Energy density, stopping and flow in 10−20 A GeV heavy ion collisions

Volume 243, number 1,2

PHYSICS LETTERS B

21 June 1990

Energy density, stopping and flow in 10-20 A GeV heavy ion collisions H . Sorge, A. v o n K e i t z , R. M a t t i e l l o , H . St/Scker a n d W . G r e i n e r Institut j~r Theoretische Physik, Johann Wolfgang Goethe Universitiit, D-6000 Frankfurt am Main, FRG

Received 15 February 1990

The Lorentz invariant molecular dynamics approach (RQMD) is employed to investigate the space-time evolution of heavy ion collisions at AGS energies (Ekln= 10A-15A GeV). The calculations for various nucleus nucleus reactions at AGS energies show a high degree of stopping power. The importance of secondary rescattering at these beam energies is demonstrated. The computed nucleon rapidity distributions are compared to available experimental data. It is demonstrated that nonlinear, collective effects like full stopping of target and projectile and matter flow could be expected for heavy projectiles only. For nuclear collisions in the Booster era at BNL we predict a stimulating future: Then a nearly equilibrated, long lived (8 fm/c) "macroscopic" volume of very high energy density ( > 1 GeV/fm 3) and baryon density ( > 5 times ground state density) is produced.

In the last few years much theoretical a n d experimental effort has been d e v o t e d to the study o f AA collisions in an energy range b e y o n d the "Bevalac energies" a r o u n d 1 GeV per projectile nucleon. At B N L silicon beams have been accelerated up to 14.6 A GeV and at C E R N oxygen a n d sulfur b e a m s up to 200 A GeV. The m a i n goal o f these experiments is the exploration o f the nuclear stopping a n d t h e r m a l i z a t i o n in such light ion i n d u c e d reactions. It sets the stage for massive b e a m s ( A > 2 0 0 ) which will b e c o m e available in the 1990's. Those will enable the search for the q u a r k - g l u o n plasma, a state in which the partons are no longer confined into i n d i v i d u a l hadrons, but can propagate nearly freely over large distances. Some o f the most i m p o r t a n t questions with respect to the possible phase transition from hadronic to quark m a t t e r are: Is a near equilibrium state formed? W h a t are the m a x i m u m energy and b a r y o n n u m b e r densities? The question whether the p l a s m a if created is baryon-rich or b a r y o n - p o o r is also vitally important for its detection, because some signals are only present in the case o f high b a r y o n n u m b e r densities (e.g. strangelets [ 1 ] ). Does the m a t t e r exhibit interesting macroscopic behaviour, e.g. collective flow? The strength o f the nuclear stopping power is a key variable for all these questions. The A G S energy seems to be very p r o m i s i n g to

achieve nuclear stopping: Experimental data for pA collisions at 24 a n d 100 G e V [2,3] indicate that a nucleon suffers a mean rapidity loss o f A y ~ 2 in a high energy collision with a heavy nucleus like lead. This r a p i d i t y loss due to interactions between the projectile and the target nucleons would lead to a high a m o u n t o f stopping at A G S energies, because the initial r a p i d i t y gap between target and projectile is a r o u n d A y = 3 only. F u r t h e r m o r e , it is expected that the f o r m a t i o n time, which is necessary for a produced secondary to materialize a n d be able to interact with its environment, is short enough that seco n d a r y rescattering can be important. Detailed calculations within the relativistic q u a n t u m molecular d y n a m i c s a p p r o a c h ( R Q M D ) for the reaction Si( 14.5A G e V ) on Au actually have c o n f i r m e d that the a d d i t i o n a l m e s o n - n u c l e o n collisions lead to a nonnegligible contribution to the total interaction and therefore enhance the stopping o f the nucleons [4,5 ]. In this letter we want to present predictions for nuclear stopping, equilibration, b a r y o n and energy densities a n d collective flow which are based on calculations within the R Q M D approach. A detailed description o f the R Q M D approach can be found elsewhere [ 6]. In the following we only s u m m a r i z e the basic features o f R Q M D . In this Lorentz invariant microscopic phase space a p p r o a c h one explicitly

0370-2693/90/$ 03.50 © 1990 - Elsevier Science Publishers B.V. ( North-Holland )

