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a~ LpC Caen, IS~IRA, IN2P3-CNRS, 14050 Caen, France, b) fï

II,, i3P 5027, 14021 Caen, France, c~DPhN/~E CEN, Saclay 91191, Gif Sur Yvette, Fr

ce, d) LPN, 2 Rue IJoa~ssiniére, 44072

tes, F

ce, e~Ripant. di Scivo®ze Fisic:~.,, ; ;®tiv. v: N?p~1®, ia;~Ov, ~ Present address : Cyclotron Institute Teas A

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Un:~..College Station, TàC, USA, g) S

, Stony P~~ook, USA, ilj I®®st . oà blade

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ho°~,China, i) Inst. of Physics, Tokyo Inst. of Technology, Tokyo, Japan, k) R.

yo University, To

o,Japan, ô~Permanent address : Inst. de Fisica, Univ. de Sao Paulo, CP 20516, Sao Paulo, Rraza,

)Present address : PZdivision, Los Alamos National Laboratory, USA, n) Permanent address : Institue of Nuclta~ Research,Shanghaï, China.

The multidetector array

ur + Tonneau has been used to erfo

a4~ detection ofcharged particles and fragments emitted in reactions etwQen

Ar , at energies ranging from25 to SS

eV/u , and 2~AI or SSi~i target. The events have been sorted as a function of theimpact par

star value.

e collective transverse momentu

in

e reactio~i plane (st ewardsflow parameter) is observed to strongly vary as a function of impact parameter and incidentenergy. At low energies, it is shown to be negative . t inverts to positive ~ slues at

amenergies in the

ge 70-I

e~i/u depending on the '

pact parameter value a~~

~; :

s ofthe system. These data are cor!?parPd to d;n~miral calcy:atïons basedon L~~ g

d

w. i~~this ~rt~~gy t~~!g~ ; the ça~~~~12t~~ n~:~i v3iae5 sire mlic

tno?'e S~nSitiv~ l~ ~~~ ~°li~~:i

n-~uCi~~ncross section in medium and to the equation of state than at relativistic energies ;therefore,quantitative info

ation can be obtained.

blishers

.~. rlil rights reserved .

Above 20

eV/u , nu aeons and clusters are em~itte

lai the first stage ~f the nccleus-nucleus encounter. Their study provides info

anon on nuclear matter in the of co

r°,seedinteraction region (the overlapvolume of the two nuclei,

sosalted

ici a~~t n,icleons~, viathe component px of

etransverse mometitu

t ofnucleons ia~ the reaction la

[1). Thisanalysis gives the sidewards,fl®w araraaeter value ~looscyra ~®~~a :~~ f~ ~r~~

i high ~ em~ies, theinteraction is

®rn:aated bj :o~,c-ü:;'b,- c..û::âs:o:.~ merit tl~1J ~u~ is at

`bated to a re uDsivemcrrtentum transfer in the compressed interaction region X21. Conversely, at a few tens of

anwies.ill the rall

nucleon cross section CFNN in nuclearalas K of infinite nuclear matter. Iincompressibin

influoncesvalues, the

al

iteraction is dominated by the attractive meapaectile direction (in c,m, frame) are expert,am aegadvc to poshWe now values sho

401- 1MMAN according to calculatictis with tine

scopic Landau-Masov model 14L

ki ,Ain di

!r et cil, i litt,e,,rsiï)ll

malier

NN and K by comparing the resultsw should be measured as a function of

the. impact parameter.

We 1-.ave designed and performed an exclusive experiment in which the charge andIvewciiy of nearly all charged products were measured on an event by event basis. We have

chosen the '0~Xr + 27AI systems from 25 to 65 MeV/u in steps of 10 MeV/u and 85 MeV/uand 40Ar+ Ni at 36-a-ad 65 ale /u .

We used two complementary detector arrays, U151dTONNEAU [61 which givethe charge (up to 8) and the velocity of all charged products : fig. t . Several characteristics ofthis set-up help to get a good impact parameter sortingand a good reaction plane determination

Y'~ geometrical efficiency, - small detection threshold (4.5 MeV/u for Z= I and 2),small value of the minimum detection ancyle (3.2'), - axial symmetry.

