId)1t,S
m:~xin~un' stopping fractions (S~ ,) fur ~~°(~- W (at 200 GeV per nucleonD sand for collisions of '°S on Al, Ag. W, Pt, Ph, and U (at 20() GeV per nucleon) in -0.1 < risah < 5.5
E~ [GeVI ET`"' [GeV) Sn, .,~
®-W
S-AI
S-Ag
S-W
S-Pt
S-Pb
S-U
264 300 O.SS
192 343 i).56
;53 420 i1,84
445 502 0.88
435 504 0 .87
432 506 0.86
472 530 0.89
table 8 for various projectiles and targets. It is seen that S increases with the target thickness but does not vary much with the size of the projectile . A similar calculation shows that even at an incident energy of 60 GeV per nucleon the full stopping limit ( S = 1) is not reached . The energy density can be estimated, assuming that the initially available energy is deposited in the relevant interaction volume V, often taken to be the geometric orentz-contracted volume . The energy density ~ = y( ET ras V ) (where y E~<<;~,~/ >~) is = 5.5 GeV/fm' and ~ b.8 GeV/fm~ in the tails of the ~~O-VV and '~S-~V distributions, respectively, consistent with earlier estimates [2, 3]. See subsect . 5 .4 for another estimate .
70
140
0-W
120
r\
60
\
229 .4
0
160 .E
1
~
100
-
W Z
\
60 40 20
Pig. fi. I~àstribution of E-r as a function of pseudorapidity, normalized to the number of events, for three values of E-r in the full region (plateau, shoulder, and tail) at 200 GeV per nucleon for (a) ~`' -tip' and (b) '~S-W collisions . IRIS predictions (dashed lines) are shown for E-r values at the same dQ/d ET as the corresponding data.
HELI S Colla
ration / Alucleus-nucletts colfision
5.4. PSEUDORAPIDITY DISTRIBUTIONS
The pseudorapidity distributions for 16 0-W and ;2S_W collisions are sh fig. 6. Whilst the shape of the distribution for each projectile in the bac region does not change very much with increasing ET9 most of the increase of is in this region. The relative contribution of the forward region changes with the projectile mass and with ET . For both projectiles, fig. 7 shows that the average pseudwapidity shifts forward with increasing projectile mass and shifts backward
3 .2
1
1
F
A
O-W 200 GeV
S-W 200 GeV
3 .0 2 .8
13
j3 0130 130
2 .6
1
0
13
0
8
0
0
2 .4 2 .2 0 L
100
200
1 .8
300
0
400
0
100 (GeV)
ET
300
400
500
O-W 200 GeV
S-W 200 GeV
1 .6
200
1 .4 E1 .2 1 .0 0 .8
Isotropic limit
0 .6
100
0
200
160
X
1
300
L
400
100 0 ET (GeV)
200
300
400
500
O-W 200 GeV
S-W 200 GeV
120
E
LLJ
0
-
40 0
00
-
0
-
100
'1140 0 0
0 0
200
300
400
0 100 Q (GeV)
200
300
400
500
Fig . 7 . The first and second moments of the pseudorapidity distributions as well as (dET/dT7),,, ;:! versus E T in the full region for "O-W and S-W collisions. The solid line indicates the F prediction .
is
HELIOS Collaboration / Nucleus-nucleus collisions
The maximum dE T /d-q value rises somewhat more rapidly with increasing than ET* The comparisons to IRIS, shown in fig. 6, are made with samples for ET values corresponding to the same da/dE T as the data. The trend is the same for both projectiles : there is a large underestimate in the backward region for all Ef"" T region but predictions are good for the plateau whiist, in the forward region, the there is an increasing small overestimate as ET"" increases . An estimate of the error in the energy density determined above can be obtained by calculating the energy density in the 13jorken longitudinal hydrodynamic limit [15]: - = I/AT(dET/d-q)mav where A is the cross-sectional area of the (smaller) projectile and -r is the expansion time, whose value is traditionally assumed to be = I fm/c. The corresponding values in this limit are - 3 .0 GeV/fM 3 and - 3.4 GeV/fM 3 . In fig. 7 we also give the r.m.s . widths of the measured d ET /d -q distributions . As does not approach that ET increases, the width of the pseudorapidity distribution expected for an isotropic distribution* but is always larger. The corresponding value in pp collisions is measured to be o-- = 1.7 [16]. Such a considerably larger width would be expected if the system of high energy density were to undergo a longitudinal expansion prior to emission of the particles . In the simplest case, one may consider a one-dimensional longitudinal expansion, as discussed by Landau [17] and more recently in ref. [14,18]. In this picture, the width depends on the ratio of the initial and final temperatures . Within this framework the expansion time is evaluated to be approximately 7 = 8 fm/c [171, compatible with an independent determination based on Bose-Einstein interferometry [19]. However, a microscopic model such as FRITIOF also predicts r.m.s. widths of the order of 1 .2, as can be seen from fig. 7. Thus we cannot make a clear distinction between the macroscopic and microscopic approaches . 6. Conclusion In conclusion, we have presented our measurements of ET with a nearly complete coverage of pseudorapidity . It was observed that for large target nuclei, max in the full region is largely determined by E T in the backward region since, as ET the total E T increases, ET in the forward region becomes independent of that in the backward one. Thus ET measured with a backward coverage or with a full coverage are equivalently good triggers for selecting high-energy density. The pseudorapidity distributions do not approach those for an isotropic fireball even at the highest measured ET , but are always considerably broader . The evaluated stopping fractions increase with the atomic number of the target, reaching values In the case of isotropy, dE T /d77 approaches the form I/cosh '(77 - 10, which has an r.m .s . width of U.