7

Volume 243, number 1,2

PHYSICS LETTERS B

follows the trajectories of all hadrons (including the produced particles). The propagation is done in the framework of relativistic constraint hamiltonian dynamics. The classical motion is determined by Lorentz invariant mass shell constraints and time fixations. The nucleons interact due to quasi-potentials which reflects "the soft part" of the nucleon interaction in matter. The quasi-potentials lead to saturation in the nuclear ground state and are repulsive at higher densities. RQMD combines the classical propagation of the hadrons with stochastic scattering and decay of unstable hadrons. Two hadrons can scatter at minimum two body CMS distance d if their cross section is high enough: d ~ < v / ~ . Pions and other mesons are not directly produced, but result from the decay of excited resonances which are produced in inelastic collisions. The resonance production probabilities in the inelastic nucleon-nucleon, pion-nucleon, pion-pion and kaon-pion channels have been fitted to available experimental data. Various resonances (e.g. for nonstrange baryons all resonances with a mass below 2 GeV) decay according to their experimentally given branching ratios after a mean lifetime given by the inverse of their width. Resonances with even higher masses decay jetlike. Their decay is based on a string fragmentation scheme with parameters giving good agreement with the experimentally observed particle multiplicities, rapidity distributions and transverse momentum spectra in binary collisions between nucleons, pions and kaons. The constituent quarks at the ends of the decaying color string can interact afterwards without time delay, because these quarks are "dressed". In the spirit of the additive quark model their interaction probability remains the same before and after the color string decays. The other produced hadrons need some time before they can interact with other particles. This leads to the inside-outside picture for fast moving particles. In fig. 1 we show proton momentum distributions for inelastic pp collisions in the AGS energy region. They are directly compared to experimental data [ 7,8 ]. The agreement for the proton stopping and the particle production is reasonable. Therefore, an extrapolation to proton-nucleus and nucleus-nucleus collisions seems appropriate. The calculated rapidity distribution for p(24 G e V / c ) + P b is also shown in fig. 1. Unfortunately experimental data are only

A(J

~D

21 June 1990

1.0

I

i

i

I

I

P(12 GeV/c) P

0.8

°" /

0.4 0.2

o

I

(a)

0.351-1.5)~~

0.6 Z

,

0.6

/

0.0 0.0

0.2

0./,

0.6

i

0.8

I

i

P 12,~G,.v/~I+ 1.0 Z

1.0

(b)

P

130 ~0

0:5

\oo

o.o 0

2

4

Rapidity

I

I

1.0

i

i

~124G

i

I

i

eV/c) + Pb(el

0.8 0.6

Z

0.Z,

°

0,2 0.0

I

I

I

2

3

~

Rapidity Fig. 1. (a) Invariant momentum distribution for p(12 GeV/ c) +p-*p + X as a function of x (inelastic collisions), x is the Feynman variable. The distribution is plotted for various values ofpt (0.35, 0.4, 0.6 and 0.8 GeV/c). (b) Rapidity distribution for protons and ions in p(24 GeV/c) + p collisions. (c) Rapidity distribution for protons in p (24 GeV/c) + Pb collisions. The lines represent the RQMD results, the point symbols the experimental data.

Volume 243, number 1,2

PHYSICS LETTERSB

available in the projectile fragmentation region. Here the calculated and the experimental data agree quite well. The experimental data are integrated over the transverse momenta [ 9,10 ]. One important message of calculations is that the proton distribution in the projectile fragmentation region depends strongly on the cross section and the excitation scheme for the projectile after the first collision [ 11 ]. In the R Q M D approach the leading diquark can be decelerated in a subsequent collision with a probability based on the diquark-nucleon cross section (~ of the NN cross section). The energy and momentum of the diquark which must be fixed for the subsequent collision is determined by the same stochastic distribution as for the leading baryon. In contrast, a leading baryon cascade - with zero formation time for the baryon and full NN cross section assumed [ 12 ] - gives too much stopping in high energy pA collisions. The other extreme, namely that the diquark of the original projectile always fragments into a leading particle (this is realized - for instance - in the L U N D model [ 13 ] ), underestimates the nuclear stopping power. At AGS experiments with 10A GeV and 14.5A GeV silicon beams on various targets have been performed. Published R Q M D calculations for the transverse energy production, the charged particle pseudorapidity distribution and the spectra of strange and nonstrange mesons agree very well with the experimental data [4,5 ]. Let us focus now on the problem of nuclear stopping. It was pointed out that the measured transverse energy production supports a picture of complete stopping in heavier targets [ 14 ], in agreement with quantitative predictions of the RQMD approach. The E802 spectrometer group analysed the proton rapidity distributions for Si ( 14.5A GeV) on an Au target for "central collisions" (the 7% highest multiplicity events) within a limited acceptance in rapidity (roughly between 1 and 1.5) [15,16]. In fig. 2 we show the calculated time evolution of the rapidity distribution of the nucleons and produced particles. The finite lifetimes of the resonances and the color flux tubes lead to a strong retardation in meson production. The final snapshot compares the calculated rapidity distribution for the protons with the experimentally measured distribution. The measured distribution has been multiplied by ~ to take the estimated experimental efficiency of 85%