In addition, the velocity of eachparticle

isobtained

directly. Therefore, its momentumper nuclecra, used to vet the flow ar'a~neter value, is gall ate

In most very peripheral reaction events (impact parameter b above 6fin, since bmax8 fm for tar + A), the projectile-like fragment is emitted below 3.2' and the reaction plane

cannot be reconstructed. We keep for further analysis only those events where the total parallelmoment,um of the detected products is above 65% of the projectile linear momentum (most atthem aire - 85 %,). This selection of well measured events keeps all central and intermediate

. .pact pau=eter reactions as well as afew well characterized peripheral reactions.

wl serqq1P

field and participant nucleonsto be deflected to negative

16 occur at an incident energyoltzmann equation [31 and the

he How values aresensitive

Wh to be nucleon-

edium and to the equation of state through theer to disentangle the respective

f such calculations to experimentalvariables, namelly the incident

The sorting of events according to b is made via the value of the average (n,.2,ss_weighted) parallel velocity 171. Above 2 fns , an impact parameter resolution of I Q ~~)is achieved for the systems studied here at energies above 40 MeV/u . This sortin allowed usto determine the number of preequilibrium nucleons (observed at mid-rapidity) [81 and tmeasure their sidewards flow as a function of the impact parameter and the incident energy 191.

3 - EXPERIMENT

nucleon, < px / A > versus the rapidity y of the detected particle (y S 0// below 100 MeV/u).Since there is some indetermination in the reaction plane direction, the value obtained is not< I/A >, but a lowervalue denoted < px','A >.

irect evidence of negative flowWhen the "spectator" projectile (rasp. target) fragment is scattered to the same side as

the forward (reap. backward) emitted pre-equilibrium particles, one cannot know wheside corresponds to positive or negative angles, i.e. whether the flow positive or negative .There is a situation where this ambiguity can be solved : at incident energies below theinversion energy, the pre-equilibrium nucleons are deflected to forward negative angleswhereas, in very peripheral reactions, the projectile-like fragment (PLF) weakly interacts withthe target nucleus and is scattered around the positive grazing angle : Fig. 2-right.

J. Péter et al. 1 Inversion of collective matter

ESULTS

One wants to get the variation of the average in-plane transverse momentum

FIGURE 2 :Negativeflow in per rnheral reactions of 35 Meillu 64Zn on

RY 10

er

75

r

is

We recently observed such a situation in reactions induced by 64Zn from 35 to60 Me% on 58Ni 1 101. The PLF was detected by additionnal telescopes . In fig. 2-left, itsdirection is taken as the impact parameter vector direction. Around yp/2 the pre-equilibritimparticles (participants) exhibit the linear variation of < px'/A > versus the rapidity whichcharacterizes directed collective motion . The negative slope means negative flow (orbiting). Atthe projectile rapidity, < px,/A > becomes much less negative, since there is a contribution ofprotons sequeitially emitted by the PLF, i.e. with positive px' values. At the target rapidity,the contribution of sequentially emitted protons is weaker, since many of them are elln 'netby the detection threshold.

Me

analysis metvalue of the

suive),

rametcases, be"Anplane

II I with the recoil vow parameter can

r

verage sidew-,irds transversemomentumWe ./c per nucleon)versus rapidity of protons atseveral impact laai-zmieter values,in 45 N eV/, U

.t Ar on

2 'AIreactions . Yp is the projectilerapidity .

t al, I Inversion of collective matterflow

E15 'L

5

201

10

A 5Y 0

V _!

_0

Z-t

r valuesion is de"ned by the transverse momentum

locity coffection IIR As said above, only the absoluteobtained (the slope of < p11'/A > versus Y is always

3 shows a series of plots of < px/A > versus y obtained at 45 MeV/u , for=I , in bins corresponding to several impact parameter values. 'Me location ofthe "spectatoe"

equilibrated nuclei is shown by a rectangle (projectile-like fragment in peripheral collisions,incomplete fusion nucleus in central collisions). Again, we aserve a well defined slope atWrapidity and this slope decreasc at the "spectators" rapidity, since the particles they emit have asmaller in-plane momentum.

J in-pianeE. flow

ba%"C

The flow parameter is the slope at mid-rapidity, multiplied by yp/2,( 1,21 . It is shownin figure 3 at 4.5 fm . Its variation versus b is plotted in figure 4 at 4 energies, for Z=1 andZ=2 . 2-5 MeV/u is similar to 36 Me", 55 MeV/u is intermediate between 45 and 65.Thet1ow parameter at 36 MeV/u does not depend as strongly on b as at the other energies andhas the largest observed values . In central collisions, at 45 MeV/u , the kinetic pressure startsto build up. Inside the interaction region, where nucleons get closer, the potential is lessattractive and the flow parameter falls to smaller values . At 55 and 65 MeV/u , this effectbecomes stronger and the flow parameter is very low at 85 MeV/u .