II LIOS Colla
ration / Articletts-nucleus collisions
19
as high as 0.9. However, stopping does not appear t depend greatly o the size of the projectile; this could be because oxygen and sulphur nuclei are small rel the heavy targets that we have investigated i detail . e estimated energy e is within the range of values predicted for the onset of the decon ne e t ase transition [1]. The HELIOS Collaboration acknowledges the dedication and excellent work of the staff of the CERN PS-SPS accelerator complex in providing ion beams of ve high quality. We thank the technical staff of CERN, and of the institutes collaborating in HELIOS, for their invaluable contributions. We are grateful for the support given by the Natural Sciences and Engineering Research Council of Canada, the Institut de Recherche Fondamentale (CEA, France), the German Federal Minister for Research and Technology, the Istituto Nazionale di Fisica Nucleare of Italy, the Science Research Council of Sweden, the Science and Engineering Research Council of the United Kingdom, the US Department of Energy, and the US-Israel Binational Science Foundation . efere ces [11 Proc. Quark Matter '83, Brookhaven, Nucl. Phys. A418 (1984) ; Proc. Quark Matter '84, Helsinki, Lecture Notes in Physics 221 (1984) (Springer, Berlin): Proc. Quark Matter '86, Asilomar, Nucl. Phys. A461 (1987) ; Proc. Quark Matter '87, Nordkirchen, Z. Phys. C38 (1988); Proc. Quark Matter '88, Lenox, Nucl. Phys. A498 (1989) [2] HELIOS Collab ., T. Âkesson et al., Z. Phys. C38 (1988) 383 [3] HELIOS Collab., T. Âkesson et al., Phys. Lett. B214 (1988) 295 [4] T. Akesson et al.. Nucl. Instrum . Methods A262 (1987) 243 [5] P. Giubellino et al., Nucl. Instrum . Methods A275 (1989) 89 [6] F. Lamarche, Ph.D. thesis, McGill University, Montreal (1989) [7] B. Nilsson-Almgvist and E. Stenlund, Comput. Phys. Commun . 43 (1987) 387; B. Andersson et al., Nucl. Phys. B281 (1987) 289 ; B. Andersson, G. Gustafson and T. Sjöstrand, Z. Phys. C6 (1980) 235 [8] J.P. Pansart, CEN-Saclay report DPhPE 89-04 (1989) [9] A. Capella and J. Tran Thanh Van, Phys. Lett. B93 (1980) 146 [10] B. Andersson, G. Gustafson and T. Sjöstrand, Z. Phys. C6 (1980) 235 [111 R. Albrecht et al., Phys. Lett. B202 (1988) 596 A. Bamberger et al ., Phys. Lett. B205 (1988) 583 [121 J. Barrette et al., Phys. Rev . Lett. 64 (1990) 1219 [13] A. Dar and J. Vary, Phys. Rev. D6 (1972) 2412 [14] J. Stachel and P. Braun-Munzinger, Phys. Lett. B216 (1989) 1 [15] J.D. Bjorken, Phys. Rev . D27 (1983) 140 [161 C. de Marzo et al., Phys. Rev . D26 (1982) 1019 [17] L.D. Landau, paper No. 74 in Collected papers of L.D. Landau, ed. D. Ter Haar (Pergamon Press. Oxford, 1965), p. 569 [Izv. Akad. Nauk . Ser . Fiz . 17 (1953) 51] [18] F. Lamarche and C. Leroy, Longitudinal expansion of hadronic matter in high-energy nuclear collisions, in Proc. 24th Rencontre de Moriond, Les Arcs, 1989. ed. J. Tran Thanh Van (Editions Frontieres, Gif-sur-Yvette, 1989) [191 NA35 Collab., T.J. umanic et al., Z. Phys. C38 (1988) 79; NA35 Collab., J.W. Harris et al., Nucl. Phys. A498 (1989) 133c
E EASU TRANSVERSE ENERGY I NUCLEUS-NUCLEUS COLLISIONS A 2 eV E NUCLEON HELIOS Collaboration T. AKESSON 3, S. ALMEHED6, A.L .S . ANGELISZ°, N. ARMENISE ', H. ATHERTON ;, P. AUBRY8, H.W . BARTELS4, G. BEAUDOIN 8, J.M . BEAULIEU 8, H. BEKER T, O. BENARY 18, D. BETTONI 3. `', V. BISI 19 , I . BLEVIS 21 , H. BOGGILD 3- ", W. CLELAND 12, M. CLEMEN 12 , B, COLLICK 12 , F. CORRIVEAU 7, S. DAGAN 111, K. DEDERICHS3. c, S. DELL'UOMO ", P. DEPOMMIER8, R.C .E. DEVENISH 3.d , N. DiGIACOM0 5, S. Di LIBERTO 13 , J.R . DODD 21), B. DOLGOSHEIN "", A. DRESS4. H. EN'YO T, B. ERLANDSSON 17 , M.J . ESTEN Z°, C.W . FABJAN T. P. FISCHER4 , Z. FRAENKELZ 1 , A. GAIDOT' S, F. GIBRAT-DEBU 1 S, P. GIUBELLINO", P. GLASSEL4, U. GOERLACH ;, R. HAGLUND`', L.A . HAME12, H. van HECKE, V. HEDBERG ;, R. HEIFETZ1s , A. HOLSCHER 4, B. JACAK5, G. JARLSKOG `', S. JOHANSSON 6, H. KRANER 2, V. KROH 4, F. LAMARCHE 7, C. LEROY 7, D. LISSAUER 2.18, G. LONDON 15, B. LORSTAD", A. LOUNIS8, F. MARTELLI'"', A. MARZARI-CHIESA 1`', M. MASERA 1`', M.A . MAZZONI ; , E. MAZZUCAT07, N.A . McCUBBIN 14, P. McGAUGHEYS, F. MEDDI 1;, U. MJÖRNMARK6, 17 M.T . MUCIACCIA1 , S. MURAVIEV`', M . MURRAY 1 -, M . NEUBERT 4, S. NILSSON , L. OLSEN Z , Y. OREN 18 , J.P. PANSART 15 . Y.M . PARK 12 , A. PFEIFFER 4, F. PIUZ T, V. POLYCHRONAKOSZ, G . POULARD;, M . PRICE3, D. RAHM Z, L. RAMELLO L. RICCATI 19 , G. ROMANO 1 ~', G. ROSA ;, L. SANDOR T, J. SCHUKRAFT ;, M . SEKIMOTO T, `, B. SELLDEN 17 , M. SEMAN T.f A . SHMELEVAy, V. SIDOROV 11 , S. SIMONE, Y. SIROIS 7, H . SLETTEN T, S. SMIRNOV "', W. SONDHEIM 5, H.J . SPECHT 4, I. STUMER Z, J.W . SUNIER 5, V. TCHERNIATIN "°, H.H . THODBERG 3, J. THOMPSON 12 , V. TIKHOMIROV", I. TSERRUYAZ1 , G. VASSEUR 15 , R.J . VEENHOF3.1 , R. WIGMANST. g . P. YEPES7 and W.J . WILLIS T 1 University of Bari and INFN 1-70100 Bari, Italy 2Brookhaven National Laboratory, Upton, NY 11973, USA
.3 CERN, CH-1211 Geneva 23, Switzerland 4 Unit,ersity of Heidelberg, D-6900 Heidelberg, Germany SLos Alamos National Laboratory, Los Alamos, NMR7544, USA 6 Uriit-ersity of Lund, S-223 62 Lund, Sweden "Visitor at CERN from : Visitor at CERN from : `Visitor at CERN from : d Visitor at CERN from : `Visitor at CERN from : r Visitor at CERN from : g Visitor at CERN from : h ,Angelo Della Riccia" h
University of Syracuse, Syracuse, NY 13244-1130, USA. Niels Bohr Institute, DK-2100 Copenhagen 0, Denmark. Ludwig-Maximilians-Universität, D-8000 Munich 40, Germany. Oxford University, Oxford OX1 3NP, UK . Institute of Nuclear Study, Tokyo 188, Japan. Slovak Academy of Sciences, CS-04353 Kosice, Czechoslovakia . NIKHEF-H, NL-1009 DB Amsterdam, The Netherlands . Fellow .
