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Nuclear Physics A661 (1999) 456c-459c

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www.elsevier.nl/locate/npe

C o a l e s e n c e , I n t e r f e r o m e t r y a n d F l o w

Michael Murray ~ for the NA44 Collaboration b I.G. Bearden, H. B0ggild, L. Conin, J. Dodd, B. Erazmus, S. Esumi, C.W. Fabjan, A. Franz, J. Gaardheje, A. Hansen, O. Hansen, D. Hardtke, H. van Hecke, E.B. Holzer, T.J. Humanic, P. Hummel, B.V. Jacak, R. Jayanti, K. Kaimi, M. Kaneta, T. Kohama, M.L. Kopytine M. Leltchouk, L. Ljubicic, Jr., B. LSrstad, N. Maeda, L Martin, A. Medvedev, M. Murray, H. Ohnishi, G. Paic, S.U. Pandey, F. Piuz, J. Pluta, V. Polychronakos, M. Potekhin, G. Poulard, D. Reichhold, A. Sakaguchi, J. Schmidt-S0rensen, J. Simon-Gillo, W. Sondheim, T. Sugitate, J.P. Sullivan, Y. Sumi, W.J. Willis, K. Wolf, N. Xu and D.S. Zachary

8Cyclotron Institute, Texas A&M University College Station, TX 77843-3366

bColumbia-CERN-Hiroshima-LANL-Nantes-NBI-OSU-SUNY-Texas ASzM-Zagreb

NA44 has measured proton and deuteron distributions from SS and SPb collisions at 200 GeV/c and PbPb collisions at 158 GeV/c. The mean PT of both protons and deuterons grows with system size but the deuterons are somewhat slower than the protons. The phase space density of protons falls with mT but increases for larger systems. The phase space density of i~s is much lower than of protons while their average freeze-out radii are similar. The proton source size increases with system size but not as rapidly as the pion source. For PbPb collisions, all radii lie on a single curve.

1. I N T R O D U C T I O N

Nucleus-nucleus coUisions at ultra-relativistic energies create hadronic matter at high energy density. By studying the transverse mass spectra of different particles one can make a detailed study of thermal, rescattering and collective expansion effects. Deuterons are particularly sensitive to collective expansion effects because of their large mass.

Near central rapidity most deuterons should be produced by coalescence since direct production will be suppressed by phase space and few pre-existing deuterons can survive the many collisions required to move them from the target or projectile into central rapidity. Since coalescence depends on the distribution of protons it is possible to derive a source size from the ratio of protons to deuterons. In order to compare with our HBT data we assumed a gaussian source, [1]. Ignoring the binding energy the radius is then:

+ 4rap E . . . . d3 Nd.u , (1) 2

da q

0375-9474/99/$ see front matter © 1999 Elsevier Science B.V. All rights reserved. PII S0375-9474(99)00496-0

I. G. Bearden et al. /Nuclear Physics A661 (1999) 456c--459c 457c

where q is the deuteron momentum corresponding to the same velocity as the proton momentum p and 6 = 1.58fm, the one dimensional RMS size of the deuteron. One can also derive the density of protons in phase space assuming that deuterons coalesce from protons and neutrons.

Ede~td 3 Ndt~t 1 daq

- 3 E,.o, d3N,.o, d~p

(2)

In this paper we compare protons and deuterons at the same velocity, namely y=1.9-2.3 and pT/A = 0. -- 0.8 GeV/c. We have assumed that the proton and neutron distributions are identical since any nucleons that end up at y=1.9-2.3 must have suffered many colli- sions and are almost as likely to end up as protons as neutrons. To help understand the dynamics the data are compared to RQMD, [2], with a coalescence after burner, [3,4].

2. A P P A R A T U S

NA44 is a focussing spectrometer [5-8], that uses conventional dipole magnets and superconducting quadrupoles to analyze the momentum of particles and create a magnified image of the target in the spectrometer. Hodoscopes, strip and pad chambers measure the position and hence the momentum of tracks. The hodoscopes measure the flight time with trT ~100 ps. A scintillator (To) is used to trigger on central events in by requiring high multiplicity in the pseudorapidity region 1.3-3.5.

3. A N A L Y S I S

To make the invariant cross-sections, the raw data were corrected using a Monte Carlo. Simulated tracks were passed through the full software chain and used to correct for geometrical acceptance, reconstruction efficiency, particle decay in flight and momentum resolution. Particles were generated uniformly in rapidity and exponentially in transverse

mass, rnT -- ~ T + rn2, with the slope determined iteratively from the data. The absolute normalization was calculated using the number of beam particles, the target thickness, the fraction of interactions satisfying the trigger, and the live time of the data-acquisition system. Centrality was determined from the multiplicity in To. The protons spectra were corrected for feed-down from weak decays. This was done using a GEANT simulation with the (A/p) and (~/p) ratios taken from RQMD. This correction is largest for PbPb, since (A/p) is larger.