Larger flow values are observed for Z--2 than for Z--1 . This effec.has already beenobserved 2,10). It has been attributed to the role of thermal motion which tends to reduce thealignment into the reaction plane due to collective motion : in the limit of completethermalization, the thermal energy of a cluster is the same whatever its mass, i.e. the thermalenergy per nucleon is lower for heavy clusters than for nucleons, and their flow parameter isless reduced [2) . Simulations on this basis, however, cannot explain quantitatively thedifference observcd . Coulomb repulsion is, at least partially, responsible for this increase offlow with Z 14).

Of +20 +1+

11T

0 J.

la 0

500

idui ~2

1 ' ' ' ' '

Cr.' *

(mb)'

11,

1 2

3

4

5 bLxp 6

401

a1 6SUeViu

J. Peter et al. / Inversion ofcollective matterflow

79c

a36 UV1u

M"-Z=2

+

Saoa

10131) rent)) 1500

Sao a 1 -'6Co (01r1b) "'SGO

i 2

3

4

5I~bexp

6Vm)

7

ex® 6(fMj

FIGURE, 4 :Absolute values offlow as afunction ofthe experimentally determined impact parameter value(bexp),for Z=1 andZ=2 Articles, Ar+Al at 36, 45, 65 and85 MeVlu . Date at 55 MeV111Pareintermediate between those at Kand65 MeVlu . Actually, theflow is negative at least upto 65 MeVlu Error bars indicate the uncertainties in getting the slopes (see Fig. 3) . Thesevalues are not correctedforIdifference between the true andmeasured reaction planes andare thus lower limits.

The variation of the flow parameter values versus the bombarding energy, for b E 3fm is shown in fig. 5 (open points), assuming it is negative. Note, however, that the point at85 MeV/Ucan as well be positive (the inversion energy is then -80 Me"11u).

For Ar + Ni, a steeper variation from 36 to 65 MeV/u is observed. It indicates tinatthe inversion energy is lower, in qualitative agreement with theoretical estimates [3,41.

I

Z=1t

I

(Om)

Measured versus real flow valuesThe measured flow parameter value is normally less than the true value because ofthe

reaction plane indetermination . It is important to understand that this deviation is due firstly to

I effects :ed 111o'k

Mative to ILwaction planinfluencethermal momen

feet atnulat

values (snialllinlitad

rarzicles as afivictioner~.qy fo, r hnpacz parameter

fin in reactions of 4OAr onAl . Open circles : uncarrecied

alues, assuined io be negazive .Closed circles : values correctedrhze diif,ference benveen the true andmzeasured reaclion planes . They areconzpared to calcidations based on theLay,:dau-Wasov inezhod for theneighbouring '!~VSC,71 40Ca+40Ca 141 .

Ii1k:11tuill, ~Upcfflllpo&

r

NN is 1he eteczive nucleon-nucleonCrOSS SeCtiol ., in Inedilan .

Inversioit of colleclive inatter fla

de to the emismon of particles havinto the flow m entum. If the thermal

t1ow momentum., the final direcO-n of the particles remain cland one gas a goW location of be reactionp ue.e. In theflow momentum on the direction of the particle is was

i, i herefoie, even with an ideal detector which detects'ass and ney resolution, the rention One indetermination ca

te were used to studthis problem on the system Ar + A! 1121 . For large flow~,%,c / nucleon), the TWence between the real and measured flow values is

, but it increases strongly for smaller flow values. Secondly, the real detectorcredse this indeteniiination, Ourdetector acceptance was found to have -a minor

MrAe, ci.,vinpared to thermal effects 1 12 1, but this is not necessarily true for other4 x arrays.

i.-thods have been devised to find the avegre angle difference between the real andIhned reaction planes J 1,21 . Correction factors obtained by these methods are used on theove, in Wer to allow for a comparison with theoretical calculations . These correction

'actors- -are, however, subject to some uncertainties.

sp

I

randomlyenturn is smallto that of thesite case, the

ut by the largcicies withbe large.