~j550-3213/91 /$03 .50 ©1991 - Elsevier Science Publishers B.V . (North-Holland)
HELIOS Collaboration / Nucleus-nucleus collisions 7111cGill Unirersit,% Montreal, P 113.4 M Canada "Unirersity of Alontreal, Montreal PQ HC? 3J7 Canada ')Lebedei - hrstitute of Physics, SU-117924 Moscow, USSR 10 hrstinite of Plrysics and Engineering, SU-115409 Moscow, USSR "histitute of Nuclear Ph®'sics, 630 090 Not~c sibirsk, USSR
' 2Urrirersi4' ofPittsburglr, Pittsburgh, PA 1-5260, USA "Unh -ersity of Rome "La Sapienza " and INFN, 1-0018-5 Rome, Italy 14Rutherford Appleton Laboratona, Didcot OXI O X, UK 'DPIWE, CEN-Saclay, E-91191 Gij-stir-Yt-cite, France l tsUnirersity ofSalerno and INFN, 144100 Salerno. Ital®v 17Uniretsity ofStockholm, S- 11346, Stock-hohn, Siveden ,'Unirersity of Tel Ark, Ramat At ,& 78, Israel Unirersity of Turin and INFX, 1-101 Turin, Italy '"Unirersity Cohtge London, London RUE 6BT, UK `1 11'eizinann Institute, 76 1 Relrorot, Israel Received 5 November 19911 The transverse energy distributions have been measured for interactions of ' 2 S nuclei with Al, Ag, W, Pt, Pb, and tI targets, at an incident energy of 200 GeV per nucleon in the pseudorapidity region -0.1 < n g g, < 5 .5. These distributions are compared with those for 16 0-W interactions in the same pseudorapidity region and with earlier measurements performed with "'0 and ' 2 S projectiles in the region -0.1 < nian < 2.9. These comparisons provide both a better understanding of the dynamics involved and improved estimates of stopping power and energy density .
1. Introduction The measurement of transverse energy produced in nucleus-nucleus collisions at high energies allows the selection of collisions yielding very dense hadronic matter. If the energy density is high enough, the hadronic matter may undergo a phase transition into a state of deconfined quarks and gluons [1]. The energy densities reached depend, among other factors, on the degree of stopping which occurs in each collision . This article presents the results of our measurements on the transverse energy (ET) with a nearly complete coverage of pseudorapidity. The maximum energy densities achieved in '60 and 32 S-W collisions have been previously estimated [2,31 from the measurement of the maximum transverse energy in the backward region and from using estimates of the relative contribution of ET in the forward region . The new measurements provide a check on the validity of these estimates . In addition, the study of the event-by-event correlation between the forward and backward transverse energies as a function of the full E T sheds light on the reaction dynamics . The dependence of the da/d ET and the d ET /dry distributions on the target and projectile is studied. Estimates of the maximum stopping and energy density reached in '6O-W and 32 S-W collisions are also obtained from the maximum value of the total transverse energy measured in the full region .
EL
ration / Nacleas- nucleus coll i ns
ee
I
31
t
The H LIO (High-Energy ton a IOn Spectrometer) detector measures the transverse energy in the backward region using r i iron /scintil ator sampling calorimeters, niu /li ui -argon calorimeter e is define for ® .1 < 'zh 2.9, whereas the forward transverse energy s ) is defined for 2.9 < l.,, < 5.5 a the "'11" r e uranium/ i til at r calorimeters have a 2 2 t the electromagnetic and a ronic sections. e li r ti analysis of the scintillator calorimeters have been described elsewhere The electromagnetic (e.m.) part U starts 3. downstream fr, target and has a 5 cm diameter hole to permit the projectile fragments to pass without interactions. This section as 1920 towers, t f them 2 2 c for larger guard areas around the periphery o its acceptance, sections in depth, 7 and 14 radiation lengths, respectively. The hadronic (had) section, just behind the e.m. section, has no hole, it as 2.5 c wide strips i the horizontal and vertical directions transverse to the beam, an it is divided i e into three sections, each about 1 .5 interaction lengths deep. e G was calibrated with electron and pion beams of momenta of 17, 5, 7 and 2 GeV/c. The calibration showed an average e/- ratio of about 1 .1 + 0.03 and a adronic energy resolution of o,/E(GeV) = 0.015 + 0.45/ ~_ E for fully contained showers. Downstream from the target, a set of three silicon ring counters (R ,, R,, and R3) [3,51 are used, as indicated below, to separate target interactions from background generated in the beam-pipe window, in the air, and in the detectors themselves .
3. The data sets During the 1987 HELIOS runs, the following numbers of triggers were collected: 15 000 O-W, 19 000 S-Al, 22 000 S-Ag, 264 000 S-W, 24 000 S-Pt, 15 000 S-Pb, and 23 000 S-U. The samples of sulphur events were filtered to remove (a) events with two simultaneous beam particles, characterized by an anomalou 3 measured total energy, (b) upstream interactions, characterized by highly correlated hits in the ring counter detectors [3], and (c) downstream interaction :, characterized by MR3 > 1.1 MR , + 10 and MR, < 40, where MR3 and MR , are the multiplicities of the most downstream and the most upstream ring detector, respectively . The oxygen sample was filtered using cuts similar to those used in ref. [2]. The remaining contamination is removed by the subtraction of spectra obtained without any target [3]. This contamination is negligible for the highest values of ET, but amounts to typically 20% for ET < 25 GeV.
HELIOS Colhibortition / Nuclells-11"clel's colli-violls
4
lysis
t
is calculated by a weighted sum of the The forward transverse energy E"' T energies found in individual towers of the e.m.section and in individual strips of ft"T the ha&oWc section of ULAC: E T mE TF"(e .m.)+ETf )"(had) [6] . The erra. contribution to ET'"' is straightforward :
E," (e .m .) .
where si is the sine of the polar angle of the ith tower, measuring energy Ei. is complicated by the lateral spread of the The hadronic contribution to E~" T showers due to the projectile fragments. To understand this effect, we have studied the shower profiles produced by sulphur ions and protons interacting at the centre of the hadronic section of ULAC. The average shower profiles for protons and sulphur ions are quite similar (fig . 1). The two central strips are excluded from the determination of ET", limiting the pseudorapidity acceptance to 77 < 5 .5, but the measured energies in these strips are used, event-by-event, to correct for leakage into neighbouring strips of the energy deposited by nuclear fragments. To correct approximately for this leakage, the hadronic contribution to ET' is experimen-
a)
b)
C(U21 0 .8
0 .8 0 .6 0 .4
flu
0 .2
0
w
2
4
6
Strip number
8
10
0 .2
0
2
4
6
8
10
Strip number
Fig . 1 . The energy of the neigl*ouring strips compared with the central strip in the ULAC as a function of strip number : (a) for incident 32 S at 200 GeV per nucleon, (b) for incident 200 GeV protons . For a strip, the energy is summed for the three hadronic sections .
DELI®S Collaboration / Nucleus-nescleus collisiot:s
5
tally defined as E"I(had)
= 2[
Xi(E.,, -,Bi E.,,,) +
Yj(E,.~
where Xi (Y) is the sine of the polar angle of the geometric centre of the ith x-strip ( jth y-strip), E., , (EY) is the energy measured in that strip, and ßi (j3) is the fraction of the energy of the central energy slab energy E, r,, (E,. ) in the ith ( j th) strip as determined in fig. 1 . Assuming azimuthal symmetry, the factor -r/2 corrects for the effect of the cartesian readout of the hadronic section of ULAC. The correspondence between the experimental definition of ET' and the true one has been investigated in a Monte Carlo simulation. We used an event generator [2], to which was added the fragment simulation of ref. [7] in order to determine the sensitivity of E T to projectile fragments, to the particle mix, and to 104
103
0
10
w
b
10-1 10-4 1 0
100
200
300
400
500
ET IGeVI
per Fig. 2. Transverse-energy differential cross section, dur/d ET , in the full region for 200 GeV nucleon 32 S on AI, Ag, W, Pt, Pb, and U collisions.