4. R E S U L T S

The m r spectra are exponential over most of our acceptance and become harder for larger systems. However below m T = 50MeV/c the PbPb proton spectrum flattens out. One measure of the spectral shape is the mean PT per nucleon (which is related to the average transverse velocity) for protons and deuterons. The (pt) /A for both p and d increases slowly with system size and is always smaller for deuterons than for protons both for data and RQMD. This could be due to the necessity of a third particle to carry away the binding energy. However the protons that we see in deuterons may have suffered

458c L G. Bearden et aL /Nuclear Physics A661 (1999) 456c-459c

.~' o.3 "~ 0.25 ~ o.2

0.15 ~ O . I

; I+.

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0.3

0.~

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O

SS

Systematic Error

due to/~P

0.1 0.2 0 O.l 0.2

(m,r-m)/A (GeV/c)

Figure 1. Radii and phase space density for Figure 2. Phase space density versus ps and ffs from NA44 and NA52 [10]. (rat - m ) / A .

fewer scatterings, and thus have a lower < Pr >, than the average proton. Once a deuteron is formed any further interactions will almost certainly break it up. A similar effect was observed when comparing p and t5 spectra, [6]. Because of this effect 15 and d spectra provide complimentary information on freeze-out, [9]. Figure 1 shows that ffs freeze-out at a lower phase space density but a roughly equal radius as protons. This may be due to the large ~ annihilation cross section.

Since deuterons are slower than protons one might expect the phase space density to be larger at low Ft. Figure 2 shows that this is indeed the case. RQMD describes the SS data but underestimates the phase space density for PbPb and misses its Pr dependence.

If the conditions of freeze-out were universal one might expect a constant relationship between the proton and pion radii. Figure 3 shows that the ratio between pion and proton invariant radii increases from SS to PbPb.

Figure 4 shows our pion, kaon and proton radii vs m r for PbPb collisions. All radii are consistent with one curve which drops as m~ "29±'°4. In an analytic hydrodynamic model [12] the HBT radii are interpreted as lengths of homogeneity and are predicted to drop as 1/v~-T. More sophisticated models predict that the "lengths of homogeneity" should have weaker dependences than vZ-m-~, [13].

5. C O N C L U S I O N S

Several features of the data suggest a strong build up of rescattering and therefore energy density. From S,, q to PbPb collisions both the size of the proton source and its phase space density increase. However the pion source size grows more quickly with the number of participants than the proton source. For PbPb collisions the pion, kaon and

I. G. Bearden et al. /Nuclear Physics A661 (1999) 456c-459c 459c

4

.~ 3

2

0 0 '

~+~+ R s (Gamow) p2/d [ ] p2[~]

pp H B T

Systematic Error from A/P

' 0.5 0 . . . . 015 ' PT (GeV/c)

+ i

..... i

/ RQMD+C

0.5

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3

2

1

HBT (R~ RL )1/3 L p2/d Rg ! pp HBT Rg

~ ..... pZld pp

kk ? ~ ? ? ~ ........ ~*

R=3.7/mT.Z~.O4 z2/ndf=4.4/5

°o "0S"0:4 0:6 0:8' i 1S'1:4'1.6 M, M irray QM 99 m T (GeV/c)

Figure 3. Proton and pion radii [5,7,8,11] vs Figure 4. Pion, kaon and proton radii vs PT for different systems, mT for PbPb collisions.

proton all fall a s mT "294-'043 consistent with transverse flow. Finally, antiprotons freeze-out at a lower phase space density than protons.

R E F E R E N C E S

1. W.J . Llope et aJ., Phys. Rev. C. 52 2004 (1995). 2. H. Sorge, H. St6cker, W. Greiner, Nucl. Phys. A 498,567c (1989). 3. H. Sorge, J. L. Nagle and B. S. Kumar Phys. Left. B 355 27 (1995) 4. J .L . Nagle, B. S. Kumar, D. Kusnezov, H. Sorge and R. MattieUo Phys. Rev. C 53

367 (1996) 5. H. Beker et al., Phys. Rev. Left. 74, 3340 (1995). 6. I. Bearden et aJ., Phys. Rev. C 57, 837 (1998), nucl-ex/9711004. 7. I .G. Bearden et al., Phys. Rev. C 58, 1656 (1998) 8. B0ggild, H. et al.; Phys. Lett. B, 458 181-9 (1999) CERN preprint: CERN-EP/98-155,

nucl-ex/9906006. 9. I. Bearden, et al for NA44, these proceedings 10. S. Kabana, et aJ for NA52, Proceedings of 'Strangeness in Quark Matter', 20-24 July

1998, Padova, Italy. Journal of Physics G: Nuclear and Particle Physics, Vol. 25 (1999) 217c Padova Conference 1998

11. D. Richold for NA44, these proceedings 12. T. Cs6rg6 and B. L6rstad, Phys. Rev. C54 1390 (1996) 13. U. A. Weidman and U. Heinz, CERN-TH/99-15, nucl-th/9901094