21 June 1990 I

I

'

I

'

I

'

I

-12

>- 100 "o Z "IT

'

50 0

=~" 100 Z •"a

5O 0

0

2

t,

Rapidity

0

2

t,.

Rapidity

Fig. 2. RQMD calculation for the time evolution of rapidity distributions in the Si( 14.5A GeV) on Au reaction at b= 1 fm. The full lines represent the nucleons (in the last picture the protons only), the dotted lines the produced particlesand the dashed line the charged mesons including those from weak neutral strange hadron decays. The final proton distribution is compared to experimental data (dots) for high multiplicityevents. [ 15 ] into account. Note that the calculated "protons" include protons bound in clusters (mainly deuterons) while the experimental data exclude those. both the calculated and the measured proton rapidity distribution show a strong deceleration of the projectile. This confirms a high degree of projectile stopping. Essentially no nucleons are left over at projectile rapidity in the calculations for central collisions. This has recently been supported by the E814 group [ 17 ]. Let us now turn to collisions between equal mass nuclei. Experiments with heavy symmetric systems (e.g. Pb on Pb) are planned at the AGS booster in the near future. Fig. 3 shows the R Q M D predictions of the final nucleon and meson rapidity distributions for three symmetric systems at 10,4 GeV: Si+ Si, Nb + Nb and Pb + Pb. The calculations were done at the same scaled impact parameter b/R: b=0.64 fm (Si), b = 1 fm (Nb) and b = 1.3 fm (Pb). The distributions for Nb and Pb look quite similar. The nucleon rapidity distribution in the Si reaction, however, exhibits a dip at midrapidity and maxima near the original target and projectile rapidities. This indicates incomplete stopping. We can compute from the final nucleon rapidity distributions the stopping

Volume 243, number 1,2 40

PHYSICS LETTERS B i

30

z

/,Y"xx

i

i

i

,

,,"

",Si(10AGeV) St.

,"'

x " Nb(10AGeV) Nb-

2O

"0

0 150

"o

100

z 50

0 /~00

y"',,,, Pbll0AGeV} Pb"

300 -o Z 200 "o 100

,,\ ,, \ ,, -1

0

1

2

3

Rapidity Fig. 3. RQMD calculation for the rapidity distribution of nucleons (full lines) and mesons (dashed lines) in the reactions Si on Si, Nb on Nb and Pb on Pb at 10A GeV beam energy. The impact parameter in units of the target radius is the same: b=0.64 fm (Si), b= 1 fm (Nb)and b= 1.3 fm (Pb).

21 June 1990

ical model [ 18 ]. Collective flow may be observable even at these ultrarelativistic energies. This in turn is o f vital importance for diagnostic purposes: The predicted bounce-off and squeeze-out effects can be used as barometers to measure the pressure built up in the hot dense participant matter. The bounce-offe.g, can be quantified via the measurement o f the directed inplane transverse m o m e n t u m transfer which has been widely used at BEVALAC energies [ 19 ]. Our previously published results show no flow effect for asymmetric systems [20]. WA80 data from C E R N do indeed show this predicted null Px at target rapidity for O(200A GeV) on Au [21 ]. However, the situation does change dramatically if suitably massive projectiles are used. In fig. 4 we present the R Q M D results for the reaction Pb ( 10A GeV) on Pb which demonstrates that strong flow effects can be observed. This prediction can be tested as soon as the booster with heavy ions becomes operational at BNL. If confirmed it would be a dramatic signal for the formation of a ultradense state of matter. The R Q M D calculations are useful not only to predict experimental observables, but also to analyse in depth the transient stages of a collision, especially the early stages where the matter is most strongly heated and compressed. In fig. 5 we show the m a x i m u m local energy and baryon densities in such collisions and their time evolution in the rest system of all participant nucleons (the fireball). A nucleon is defined as