HE1.IOS Collaboration / Nucleus-nucleus collisions
6
the momentum distributions. The converted energy is defined as the kinetic energy of the baryons and the total energy of all oth-: particles including the antibaryons . The calorimeter simulation included the response to different particles (e 1 70, the " energy leakage (affecting the energy scale), and the resolution (affecting the shape). The evaluation of the systematic uncertainty included that already evaluated for the backward direction C7.1%) [2] as well as the errors in the evaluation of the forward E T, which were due to the following : subtraction of leakage of fragment energy (2%), calibration (2%), particle composition (3%), and e/-7r ratio (3%). The combined systematic uncertainty on the ET" scale is 5.0%. Our data TABLE 1
The transverse-energy differential cross section dQ/d ET in the full region for 200 GeV per nucleon 32 S-Al collisions ET [GeV]
Bin half-width [GeV]
do-/d ET [mb/GeV]
Error [mb/GeV]
36 .5
2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4
9.94 x 10' () 9.07 x 10 + " 9.13 x 10' ° 9.27 x 10"' 8.62 x 10 +° 8.75 x 10 + " 7.07 x 10 + ° 6.87 x 10" ) 6.75 x 10 +° 5 .41x10+° 5 .65 x 10' () 5 .69 x 10+" 4.96 x 10'() 4.81 x 10+" 4.74 x 10'() 4.50x10"' 3.97 x 10+" 3.74 x 10 +" 2.98 x 10+ ° 2.94 x l0'" 2.41 x 10 +" 1.76 x 10 +° 1.92 x 10 +° 1.44 x I0,() 1.02 x 10 +() 5.31 x 10 - ' 4.90 x lo -, 3.99 x 10 -1 2.40 x 10 - 1 1 .15 x 10 - ' 6.07 x 10 -2 2.92x10 - '1 .23 x 10 -2 4.08 x 10 -3
4.68 x 10 - ' 4.52 x 10 - ' 4.44 x 10 - ' 4.35 x 10 - ' 4.16 x 10 - ' 4.12 x 10 - ' 3.77 x 10 - ' 3.71 x 10 - ' 3.57 x 10 - ' 3.26x10 - ' 3.20 x 10 - ' 3.16 x 10 - ' 2.87 x 10 - ' 2.79 x 10 - ' 2.70 x 10 - ' 2.61x10 - ' 2.45 x 10 - ' 2.38 x 10 - ' 2.11 x 10 -1 2.07 x 10 -1 1.87 x 10 - ' 1.72 x 10 -1 1.72 x 10 -1 1 .49 x 10 - 1 1.24 x 10 -1 8.87 x 10 -2 8.66 x 10-2 8.99 x 10 -2 7.43 x 10-2 4.19 x 10 -7.83 x 10 -3 6.21x10 - ; 4.74 x 10 - ; 3.71 x 10 - ;
41.4 46.2 51.1 56.0 60.8 65.7 70.6 75.4 80.3 85.2 90.0 94.9 99.8 104.6 109.5
114.4 119.2 124.1 129.0 133.8 138.7 143 .6 148.4 153.3 158.2 163.0 167.9 172.8 177 .6 182 .5 187.4 i92.2 197.1
HELIOS Collaboration / Ntcletts-nucleus collisions
on the almost symmetrical system 32 S- 2'AL were use to check r evaluation ETack ET°`~ relative to as a function of ET, and was found to e consistent with. the expectation . To compute the pseudorapidity density of E T, a pseudorapidi st be attributed to each channel of ULAC . There is a unique pseudorapidi for each tower of the e.m. section, but each strip of the hadronic section covers a rather large range of pseudorapidity . The Nlonte Carlo calculation shows that the pseudorapidity is correctly measured, on the average, if we give each strip the pseudorapidity of its centre minus 0.31. An effective pseudorapidity resolution of 0.~ in most of ULAC and of 0.4 near q = 5.5 is attained .
TABLE 2
The transverse-energy differential cross section do,/d ET in the full region for 200 GeV per nucleon 32 S-Ag collisions ET [GeV]
Bin half-width [GeV]
4 .7 14 .1 23 .5 38 .1 51 .7 61 .1 79 .9 108 .2 127 .0 145 .8 164 .6 174 .0 183 .4 192 .8 202 .2 211 .6 221 .0 230-4 239 .8 249 .2 258 .6 268 .1 277 .5 286 .9 296 .3 305 .7 315 .1 324 .5 333 .9 343 .3 352 .7 362 .1
4.7 4 .7 4.7 9 .4 4.7 4 .7 14.1 14 .1 4.7 14 .1 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7 4 .7
da/d ET [mb/GeV]
Error [mb/GeV]
x x x x x x x x x x x x x x x x x x x x x x x x x x
2.58 x 10 +2 6.59 x 10 + ' 3.07 x 10 +0 1 .95 x 10 + " 2.69 x 10 +° 2.50 x 10 +° 1 .17 x 10 +° 8.78 x 10 - ' 1.49 x 10 +° 7.80 x 10 - ' 8.83 x 10 - ' 9.89 x 10 - ' 1.10 x 10+ ° 2.08 x 10 - ' 2.08 x 10' 2.08 x 10' 1.96 x 10 - ' 1 .92 x 10 - ' 1.83 x 10 - ' 1.76 x 10 - ' 1 .72 x 10 - ' 1.67 x 10 - ' 1 .42 x 10 - '
3 .30 8 .22 2 .36 1 .54 8 .91 9 .53 4 .83 2 .76 6 .02 4 .40 3 .64 4 .31 4 .65 4 .15 4 .15 4 .14 3 .65 3 .51 3 .17 2 .97
2 .72 2 .66 1 .92 1 .65 9 .89 5 .40 3 .48 x 1 .78 x 7.33 x 2 .33 x 8.69 x 1 .33 x
10 +10 + ' 10 + ' 10 + ' 10 +° 10 ' + 10 +° 10 +(' 10 +° 10 +° I0+ ° 10 + " 10 +° 10 +° 10 +(' 10 + " 10 +° 10 +° 10 +° 10 +° 10 + " 10 +0 10 +° 10+ () 10 - ' 10 - ' 10 - ' 10 - ' 10 -2 10 -2 10 - ; 10 -3
1.31 x 10 -1 1.01 x 10 - ' 7.43 x 10-2 2.24 1 .58 9.88 4.01 2 .25 9.41
