N

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14 March 1991

Beam energy independence of the target fragmentation above Ekin = 1 G e V / N J. Jaenicke and J. Aichelin Institut fiir Theoretische Physik, Universitdt Heidelberg, Philosophenweg 19, W-6900 Heidelberg 1, FRG Received 25 May 1990; revised manuscript received 26 December 1990

Above a beam energyof I GeV/N the distributions of protons and fragments in the target rapidity regime become independent of the beam energy. The reaction scenario is close to that expected from the simple geometricalparticipant-spectator model. The difference between the rapidity distributions of baryons reported for the reaction of Ne (2.1 GeV/N)+ Au and O (200 GeV/ N ) + Au is caused by a different experimental acceptance. The slope of the measured transverse energy spectra of protons at 200 GeV/N ( ( Et ) = 75 MeV) is very close to that calculated at 2.1 GeV/N ( (Et) = 86 MeV ). Thus spectator matter does not act as a "detector" for particles created at high beam energiesas hoped. This is the result of the "quantum" moleculardynamics (QMD) calculations employed for these asymmetric systems.

With the advent of the CERN Heavy Ion Program [ 1 ] it has become possible to study the reaction of asymmetric systems up to 200 G e V / N . This is an increase of almost a factor of 100 in energy as compared to the highest energy (2.1 G e V / N ) which was available previously at the Bevalac in Berkeley [ 2,3 ]. It is of course one of the most interesting questions how different observables change from 2 G e V / N to 200 G e V / N . The data at 2.1 G e V / N and at 200 G e V / N , as analyzed so far, display striking similarities but also unexpected large differences in the target rapidity regime. Aleklett et al. [4 ] found that the yield of specific Na and Sc isotopes does not change above 1 G e V / N . This points towards a similar reaction mechanism as far as the target (spectator) fragmentation, the most probable source of these heavy ions, is concerned. This observation was confirmed by B r e c h t m a n n et al. [ 5,6 ], who measured the production cross section of fragments with charges between 6 and 15. Also the d n / d y distribution of shower particles, measured in emulsion experiments, points towards an energy in-

"~ This work has been funded in part by the German Federal Minister for Research and Technology (BMFT) under the contract number 06 HD 710 and by the Gesellschaft f'tir Schwerionenforschung(GSI).

dependence of the observables in the target rapidity region [ 71. The baryons and light clusters, however, seem to show dramatic differences in the target rapidity domain. The slope of the transverse kinetic energy spect r u m of protons has been reported to be 66 MeV for O (200 G e V / N ) + A u as compared to 123 MeV for the Ne (2.1 G e V / N ) + A u reaction [8]. Also the rapidity distribution differs significantly. These differences are quite unexpected. It has been claimed theoretically and found in experiments that the participant-spectator model describes the basic features of a heavy ion reaction already at beam energies around 1 G e V / N . At larger beam energies the assumptions of this model are even more justified and therefore we do not expect that at higher energies the experimental results deviate strongly from the predictions. In this model the nucleons in the geometrical overlap of projectile and target, i.e. the participants, form a more or less equilibrated fireball whereas the nucleons outside of the geometrical overlap, i.e. the spectators, remain cold. The spectator matter may crack into nucleons and fragments on a timescale which is long as compared to the formation time of the fireball. The physical reason for the validity of this model is the strong forward peaking of the elastic n u c l e o n -

0370-2693/91/$ 03.50 © 1991 - Elsevier SciencePublishers B.V. ( North-Holland )