Pb(10AGeV) Pb

ratio S[dN/dy(YcMS) ] I [dN/dy(O) ]. S is equal 2.0 for Si and increases strongly to 4.3 for the Nb and 5.6 for the Pb reaction, i.e. there is substantially more stopping in the P b + P b reaction than with medium mass nuclei like Nb. Note that an independent fragmentation approach with simple straight line geometry predicts only 1050 collisions between the nucleons of the two lead nuclei to occur. In contrast, in the R Q M D calculations 5500 collisions are predicted. The importance of rescattering at AGS energies is obvious. This large number of collisions (more than 5 per panicle on the average) is of utmost importance: It demonstrates that substantial equilibration may be achieved, which may lead to macroscopic,collective behaviour predicted on the basis o f the fluid dynam10

0.1 A

"~x GL V

0.0

-o.1 I

-

I

I

1

I

I

0

1

2

3

/,

Rapidity Fig. 4. T h e m e a n p~ o f the n u c l e o n s as a f u n c t i o n o f the r a p i d i t y .

Px is the projected transverse momentum in the collision plane. the reaction is Pb on Pb at 10A GeV beam energy with impact parameter b= 3 fro.

Volume 243, number 1,2

PHYSICS LETTERS 13

(a) ~.~ E

5

I0

15

0

5

~0

15

o

5

10

15

I0

15

(b)

E

-8

g 5

time ( f r o / c ) (c)

time

1o !

(fm/c)

I.O~, '

,°

,oo

~o. 08

os

.o

06

os

-~ o2 00

•,

•

• •

02

i

i

i

o

5 10 time ( f r o / c )

i

15

O0

i 0

i 5 time

i 10 (fro/c)

i 15

Fig. 5. (a) Local energy density, (b) baryon number density and (c) degree of isotropy (p~)/2(p~) for the two reactions Si( 14.5A GeV) on Au and Pb( 10A GeV) on Pb at fixed impact parameter b= 1 fro. These variables are plotted for the cell of maximum energy density at given time in the fireball system.

a participant if its position lies in the volume which is swept out by the projectile moving on a straight line through the target. We compare the asymmetric reaction Si(14.5A GeV) on Au with the symmetric high mass system Pb ( 10A GeV) on Pb for very central collisions (b = 1 fro). Note that the observer system is different in these two cases, because in the asymmetric case much more target than projectile participants shift the fireball rapidity ( y = 1.2) towards the lab rapidity. In contrast, the number of participants is equal for target and projectile in the Pb on Pb reaction just because of symmetry. However, the reaction time scale which is given by the time needed by the projectile to pass without interaction through the target is quite similar (around 5.6 f m / c ) in these different observer frames. Fig. 5 shows averages over cells of finite volume (2 fm × 2 fm × 1.5 fm). Just after the collision has started the local maximum densities are simply given by an addition of

21 June 1990

the projectile and target densities in the observer frame in which projectile and target frame have the same speed, i.e. for the 10A GeV collision we expect an initial maximum local baryon density of 0.81 fm -3 and for the 14.5A GeV collision a value of 0.95 fm -3 (5 and 6 times ground state nuclear matter density). However, these baryon densities and the associated energy densities are relevant for macroscopic processes (like a phase transition) only if these two matter currents do indeed stop each other in a time which is short compared to the expansion time scale. We see (fig. 5) that in the reaction Si on Au this "kinematic limit" for the local baryon density can be reached in the early stage of the collision. In contrast, the baryon density in the reaction Pb ( 10.4 GeV) on Pb exceeds its kinematic limit by far. This can be understood as a shock compression due to multiple collisions with a density pile up. The time evolution of the maximum energy and baryon densities is strongly correlated as can be seen from fig. 5. How large is the region of high densities in these reactions and what is its lifetime? Let us define the high density region by the prescription that the local energy density exceeds 1 G e V / f m 3. The R Q M D results are that in the Si on Au collisions a volume of about 14 fm 3 - containing an average number of 20 hadrons - has a larger energy density for a time interval of approximately 4 fm/c. In the case of the Pb on Pb reaction a corresponding volume of 35 fm 3 containing 60 hadrons exists for a time interval of 8 f m / c. Afterwards the volume of high density drops quickly. The "macroscopic" high density region in the Pb on Pb collisions therefore has roughly double the lifetime than in the case of the Si on Au collisions. The achieved thermal equilibration can be quantified by computing the degree of anisotropy locally which can be expressed by the ratio R=(p2t)/ 2 ( p 2 ). R = 0 means total anisotropy which is characteristic for the first stage of a collision in which the two nuclei start to overlap and no transverse momentum has been created yet. An isotropic momentum distribution would lead to R = 1. In fig. 5 the time evolution of R is plotted for the cells of maximum density. For both systems it lasts typically 5 fm/c until R jumps to values above 0.5. Due to the larger lifetime of the high density region in the Pb on Pb reaction the matter becomes nearly equilibrated while the region of high density is still existing. 11