x k x x x x
10-2 iÛ -2
10 --'` 10 --3 10 - ; 10 -4
8
L.1~~~ C~~lhal~c~atat~rara
,~ a~laac°Ic'ate-raatc°la.~aa~+ ~°~~lllslc~aa~ r,a~t ~ 3
/d ~~- in flee full region `i e crans`°erse¢cnergy differential cross section for 2(i0 GeV per nucleon ?`S-V~ collisions E~ [Ge`']
13in half-®vidt [GeV]
da~/d ~~- [ b/GeV]
32,9
4.7
1 .25 x 10+'
136.4
4,7
42,3 51,7 61 .1 70.5 79.9 59,4 95.5 105.2 117.E i 27 .0 145.8
164.E 174.0 183.4 192 .8 202.2 211.E 221.0 230,4 239.5 249,2 258,6 265.1 277, i 256.9
29b .3 305 . 7 315 .1
324 .5 333,9 343 .3 352.7 362.1
371 .5 38(1 .9
390,3
399,7 409.1 415.5 427,9
437 .4 446 .8
456,2
~rror [ b/GeV]
4.7 4,7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4, 7
1 .58 x 1 .13 x 1.00 x 1 .06 x 8.97 X 5 .63 x 7.10 x 6.02 x 7.11 x 7 .66 x
4.7
7.38 x 10 +"
1.75 x 1 .45 x 1 .45 x 1 .32 x 1 .24 x 1 .OU x 9,91 x 8 .68 x 7.87 x 6.82 x 4.75 x 3.68 x 3.25 x
4.7 4.7 4.7 4.7 4.7 4.7 4 .7 4, 7 4.7 4, 7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7
6.76 x 10 +" 6.19 x 10 +° 5.98 x 10 +" 6.18 x 10 +" 6A6 x 10 ~ ° 5 .14x10 1 " 4.61 x 10 +° 4.67 x 10 +" S .IO x 10 +" 4.98 x 10 +" 4 .93 x 10 +° 4.99 x 10 +" 4 .96 x 10 +" 4.81 x 10 +" 4.66 x 10 +" 4.32 x 10 +" 4.06 x 10 + " 3.70 x 10 +" 3.14 x 10 + " 2.46 x 10 +° 1 .79 x 10 + " 1 .18 ~: IOY" 7.95 x 10 - ' 4.73 x 10 - ' 2 .79 x 10 - ° 1 .34 x 10 - ' 6.12 x 10 - 2 .84 x 10 --' 1 .28 x 10 --'
3.15 x 10 -' 3.02 x 10 - ' 2.96 x 10 - ° 3.02 x 10 -' 3.00 x 10 -' 1.11x10 - ' 7.95 x 10 - ' 7.93 x 10 - -' 7.11 x 10 --' 7.02 x l 0-6.97 x 10 -7.02 x 10 -7.05 x 10 -' 6 .90 x 10 6.77 x 10 6.49 x 10 - -' 6.32 x 10 -2 4.17 x 10 3.85 x 10 --' 2 .71 x 10 - ~ 2.32 x 10 --' 1 .33 x 10 - ~ 1 .08 x 10 - ' 8.32 x 10 --' 6.38 x 10 - ; 4.38 x 10 2,93 x 10 2.03 x 10 - ; 1 .38 x 10 --~
4.7
l .49 x 10 - ; 5 .80 x 10 - `'
8,65 x 10 - ~ 3.36 x 10 - ~
4.7 4.7
10 + ° 10 + ' 10 +' 10 +' 10 +" 10 Y ° 10 +" 10 +° 10 +" 10 +"
6.78 x 10 +"
3.48 x 10 - ;
10+° 10 +" 10+" 10 +" 10 +" 10 +" 10 t" 10 -' 10 - ' 10 - ' 10 -' 10 -' 10 -'
7.47 x 10 - ;
S colla ration / Nucleas-nucleits colfisions
5.
Its
5.1 . TARGET DEPENDENCE
The differential cross sections da/dET in the full region are presented as function of ET in fig. 2 and in tables 1-6 for collisions of -32 S with various targe nuclei at an incident energy of 200 GeV per nucleon. For all targets, the distributions have the shape that was previously observed for incident oxygen a sulphur beams in the backward region [2,3]: a plateau (shorter for the A] target) followed by a steeply falling tail .
TABLE 4 The transverse-energy differential cross section dar/dE T in the full region for 200 GeV per nucleon ;2S-Pt collisions ET [GeV]
Bin half-width [GeV]
da/d ET [mb/GeV]
Error [rnb/GeV]
319 61 .1 814 117.6 145.8 1710 2012 221.0 230.4 2348 2442 258.6 268.1 277.5 286.9 296.3 305.7 315.1 3215 333.9 343.3 3517 362.1 371.5 3819 390.3 399.7 4011 418.5 427.9 437.4 46 .8
14.1 14.1 14.1 14.1 14.1 14.1 14.1 4.7 17 4.7 4.7 17 47 4.7 47 17 17 17 4.7 17 17 4.7 17 47 17 4.7 17 17 17 4.7 17 17
1 .39 X 10' 8 .23 X 10+°' 9.31 X 10"' 9.29 X 10" ) 6.30 x 10' ( ' 6.40 X 10"' 6.81 x 10+ 1) 5.93 X 10' 5.93 X 10' 5.30 x 10 +" 4.53 X 10` 5.43 X 10"' 5.51 x 10+ 1) 4.86 X 10+" 5.27 X 10'° 5.25 X 10 " 4.66 X 10+() 5 .26 x 10+(' 4.71 X 10' 3.72 X 10 + " 3 .61 X 10 +) 2.85 X 10' 2.07 x 10+ 11
7.63 X 10 - " 1.77 X 10 -e 1 .54 X 10" ) 1 .35 X 10 - 'e 1 .10 X 10l le 1 .03 X 10' 1 .05 X lo', 3.38 X 10+ 1 3.38 X 10- ' 3.19 X 10- 1 2.95 X 10 -1 3.23 X 10 -1 3.26 X 10 - ' 3.06 X 10 - ' 3.19 x 10 - ' 3.18 x 10 - 1 3.00 X 10' 3.19 x 10 - ' 3 .02 X 10' 2.68 X 10 - ' 2 .64 X 10 - 1 1 .05 X 10' 8 .89 X 10 -'7.12 X 10 -2 5.68 X 10-'4.10 X 10-2 2.91 X 10 ` 2.34 X 10 - 2 1 .29 X 10-, 3.46 X 10 -3 2.57 X 10 -3 1 .57 X lß - '
1 .34 x 10 -4)
8 .63 X 10- ' 4 .56 X 10- 1 2 .35 X 10- ' 1 .56 X 10- 1 4.83 X 10 -2 1.42 X 10 -2 8.12 X 10 -3 3. 1.4 X 10 - -3
-allon / Nucleus -- nucklo cafli's 'MR t 3 dtr/dEf in the full region for The ttmovevse-enetg~, 200 GeV pet nucleon 12S-Pb collisions
f-mvidth
412 511 10,2 .7 162.2 221,2 231 1 .0 M7 27M4 2W 3%7 3145 3244 3342 349 .0 350) 3617 3745 38&4 3W 40&0 AM 4217 4414
19 4.9 117 117 117 117 117 01) 19 19 19 19 it) 4.19 4.9 4.9 19 19 4.9 19 19 19 4.9 4.9 19 19 4.9 19 4.9 19 18
WeVI las X au I= X 1"
VA I X
I
.