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nucleon cross section. It causes the trajectories of the projectile nucleons being close to parallel to the beam axis and little momentum can be transferred to the spectator matter. Because above an energy of 1 GeV/ N the momentum transfer in elastic nucleon-nucleon collisions is constant (about 400 MeV/c) we do not expect a change in the behaviour of the spectator matter above this energy as far as elastic collisions are concerned. Inelastic collisions change dramatically between 1 G e V / N and 200 GeV/N. Thus those observables which are influenced by inelastic collisions have to show a strong beam energy dependence. In this letter we investigate the target rapidity regime (Ylab<0.2). There we do not expect to see nucleons which have suffered inelastic collisions. Any inelasticity of a nucleon-nucleon collision reduces the relative momentum of the collision partners in the nucleon-nucleon center-of-mass frame and thus lowers strongly the probability that the targetlike collision partner leaves the collision with a small rapidity in the laboratory system. The center-of-mass momentum of the nucleon-nucleon center-of-mass with respect to the laboratory system places both collision partners at positive rapidity. The shift in rapidity depends on the beam energy and on the inelasticity of the process. The least inelastic process is the creation of a A-resonance. The change of a target nucleon into a A goes along with a rapidity shift of Ay~ 0.2 at large beam energies and of A y e 0 . 4 at 2.1 GeV. Thus on the average the nucleon created in the decay of the A is not observed anymore in the investigated rapidity window. At a beam energy of 200 G e V / N the probability for the formation of a A resonance is very small. The dominant process is the formation of large mass resonances or of strings. For these processes the rapidity shift is much larger because of the larger inelasticity. Thus nucleons involved in an inelastic nucleon-nucleon collision should not be observed in the considered rapidity window. This fact is the prerequisite for the possibility of comparing calculations at 2 and 5 G e V / N with experimental results obtained at 60 and 200 GeV/N. However, light decay products of strings are observed at backward rapidity and if they cross the spectator matter they may cause a difference of the baryon spectra. Instead of investigating in detail the space-time evolution of these hadrons we investigate 342

14 March 1991

whether the baryon spectra change at all with increasing energy (which means an increase of the number of produced particles) at backward rapidities. Unfortunately, if there is no noticeable influence of the decay products one cannot use the spectator matter as a detector for the products of string fragmentation, as hoped. Also this would render any conjectures about an observable space-time overlap of these products and target rapidity protons useless. This conjecture was based on the observation that both types of particles are observed at the same rapidity. Theoretically the baryon spectra in the target rapidity domain at 200 G e V / N and 2 G e V / N have not been analyzed so far with the same theoretical models. The reaction Ne ( 1.05 G e V / N ) + A u has been investigated with the "quantum" molecular dynamics (QMD) model [9]. The results, as far as fragments are concerned, are in very good agreement with the experimental data. The single particle observables have been published only recently [ 3 ] and have not been analyzed theoretically yet. Besides hydrodynamical calculations [10], which fail to describe the baryon rapidity distribution at 200 GeV/N, only Monte Carlo based models like VENUS [ 11 ], RQMD [ 12] and MCFM [ 13] were employed to investigate the baryon rapidity and transverse energy distributions. These models were designed to describe observables which depend on inelastic nucleon-nucleon collisions, i.e. the meson spectra, and little effort has been made to describe the dependence of the observables on elastic collisions. In some of these models [ 12,13 ] the spectra depend on the so-called formation time, which is not yet physically well defined, but is used to account for the assumption, that a certain time is required after the formation of a hadron before it can interact with another hadron with the free cross section. However, even with the most favorable formation time, we observe strong differences between theory and experiment at negative rapidities. The aim of this letter is twofold: First we investigate the reaction N e + A u at 1.05, 2.1 and 5 G e V / N in the QMD approach. We compare the rapidity and transverse energy distributions with the recently published experimental results [3,8] to make sure that the essential physics is reproduced. Then we proceed, comparing the fragment yields at different energies, to demonstrate that QMD produces indeed

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a constant fragment yield beyond 1 G e V / N . Finally we take advantage of this energy independence and compare our results with the data O (200 G e V / N ) + A u of the WA80 Collaboration [8]. We find that our calculation at 2.1 or 5 GeV - which are almost identical - agree better with the experimental data than any of the event generators [ 11-13 ]. This stresses the fact that target fragmentation even at 200 G e V / N is governed by low energy physics, i.e. Fermi motion, binding of the nucleons (a large fraction o f the spectator nucleons is bound in unobserved clusters) and reasonable nuclear forces. These features are not fully incorporated in the event generators yet. We find that the introduction of a formation time is not necessary to describe the baryon data in the target rapidity domain. To investigate the reaction mechanism we perform simulations of the heavy ion reactions employing the n-body Q M D approach [9]. In this approach each nucleon i is represented by a distribution function in Wigner space:

f(r,p,

t)=

×exp{

exp

2L

[p-p,o(t)]22L},

( 1)

where L = 1.08 fm 2 corresponds to the root mean square radius of the nucleons of about 1.8 fro, and h is set equal to 1. The vectors rio(t) andpio(t) give the centers of the gaussian wave packets in coordinate and m o m e n t u m space respectively. They are propagated under the influence of mutual two- and three-body interactions (we use phenomenological forces: local Skyrme type interactions, a long range Yukawa interaction and an effective charge Coulomb interaction ) as described by the Poisson brackets /iio ={P,o, H } ,

i,o ={rio, H } ,

(2/

where the hamiltonian H contains the total kinetic energy and the total potential energy of all nucleons. During their evolution in time, nucleons can collide (if this possibility is not suppressed by the Pauli blocking). For the calculations we neglect the blocking of the intermediate states and use the measured free elastic and inelastic p - p and p - n scattering cross sections in the parametrization of Cugnon [ 14 ]. We employ two different parametrizations to investigate the influence of the cross section on the results.

14 March 1991

In the Q M D approach the kinematics of the particles are treated relativistically, whereas the forces are calculated nonrelativistically. However, it has been shown that a fully covariant solution of the time evolution equation yields practically identical results as compared with the nonrelativistic treatment of the forces, even for reactions in the 1 G e V / N region [ 15 ]. This, as well as the good agreement with experiment as far as fragments are concerned, makes it certainly worthwhile to study this energy regime in the Q M D approach, which allows to sample much better statistics than it is possible with its relativistic counterpart. Further details, as well as test results, can be found in ref. [ 9 ]. We start with the reaction Ne (2.1 G e V / N ) + A u , which has been measured quite extensively by the Plastic Ball Group at the Bevalac in Berkeley [2,3 ]. The results - as far as fragments are concerned - have been compared with the results of Q M D calculations [ 9 ]. We concentrate first on single observables, which have been published recently and are of special importance, since they differ from the data at 200 G e V / N measured recently at CERN by the WA80 Collaboration. As mentioned the results as far as fragments are concerned are very similar for both energies. In fig. 1 we display the experimental baryon rapidity distribution dn/dy for the collision of neon on gold at 2.1 G e V / N for the multiplicity bin 53 as compared with the theoretical results calculated at the impact parameter b = 1 fm. This rapidity distribution includes all singles and clusters with Z~< 2. The theoretical results in fig. l b were obtained with a cross section fitted to n - p and p - p scattering data separately, whereas in the calculation displayed in fig. la it was assumed that all nucleons collide with the p - p cross section. The theoretical results were filtered with the Plastic Ball filter SIMDAT [ 16] to account for the experimental acceptance. Within a factor of two the experimental rapidity distributions are reproduced in the Q M D calculations. As we see, the influence of the different cross sections is rather small, being on the level of 20%. There is obviously no projectile remnant which should appear at .Flab= 1.8. However, the unfiltered theoretical results show a small enhancement at this rapidity. On the average one nucleon o f the projectile survives the reaction with a final rapidity close to the beam rapidity, but the probability of being detected is small. Most of the 343

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14 March 1991

10 3

('21b0' M6V)nLtci.) '

NE'+ IAU **~ tO 2

°DATA " MUL5 m

•~

• %

oQMD H O b

=

ifm

101

d

L00

lO-I

NE +'AU (2100 M,!~V/nucl.) . ~ tO 2

~

°DATA: MUL5 •

e%¢

eQMD HN b =

lfm

tO 1 .

.

d

tO 0

,

IIIIIIl

i0-1

to-2

IIII -i

.

.

.

.

I

. . . .

I

0

I

.

.

.