Volume 243, number 1,2

PHYSICS LETTERS B

Finally we would like to point out that such large regions of high density living for such large times as found in the R Q M D calculations for the Pb on Pb collisions pose the important question whether the parametrization of this many-body problem in terms of two particle collisions is still justified. However, it is unknown at which energy and baryon densities irreducible many-quark and gluon interactions - for instance a quark-gluon plasma - show up. The RQMD calculations presented here should be seen as a first step to explore this unknown region of nature. Thermal matter at such high baryon densities has probably not been produced since the big bang. Therefore we are looking forward for an exciting future with the AGS Booster experiments.

References [ 1 ] C. Geiner, P. Koch and H. St6cker, Phys. Rev. Lett. 58 (1987) 1825 [2] J.V. Allaby et al., CERN 70-12 ( 1970); D.S. Barton et al., Phys. Rev. D 27 (1983) 2580; W.S. Toothaker et al., Phys. Lett. B 197 (1987) 295. [3] W. Busza and A.S. Goldhaber, Phys. Lett. B 139 (1984) 235. [4] H. Sorge, A. yon Keitz, R. Mattiello, H. St6cker and W. Greiner, in: Proc. NASI School on The nuclear equation of state (Peniscola, Spain, 1989) (World Scientific, Singapore), to be published. [5] R. Mattiello, H. Sorge, H. St/~cker and W. Greiner, Phys. Rev. Lett. 63 (1989) 1459. [6] H. Sorge, H. St6cker and W. Greiner, Ann. Phys. (NY) 192 (1989) 266.

12

21 June 1990

[7] H.J. Miick et al., contrib. 4th Intern. Conf. on High energy collisions (Oxford, 1972); Phys. Lett. B 39 (1972) 303. [ 8 ] V. Blobel et al., Nucl. Phys. B 69 (1974) 454. [9] T. Eichten et al., Nucl. Phys. B 44 (1972) 333. [ 101W. Busza and R. Ledoux, Annu. Rev. Nucl. Part. Sci. 38 (1988) 119. [ 11 ] H. Sorge, A. yon Keitz, R. Mattiello, H. St6cker and W. Greiner, in preparation. [ 12] C.Y. Wong, Phys. Rev. lett. 52 (1984) 1393. [ 131 B. Andersson, G. Gustafson and B. Nilsson-Almqvist, Nucl. Phys. B 281 (1987) 289. [14] E802 Collab., T. Abbott et al., Phys. Lett. B 197 (1987) 285; M.S. Tannenbaum, Nucl. Phys. A 488 (1988) 555c; Intern. J. Mod. Phys. A 14 (1989) 3377; E814 Collab., P. Braun-Munzinger et al., Z. Phys. C 38 (1988) 45. [ 15 ] E802 Collab., M. Sarabura et al., Nucl. Phys. A 498 (1989) 409. [ 16 ] E802 Collab., T. Abbott et al., submitted to Phys. Rev. Lett. (1989). [ 17 ] E814 Collab., J. Barrette et al., submitted to Phys. Rev. Lett. (1989). [ 18] For a review and further references see H. SttJcker and W. Greiner, Phys. Rep. (1986) 137. [19] H.A. Gustafson, H.H. Gutbrod, B. Kolb, H. L6hner, B. Ludewigt, A.M. Poskanzer, T. Rennet, H. Riedesel, H.G. Ritter, A. Warwick, F, Weik and H. Wieman, Phys. Rev. LeU. 52 (1984) 1590; H.G. Ritter et al., Nucl. Phys. A 447 ( 1985 ) 3c; K.G.R. Doss et al., Phys. Rev. Lett. 57 (1986) 302; R.E. Renfordt, D. Schall, R. Bock, R. Brockmann, J.W. Harrris, A. Sandoval, R. Stock, H. Str6bele, D. Bangert, W. Rauch, G. Odiniec, H.G. Pugh and L.S. Schroeder, Phys. Rev. Lett. 53 (1984) 763. [20] H. Sorge, H. St/Scker and W. Greiner, Nucl. Phys. A 498 (1989) 567c. [21 ] WA80 Collab., H.R. Schmidt, Z. Phys. C 38 (1988) 109.