lui
~ 41
S33 X Io , 6m4 X lo" , 7.(lh X 10 ' 5. Î9 X 10 610 X Io -,, 6ag X Io "I 5.40 X 10 , 'l 5cq X 1(1+I 9 5.73 X lo' , S. ',s X Io -,, 523 X lu - " 5.57 X 10"' SAU X lu -Il 4.95 X lo' , 539 X Io", 37 X 10 4AI X 10"' 435 X 10"' ,.60 X Io 2.79 X 10 L79 X Ur' 1.29 X 10"' smi X Io -, 3 .34 X 10 134 X 10 -5.20 X 10 - 2 2.30 X 10 -2 93(1 X I o-
1 .4.1
1
n-40
a n-0
wo I n -40 sm s X Io -, SA7 X 10 177 X 10 421 X 10 -1 7.64 X 10 -1 7M3 X 10 -1 Til X Io -, M X 10 -1 2AS X 10 -1 2AO X 10 -1 237 X 10 -1 2A7 X 10-1 2A6 X 10 -1 231 X 10-1 2A5 X 10- 1 2AI X 10-1 213 X 10 - 1 2.17 X 10 1 .97 X Ur' 113 X 10 -1 1.38 X 10 - 1 121 X Io -, 4M2 X 10- 1 141 x 10-2 136 X 10-2 9m5 X 10-2 W x 10-3 9.30 X 10-3 I
iaximum Ques of ET obtained in the full region (from ET 21-' 190 GeV Or o E-, ~ 470 GeV Or 32 S-U) are subtan6ally larger than the values Ou 31 in the back-waTd region 94 GeV and = 339 GeV, respectively) . The E T sured with full coverage, relative to that in the backward region, increases sistently more for average central collisions (defined as the value of ET for \%hich da/d is half the plateau value) than for the high-ET tail. For example, i S-W Collisio 200 GeVner nucleon, the extension from the backward to the ses ET for average central collisions from 198 to 327 Ge eV in the tail (fig . 3). The ET distributions for 200 GeV per W targets are compared in fig. 3 with the predictions of the IS 3).05 193 event generators. FRITIOF uses independent
~ä~~~ ~
r r~ ~l
37 .6 51®7 61 .1 70 .5 79. 98.8 117.E 136.4 155 .2 164.E 174. 183 .4 192 .8 2 2 .2
211 .E 221 .0 230.4 239.8 249 .2 258 .6 268 .1 277 .5 285 .9 296.3 305 .7 315 .1 324.5 333.9 343.3 352.7 362 .1 371 .5 38 .9 3 3 399.7 4 1 -118.5 427.9 -i37.4 6,8 -156,2 5,6 475, 4
9 .4 4a7 4 .7 4 .7 4 .7 14 .1 4.7 14.1 4.7 4.7 4.7 4 .7 4 .7 ~1 .7 4 .7 4 .7 4.7 4.7 4.7 4.7 4.7 4 .7 4 .7 4 .7 -1 .7 4.7 4 .7 -1.7 4.7 4.7 4.7 4.7 4 .7
"tp~~~~4~~,~~~~p
~~ ~
9.72 1. 6 .81H .36 4 .62
°~ee~~~
~~~~~b~~~~~~~
~
~ 11~~~
x 1
x x x x 6.20 x 4 .12 x 3 .82 x 9.24 x
1 1 1
°aa 10°~a
l0 `a" 1 T aa 10'~~ 1 ° ~a -~~ 5 .5x1 °~a 5.95 x 1 6.83 x 10" r` - ~a 3.36 x 1 5.68 x 10°~ a 6. x !0°~r~ °aa 5 .49 x 10 `"a 5 .77x 1 5 .&5 x 1®' aa 4 .99 x 10 -aa 5 .92 x 1 ` aa S .D7 x 10 - ~a 5 .55 x 10 -6a 5.52 x 10 -aa 5.79 x 10` p `~ 5 .88 x 1 -~a ae 5 .47 x 10` -Fa 4 .43 x 10 T ar~ -# .92 x 1 4 x 10 -aa +°a 3 .57 x 10 - ar, 2.62 x 1
-c'a
4.7 -1,7 .H .7
2.11x1 x l -~ 1. ..ct 1 .18 x 1 6.82x 1 -° -~.43 x 10- c _c 2 .~r1x1 1,73x 1 -° 8 . a x H~~ -= ~,33 x 10 - T .13 x 10 -
~ .7 -H .7
~.59x 10~~
4 .7 4 .7 -1 .7
4 .7 -1.7 407
6.3~9 x 1 6.6P' x D ° 4 .91 x 10 r~ 3. x 10' r ~ 2. . x 1 °E~ 3.07 x D 0 °
2.95
2.29 x 10` r 2 .34x 2.25 x 2 .3~3 x x 1. 2.05 x 4.45 x 4.D6~ x
10~ ar 10 ~ cr ~ ° ~r fr DO° cP D0~° DO" c 10° a D0_ a 10" a DO- a DO` H ¬H- a DO - ~' D0_ a
4.14x 4.05 x 3.85 x 4.D9 x 3.92 x 4. x 4. x 4 .D0 x -1 .D4 x DO -° 3.9 x 1 - a 3 .59 x 10- a 3.78 x 10 " ~ 1 .53 x 10" ~ t' 1. x 10c 1. x 10~ 1 .1Ox10~~ 9 . ' ~ ~ 10 - t' 8. x HO~ r 6 .ZZx 10~~ 2 ~0 x DO 1 .~#1x10 -® 1 .5~5, x 1C~~ d 1 .E0 x DO" m 7.55 x D
-D, 3~ D~~
12
HELIOS Collabortition / Nucleus-nucleus collisions -0.1
0
100
200
300
ET AT
400
500
Fig. 3. The differential cross section duld ET for 32 S-W collisions at 200 GeV per nucleon in the full (A) . forward (v), and backward W regions. The predictions for FRITIOF (continuous line) and IRIS Washed line) are shown for the backward and full regions . Also shown is the IRIS prediction (dashed line) for the forward region . The horizontal error bars indicate the systematic error of 717i on the ET scale. nucleon-nucleon interactions, whilst IRIS is based on colour exchange, with the dual parton model [91 as the starting point. Both models use the Lund fragmenta-
tion model [10] . The ET in the forward rapidity region is somewhat overestimated in the tail of the distribution by the IRIS generator. In the full and backward regions, and for both projectiles, the models reproduce the plateau in a satisfactory
fashion, but fall short, by about 15%, of describing the extent of the tail . This may
be due to an underestimation of the stopping power and/or to cascading in the target nucleus, not included in the models .
The target mass dependence of E"n"" can be fitted to the form A"" [2,3]. The T value of a varies with the pseudorapidity window and decreases from a = 0.5 in
the back-ward
region [3](0.48 ± 0.02 and 0.53 ± 0.04 for '6 0 at 60 and 200 GeV per 32 nucleon, respectively, and 0.53 ± 0.05 for S at 200 GeV per nucleon), to a = 0.39 32 + ON (W S at 200 GeV) in the full region . The latter value is closer to a = -L 3 expected from naive scaling with target nucleus thickness, and was also reported
0
HELIOS Collaboration / Aluclens-nuclens colfi_%
the WA80 and NA35 [111 experiments. The rise of E~"' interpreted as a sign of "partial stopping", since, in the case of full s Ecentral would cease to rise beyond a certain size of the target. T Full stopping, however, is observed at lower energies, e.g. at BNL in collisi VsNN = 5 GeV, already in medium-size nuclear targets [121. 5.2. FORWARD VERSUS BACKWAR
TRANSVERSE ENERGY DEPOSITI
Fig. 4 shows a contour plot of the event-by-event differe I c Ss sect ETback versus for S-W collisions . The most probable Ell is proportional to ETf" T ntral , ETback up to a value close to ET where the sulphur nucleus fully overlaps the ET target . Beyond this, ETfo' appears to be saturated and is independent of ETback This saturation can be interpreted in several ways: for example, (a) after full overlap, the number of participating projectile nucleons no longer increases, while that for the target continues to increase ; the backward rapidity shift occurring when more target nucleons are participating forces ETfo'IET to decrease, so that Efo' is approximately independent of ETback at large enough E-r, T, or (b) the production mechanism for ETf" is independent of the production mechanism for
i i
2P.-
UJ
320 280 240 200 160 120 80 40 0
40
80
12O
160
200
Forward/backward contour plot
240
28
320 OTI-,11ft (GeV1
Fig . 4. Contour plot of the differential cross section d2or/(dEfa`IEIV I ) for the production of E-F in the backward region, and of E T in the forward region at 200 GeV per nucleon . Successive contours are separated by a factor 1 /e. The IRIS prediction for one contour is shown as a dashed line .