I

.

i

2

Ytaa

Fig. 1. The rapidity distribution for the reaction of neon on gold at the beam energy of 2.1 OeV/N. Only outcoming baryons are measured and the data [ 3 ] of the most central collisions (MUL5) are compared with the results of theoretical simulations with an impact parameter of b = 1 fin and a cross section fitted to (bottom) n - p and p - p scattering data separately or (top) p - p scattering data only.

projectile nucleons are considerably degraded in momentum in these central collisions. Having established that this single particle observable is well described in our approach, we can proceed to investigate the reaction in more details. Fig. 2 displays the initial coordinate space distribution of nucleons as a function of their final state. We display this distribution separately for those nucleons being finally observed as singles and those being entrained in clusters of the size of 5
A > 50. r0 is the distance relative to the impact point b of the projectile. The participant-spectator model would predict that all nucleons with ro< 3.4 fm, the radius of the projectile nucleus, are participants and contribute to the fireball, whereas the nucleons located at ro> 3.4 fm are the spectators, which survive the reaction mainly as part of clusters. We see that this model indeed predicts the gross features of the reaction. However, also many protons and neutrons come from the spectator part which cracks into many

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14 March 1991

0.1

0.5[

5-15

A=I 0.8 ~

0.075

0.6

0.05

--- 5 GeV/N -- - - 2.1 GeV/N -1.05 GeV/N

o.~

0.3 i ....

J !..~ _1'.

0.2

0.025

o

0

o

2

6 r0 0m)

8

10

_v:

0.1

"

4

_~j_

0.2

0 2

> 50

0.4~

6

r 0 (fm)

8

10

I

I

I

I

2

4

6

8

10

r0 ([m)

Fig. 2. Fraction of nucleons ending finally as singles or in a cluster in a given range as a function of the relative distance ro to the impact point for the reaction of neon on gold at energies of 1.05 (solid line), 2.1 (dashed line) and 5 (dotted line) GeV/N. clusters. Also participant nucleons can finally be t r a p p e d in a large cluster, although the probability is low. We observe an almost identical coordinate space distribution for the three energies investigated. The differences are within the statistical errors. This means that the correlation between initial location and the final state as well as the mass distribution are the same for the three energies considered here. In almost all cases we observe one heavy target r e m n a n t with a mass larger than 50 and a couple o f light fragments. H o w can this be understood? To investigate this question we calculated the energy transfer to the spectator nucleons. We found that the spectator nucleons gain 51, 66 and 69 M e V / N at b e a m energies o f 1.05, 2.1 and 5 G e V / N , respectively. This is a small a m o u n t as c o m p a r e d to that expected for a complete t h e r m a l i z a t i o n o f the system. Also the longitudinal m o m e n t u m transfer to the spectator nucleons is small and o f the o r d e r o f some h u n d r e d M e V / c per nucleon. Thus a higher b e a m energy affects only the p a r t i c i p a n t nucleons, and the spectator physics remains the same for b e a m energies larger than 1 G e V / N. Hence our results confirm the e x p e r i m e n t a l results found by Aleklett et al. [4] and Brechtmann et al. [5,6]. The invariance o f the spectator fragmentation with respect to the b e a m energy raises the question, why the baryons in the target r a p i d i t y d o m a i n , which d o m i n a n t l y come from the decay o f excited clusters m a d e o f spectator matter, show the strong energy dependence observed in c o m p a r i n g the d a t a o f WA80 [8] with the Plastic Ball results [3,8]. N o t only the rapidity distribution is quite different there, but also