HELIOS Collaborinion J1
1
A'ucleus -nuclcus collisions
S prediction for one of the contours is shown; e overshoot in is apparent an there is less saturation i the prediction . Perhaps this is a consequence of an underestimate of stopping and/or cascading. T of the -fr"' distribution to be considerne would expect the tails of r,/ ably steeper than those of back, an fig. 3 shows that this is indeed the case . The /E~l" is determined only saturation of E" means that the width of the tail o y the event-to-event fluctuations n E~" and is independent of the S- geornet . The widths of the contours of fig. reflect the magnitude of the event-to-event fluctuations of" versus E back . Analysis of the contours shows that for central collisions the r. .s. width of the event-to-event fluctuations in ET " is 12-15 GeV, or about 10%. The contour widths do not depend strongly on the transverse ° '°'`
k
[I .1] .
~tom
TABLE 7 The transverse-energy differential cross section da/d E-1- in the full region for 200 GeV per nucleon "'O-W collisions E T [GeV]
Bin half-width [GeV]
do-/d ET [mb/GeV]
Error [mb/GeV]
124 .6 129 .3 134 .0 138 .7 143 .4 148 .1 152 .8 157 .5 162 .2 166.9 171 .6 176.4 181 .1 185 .8 190.5 195 .2 199 .9
2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2 .4 2.4
6.92X10 + " 1 .05 X 10" 9.71 X 10 + ` 1 9.34 X 10 +° 1 .04 X 10" 8.58 X 10 +° 8.97 X 10 +° 7.05 X I0+()
2.31X10 +° 1 .00 X 10 +° 9.67 X 10 9.48 X 10 1 .00 X 10 +° 9.10 X 10 -, 9.31 X 10 - ' 8.25 X 10 -1 8.69 X 10 -1 7.91X10 -1 8.25 X 10 -1 7.48 X 10 -1 7.95 X 10 -1 6.88X10 -1 7.57 X 10 -1 6.64 X 10 -1 6.48 X 10 -1 4.67 X 10 - 1 4.45 X 10 -1 4.22 X 10 -1 1 .42 X 10 -1 1 .29 X 10 -1 1 .13 X 10 -1 8 .23 X 10-2 7 .30 X 10-2
204 .6 209 .3 214 .0 218 .7 223 .4 218 .1 232 .8 '37 .5 242.2 246 .9 2_>1 .6 256.3 265.7 270.4
2.4 2.4 2.4 2.4 2.4 2 .4
7.82 X 10 +° 6.47X10 +° 7.05 X 10 +° 5 .79 X 10 +° 6.56 X 10 +° 4.91X10 +° 5 .96 X 10 +° 4.60 X 10 +° 4.40 X 10 +° 2 .29 X I0+() 2 .09 X 1 .89 X 1 .07 X 8 .96 X 6 .86 X 3 .68 X 2 .92 X 1 .27 X 7 .16 X 3 .55 X 3 .51 X 1 .03 X 3 .38 X
10+ ()
10 + " 10 + " 10 - ' 10 -° 10 - 1 10 - 1 10 - ' 10 -2 10 -2 10-2 10 -2 10 --'
4 .78 3 .58 2 .51 2 .48 5 .93 3 .38
X X X X X X
10 -2 10 -10 -2 1()-2 10 -3 10 - ;
S Collaboration / Nucletes- uclens collQsions
energy; the fluctuations about 1 eV.
T r``
or peripheral collisions (low, values of
'r
5.3. PROJECTILE DEPENDENCE
Comparison with the data taken with incident 16 illustrate the e e e ET production on projectile mass. The ET differential cross section for collisions is given in table 7 and compared with that for 32S_W collisions in fig. 5. 32S '6G The increase of ET for over is 62% for average central collisions an 55% in the tail. An estimate of the maximum stopping fraction S can be obtained from the ratio S(ET) --- ET/ETa''. We determine Ea"a'' by distributing the available energy according to our measured d ET/d r7 for the highest ET [141 [where Eavail = VFS m(Np + Nt) is the available centre-of-mass energy, with s = 2 x 2 x NP x , x GeV2 ; NP and Nt are the number of participating projectile and target nucleons, respectively, and m is the nucleon mass]. The values of S for ET such that da/d ET reaches 10-4 times the plateau value in the full region are reported in 104 103 102 10
w E
W
10-1 10-2 10-3 'In-4
0
100
200
300
ET (GeV)
400
Fig. 5. Comparison between the ET distributions over the full region for 16Oat 2 GeV per nucleon.
500
and ~?S-
(A)
_~~~~ ~t)~~a7~)i))CJlld)13
1()
°ihc~
r
ä~tl(°~('1tS--l11Q(°~('dl " (°t)~~ISId)1t,S
m:~xin~un' stopping fractions (S~ ,) fur ~~°(~- W (at 200 GeV per nucleonD sand for collisions of '°S on Al, Ag. W, Pt, Ph, and U (at 20() GeV per nucleon) in -0.1 < risah < 5.5
E~ [GeVI ET`"' [GeV) Sn, .,~
®-W
S-AI
S-Ag
S-W
S-Pt
S-Pb
S-U
264 300 O.SS
192 343 i).56
;53 420 i1,84
445 502 0.88
435 504 0 .87
432 506 0.86
472 530 0.89
table 8 for various projectiles and targets. It is seen that S increases with the target thickness but does not vary much with the size of the projectile . A similar calculation shows that even at an incident energy of 60 GeV per nucleon the full stopping limit ( S = 1) is not reached . The energy density can be estimated, assuming that the initially available energy is deposited in the relevant interaction volume V, often taken to be the geometric orentz-contracted volume . The energy density ~ = y( ET ras V ) (where y E~<<;~,~/ >~) is = 5.5 GeV/fm' and ~ b.8 GeV/fm~ in the tails of the ~~O-VV and '~S-~V distributions, respectively, consistent with earlier estimates [2, 3]. See subsect . 5 .4 for another estimate .
70
140
0-W
120
r\
60
\
229 .4
0
160 .E
1
~
100
-
W Z
\
60 40 20
Pig. fi. I~àstribution of E-r as a function of pseudorapidity, normalized to the number of events, for three values of E-r in the full region (plateau, shoulder, and tail) at 200 GeV per nucleon for (a) ~`' -tip' and (b) '~S-W collisions . IRIS predictions (dashed lines) are shown for E-r values at the same dQ/d ET as the corresponding data.
HELI S Colla
ration / Alucleus-nucletts colfision
5.4. PSEUDORAPIDITY DISTRIBUTIONS
The pseudorapidity distributions for 16 0-W and ;2S_W collisions are sh fig. 6. Whilst the shape of the distribution for each projectile in the bac region does not change very much with increasing ET9 most of the increase of is in this region. The relative contribution of the forward region changes with the projectile mass and with ET . For both projectiles, fig. 7 shows that the average pseudwapidity shifts forward with increasing projectile mass and shifts backward
3 .2
1
1
F
A
O-W 200 GeV
S-W 200 GeV
3 .0 2 .8
13
j3 0130 130
2 .6
1
0
13
0
8
0
0
2 .4 2 .2 0 L
100
200
1 .8
300
0
400
0
100 (GeV)
ET
300
400
500
O-W 200 GeV
S-W 200 GeV
1 .6
200
1 .4 E1 .2 1 .0 0 .8
Isotropic limit
0 .6
100
0
200
160
X
1
300
L
400
100 0 ET (GeV)
200
300
400
500
O-W 200 GeV
S-W 200 GeV
120
E
LLJ
0
-
40 0
00
-
0
-
100
'1140 0 0
0 0
200
300
400
0 100 Q (GeV)
200
300
400
500
Fig . 7 . The first and second moments of the pseudorapidity distributions as well as (dET/dT7),,, ;:! versus E T in the full region for "O-W and S-W collisions. The solid line indicates the F prediction .
is
HELIOS Collaboration / Nucleus-nucleus collisions
The maximum dE T /d-q value rises somewhat more rapidly with increasing than ET* The comparisons to IRIS, shown in fig. 6, are made with samples for ET values corresponding to the same da/dE T as the data. The trend is the same for both projectiles : there is a large underestimate in the backward region for all Ef"" T region but predictions are good for the plateau whiist, in the forward region, the there is an increasing small overestimate as ET"" increases . An estimate of the error in the energy density determined above can be obtained by calculating the energy density in the 13jorken longitudinal hydrodynamic limit [15]: - = I/AT(dET/d-q)mav where A is the cross-sectional area of the (smaller) projectile and -r is the expansion time, whose value is traditionally assumed to be = I fm/c. The corresponding values in this limit are - 3 .0 GeV/fM 3 and - 3.4 GeV/fM 3 . In fig. 7 we also give the r.m.s . widths of the measured d ET /d -q distributions . As does not approach that ET increases, the width of the pseudorapidity distribution expected for an isotropic distribution* but is always larger. The corresponding value in pp collisions is measured to be o-- = 1.7 [16]. Such a considerably larger width would be expected if the system of high energy density were to undergo a longitudinal expansion prior to emission of the particles . In the simplest case, one may consider a one-dimensional longitudinal expansion, as discussed by Landau [17] and more recently in ref. [14,18]. In this picture, the width depends on the ratio of the initial and final temperatures . Within this framework the expansion time is evaluated to be approximately 7 = 8 fm/c [171, compatible with an independent determination based on Bose-Einstein interferometry [19]. However, a microscopic model such as FRITIOF also predicts r.m.s. widths of the order of 1 .2, as can be seen from fig. 7. Thus we cannot make a clear distinction between the macroscopic and microscopic approaches . 6. Conclusion In conclusion, we have presented our measurements of ET with a nearly complete coverage of pseudorapidity . It was observed that for large target nuclei, max in the full region is largely determined by E T in the backward region since, as ET the total E T increases, ET in the forward region becomes independent of that in the backward one. Thus ET measured with a backward coverage or with a full coverage are equivalently good triggers for selecting high-energy density. The pseudorapidity distributions do not approach those for an isotropic fireball even at the highest measured ET , but are always considerably broader . The evaluated stopping fractions increase with the atomic number of the target, reaching values In the case of isotropy, dE T /d77 approaches the form I/cosh '(77 - 10, which has an r.m .s . width of U.
II LIOS Colla
ration / Articletts-nucleus collisions
19
as high as 0.9. However, stopping does not appear t depend greatly o the size of the projectile; this could be because oxygen and sulphur nuclei are small rel the heavy targets that we have investigated i detail . e estimated energy e is within the range of values predicted for the onset of the decon ne e t ase transition [1]. The HELIOS Collaboration acknowledges the dedication and excellent work of the staff of the CERN PS-SPS accelerator complex in providing ion beams of ve high quality. We thank the technical staff of CERN, and of the institutes collaborating in HELIOS, for their invaluable contributions. We are grateful for the support given by the Natural Sciences and Engineering Research Council of Canada, the Institut de Recherche Fondamentale (CEA, France), the German Federal Minister for Research and Technology, the Istituto Nazionale di Fisica Nucleare of Italy, the Science Research Council of Sweden, the Science and Engineering Research Council of the United Kingdom, the US Department of Energy, and the US-Israel Binational Science Foundation . efere ces [11 Proc. Quark Matter '83, Brookhaven, Nucl. Phys. A418 (1984) ; Proc. Quark Matter '84, Helsinki, Lecture Notes in Physics 221 (1984) (Springer, Berlin): Proc. Quark Matter '86, Asilomar, Nucl. Phys. A461 (1987) ; Proc. Quark Matter '87, Nordkirchen, Z. Phys. C38 (1988); Proc. Quark Matter '88, Lenox, Nucl. Phys. A498 (1989) [2] HELIOS Collab ., T. Âkesson et al., Z. Phys. C38 (1988) 383 [3] HELIOS Collab., T. Âkesson et al., Phys. Lett. B214 (1988) 295 [4] T. Akesson et al.. Nucl. Instrum . Methods A262 (1987) 243 [5] P. Giubellino et al., Nucl. Instrum . Methods A275 (1989) 89 [6] F. Lamarche, Ph.D. thesis, McGill University, Montreal (1989) [7] B. Nilsson-Almgvist and E. Stenlund, Comput. Phys. Commun . 43 (1987) 387; B. Andersson et al., Nucl. Phys. B281 (1987) 289 ; B. Andersson, G. Gustafson and T. Sjöstrand, Z. Phys. C6 (1980) 235 [8] J.P. Pansart, CEN-Saclay report DPhPE 89-04 (1989) [9] A. Capella and J. Tran Thanh Van, Phys. Lett. B93 (1980) 146 [10] B. Andersson, G. Gustafson and T. Sjöstrand, Z. Phys. C6 (1980) 235 [111 R. Albrecht et al., Phys. Lett. B202 (1988) 596 A. Bamberger et al ., Phys. Lett. B205 (1988) 583 [121 J. Barrette et al., Phys. Rev . Lett. 64 (1990) 1219 [13] A. Dar and J. Vary, Phys. Rev. D6 (1972) 2412 [14] J. Stachel and P. Braun-Munzinger, Phys. Lett. B216 (1989) 1 [15] J.D. Bjorken, Phys. Rev . D27 (1983) 140 [161 C. de Marzo et al., Phys. Rev . D26 (1982) 1019 [17] L.D. Landau, paper No. 74 in Collected papers of L.D. Landau, ed. D. Ter Haar (Pergamon Press. Oxford, 1965), p. 569 [Izv. Akad. Nauk . Ser . Fiz . 17 (1953) 51] [18] F. Lamarche and C. Leroy, Longitudinal expansion of hadronic matter in high-energy nuclear collisions, in Proc. 24th Rencontre de Moriond, Les Arcs, 1989. ed. J. Tran Thanh Van (Editions Frontieres, Gif-sur-Yvette, 1989) [191 NA35 Collab., T.J. umanic et al., Z. Phys. C38 (1988) 79; NA35 Collab., J.W. Harris et al., Nucl. Phys. A498 (1989) 133c