the experimental slope o f the transverse distribution differs by a factor o f 2. In order to investigate this question, we applied the experimental cuts (300 MeV > Ekin/N > 20 MeV and - 1.7 < q < 0.6 ) to our theoretical baryon (all singles and clusters with Z~< 2 ) rapidity distribution (see fig. 1 ) at 2.1 G e V / N and 5 G e V / N and c o m p a r e d them in fig. 3 with the experimental results for O (200 G e V / N ) + Au. We observe that the experimental results are almost in complete agreement with both calculations, although the calculations are p e r f o r m e d at an energy 40 times lower than the experimental energy. The large difference between the rapidity distributions at 2.1 GeV and 200 GeV f o r y < - 0 . 4 is due to the acceptance cut in the total energy (Ekin/N< 300 M e V ) . F o r positive y-values the yield is reduced due to the cut in r/. We would also like to m e n t i o n that about 40% o f the nucleons are b o u n d in larger clusters and are not counted here. Please note that the calculations at 2.1 G e V / N presented here and in fig. 1 are the same and differ only by different filters. In fig. 4 we c o m p a r e the experimental transverse energy distribution for Ne (2.1 G e V / N ) + A u for different rapidity windows and that of O (200 G e V / N ) + A u with the calculations at 2.1 G e V / N and 5 G e V / N for neon on gold. We start with the top row, where we c o m p a r e experiment and theory at 2.1 G e V / N for the rapidity window 0 . 0 6 5 < y < 0 . 4 4 3 . The average experimental ( E t > is 123 MeV [ 8 ]. The theoretical results are filtered with the Plastic Ball filter routine S I M D A T [ 16 ]. The Q M D reproduces the slope quite well for energies larger than 120 MeV. Below that there are discrepancies. They m a y be due to the insufficient t r e a t m e n t o f small clusters in Q M D or due to a not perfect acceptance filter. The same 345

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Volume 256, number 3, 4

t°3

~

r

10 2

T

~

f

101

-

~

°DATA: 0

+ AU

200 e.

14 March 199l

[0 0

-

,QMD

i~

GeV/nucl.

eentr.

HN NEI + AU

2.1

GeV/nucl.

b =

lfm

10-1

I T

. . . .

. . . .

I ]

. . . .

I

,

y

[0 2

I

t01

-

~

° D A T A : 0 + AU 200

GeV/nuel.

centr.

o

tO 0

-

e~ ~J

~QMD:

HN NG + AU

5

GeV/nucl.,

b =

lfm

tO 1

t0-2 -

0

1

2

Ylab

Fig. 3. The theoretical rapidity distributions for the reaction of neon on gold at beam energies of 2.1 and 5 G e V / N as compared with experimental data of the reaction of oxygen on gold at 200 GeV/N.

result we obtain when comparing theory and experiment in the rapidity window 0.1 < y < 0.2 in the middle figure. Again the slope is well reproduced above Et= 120 MeV. In the energy interval between 200 MeV and 425 MeV, where almost all particles are detected and therefore the influence of the acceptance filter is small, we find an ( E , ) of 105 MeV for the experiment and an ( E t ) of 97 MeV for the QMD calculations. Please note that the slope is steeper here as compared to the larger rapidity bin. The bottom figure displays our results for 2.1 and 5 GeV filtered 346

with the above mentioned CERN Filter as well as the experimental data of the WA80 group for 200 GeV/ N O + Au. A closer inspection reveals that the CERN filter changes the spectra at Et < 100 MeV (due to the cut in q) and at Et> 250 MeV (due to the cut in Etot). In between theory and experiment agree quite well above E~= 100 MeV, although the calculation is done at a 100 times lower energy. The calculations at 2.1 GeV/N give an (Et) = 86 MeV as compared with the experimental value of (E~) =75 MeV at 200 GeV/ N.

Volume 256, number 3, 4

. . . .

I

PHYSICS LETTERS B

. . . .

8~eS -

tO 3

I

. . . .

mlss

Itg tt~

. . . .

-m

I

. . . .

b = I fm

+

QMD with PB FILTER

o

DATA

mmmmmmmm~ m 10 2

I

NE(2.1 GeV/N) + AU

.065 < y < .443 m

=

I0 t L~J Z

10 0

NE(2.1 GEV/N) + AU b = 1 fm

10 3 mmmm~mm ~:z t~tll~

+

QMD with PR FILTER

c

DATA .1 < y < .2

10 2

t I

mmtll~m~_

10 t UJ Z -o

tO 0

+DATA 200 GeV/N 0 + Au (WA 80) 10 3

~ - m

OQ~D CERN FILTER, 5 GeV/N Ne+Au b = I Irn QMD CERN FILTER, 2.1 GeV/N Ne+Au b = I fm ]~

.1 < y < .2

tO 2 R v

xx 101

xZ

Z

l0 o

t0-~

. . . . 0

J . . . . 200

I . . . . 400

I . . . . 600

I 800

....

1000

E t r a n s [MeV]

Fig. 4. The calculated transverse kinetic spectra as compared with experiment. In the top and middle row we display theory and experiment for two different rapidity windows and for the reaction Ne (2.1 GeV/N ) + Au [ 8,17 ]. The bottom figure compares calculations at 2.1 GeV with the experiment at 200 GeV/N [8]. The theoretical calculations are filtered with the Plastic Ball filter SIMDAT [16] (top and middle) and with the CERN Filter (bottom).

14 March 1991

Thus the different rapidity distributions and the different slopes o f the transverse energy distribution published for the reactions Ne (2.1 G e V / N ) + Au and O (200 G e V / N ) + A u can be a t t r i b u t e d to different experimental set ups, in which a different part o f the phase space is detected. The small differences in
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m o d e l v e r y carefully, b u t are usually not t r e a t e d well in M o n t e C a r l o m o d e l s like M C F M [ 13 ] or V e n u s [ 1 1 ]. T h e r e f o r e it is n o t surprising t h a t the Q M D gives up to n o w the best a g r e e m e n t w i t h e x p e r i m e n t in this r a p i d i t y regime. Finally, to d e s c r i b e the target r a p i d i t y d o m a i n there s e e m s to be no r o o m b u t also no n e e d to i n t r o d u c e the not well d e f i n e d c o n c e p t o f a f o r m a t i o n time. O n e m a y c o n j e c t u r e t h a t this free p a r a m e t e r serves o n l y to r e c o v e r effects w h i c h h a v e b e e n n e g l e c t e d and w h i c h can be t r e a t e d accurately. We are grateful to H . R . S c h m i d t and H . H . G u t b r o d for discussions, for s e n d i n g us the e x p e r i m e n t a l d a t a a n d for e x p l a n a t i o n s a b o u t the e x p e r i m e n t a l set ups. We t h a n k H . R . S c h m i d t for h a v i n g p r o v i d e d us w i t h the transverse energy spectra for different rapidity bin p r i o r to p u b l i c a t i o n a n d K . H . K a m p e r t a n d K. Werner for a careful r e a d i n g o f the m a n u s c r i p t .

References [ 1] Proc. Seventh Intern. Conf. on Ultrarelativistic nucleusnucleus collisions (Lenox, MA, 1988). [2] A.I. Warwick et al., Phys. Rev. C 27 ( 1983 ) 1083.

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[3] H.H. Gutbrod et al., GSI preprint 90-07 (1990), Z. Phys. A, in print. [4] K. Aleklett et al., Phys. Left. B 197 (1987) 34. [5] C. Brechtmann and W. Heinrich, Z. Phys. A 330 (1988) 407. [6] C. Brechtmann and W. Heinrich, Z. Phys. A 331 (1988) 463. [ 7 ] L.M. Barbier et al., Phys. Rev. Lett. 60 ( 1988 ) 405. [8] H.R. Schmidt and H.H. Gutbrod, lectures given at the Intern. Advanced Course on the nuclear equation of state ( Peniscola/Spain, May-June 1989 ). [9] J. Aichelin and H. St6cker, Phys. Lett. B 176 (1986) 14; J. Aichelin et al., Phys. Rev. C 37 (1987) 2451. G. Peilert et al., Phys. Rev. C 39 (1989) 1402. [ 10] T. Rentzsch et al., Mod. Phys. Lett. A 2 (1987) 193. [ 11 ] K. Werner and P. Koch, CERN preprint CERN-TH-5607/ 89 (1989). [12] H. Sorge et al., Ann. Phys. (NY) 192 (1990) 266. [ 13 ] J. Ranft, Z. Phys. C 43 (1989) 439. [14] J. Cugnon and M.-C. Lemaire, Nucl. Phys. A 489 (1988) 781, and references therein. [15]T. Maruyama, N. Ohtsuka and A. F~issler, private communication. [16]A. Poskanzer, Plastic Ball filter SIMDAT, private communication. [ 17 ] H.R. Schmidt, private communication.