Actually, there is one point where such correction factors areinversion energy (or balance energy 111 1) where the flow is zero . In earlier cvalue was found to be strongly dependent on M and K . More complete calculations haveshown that this single point is not sufficient and the flow variation around the inversion eneTshould be studied An important fact, however, remains : the calculated values are mucmore sensitive to the ingredients of the calculation in this energy range In at energies above

eWu . Therefore, quantitative pieces of information should be obtained through acompa son to experimental da

A

5-T E FUTURE OF FL

ISON WITH THEORETICAL CALCULATI

J. Péter et 1. / Inversion of collective mauerflo

STUDIES

t needed :theIculations [31, this

p to now, such comparisons hue ken made by correcting the data for the reactionplane indetermination . These points, in black hi fig.5, are compared to a calculation basethe Landau-Vlasov equation, with the Uehling-Uhlenbeck collision term, including Coulombeffects 141 . Depending on whether the flow at 85 MeV/u is still negative (as plotted in the

re) or already positive, the effective '.'alue of (YNN used in the calculation should eitherreduced to - 80% or is correct. Additionnal data above 75 MeV/u could elucidate thisquestion. That shows how accurate information can be gained from such comparisons.

Anothercomparison has been made to quantum molecular dynarnics calculations 1 131 .ycomparing the Gogny force and the Wada force (large K value, no momentum dependence

of the mean field), it is shown that the incident energy dependence only by the densitydependence is not capable ofreproducing the experimental data. T'he momentum dependence ofthe mean field is necessary. One should note that this momentum dependence can be mockeby a large K value (stiff EOS) at incident energies above the inversion point 1 13 1, but this isnot possible below the inversion energy 11`1 .

As seen above, the experimental information cannot be restricted to the values of theinversion energy versus the impact parameter and target projectile masses . "Ie variation belowand abo-ve the inversion energy must be taken into account.

Instead of correcting the experimental flow parameter values for he reaction plane;ndetermination, a better way is to include this efftct in the calculated values . The real reactionplane should be forgotten and its direction should he obtained by the same transversemomentum technique III as the experimental events . Firstly, a perfect detection of all finalproducts should be assumed. That takes into account the effects due to random thPrr::al motion(and also the small effect due to the exclusion of the particle of interest 11 1), leading to asubstantially less steeper slope of <px/A > versus the rapidity, i.e. a reduced flow value.

Secondly, this calculation should be repeated with a software filter which reproducesall detector limitations. A good quality 4n array should not modify much the flow value ascompared with the perfect detector. If it does, the comparison to experimental data will beuestionnable.

Fig. 6 shows an example of such a comparison between uncorrected experimental< px'/A > values and calculated values taking into account the reaction plane indetermination(which has a large effect) and the MUR + TONNEAU limitations (which have aminor effect).

In addition to me Row param.star value, another piece of information is the number ofnucleons emitted from the; interaction region, which has a strong impact parameter dependence[8] . At relativistic incident energies, this number is simply governed by geometry (participantnucleons in the overlap volume), but below 150 MeWu , this nt.mber is sensitive to theeffective interaction. WhenevPr possible, not only this number of nucleons should be studied,

J, Peter et ah I Inversion of collective matterflow

but also their rapidity distribution dN/dy . Also, out-of-plane transverse momentum valuescontain some information about squeeze-out of matter and/or rotation-like behaviour of theinteraction region 1 15 1.

conclude, an effort is feasible on the experimental side to get reliable data withquality 4it detector arrays. On the theoretical side, the reaction plane indetermination and

the detector limitations should .be taken into account. Then, an extensive set of data andcalculations should be made to measure the sidewards flow parameter values, the number ofnucleons emitted from the interactive region andthe out-of-plane flow component.

Such studies, in the energy range 05150 MeV/u , as a function of the impactparameter and for different systems, provide a tool to get quantitative information on thenucleon-nucloon cross section in nuclearmedium and the equation of state (incompressibilitymodulus, out-of-equilibrium matter properties).

IGURE 6 :Alwi sWivards transverse moinenuan per nucleon as afunction ofthe longitudinal rapidity .nefilledsquares and black circles show the experimental resultsfor Z=I, Z=2 fragmentsthe theoretical results are shown by open circles . From Ref. 13 .

EFERENCES1) P. Danielewicz and G. Odyniec ; Phys. Lett. 157B (1985) 146P. Danielewicz & al ; Phys. Rev. C38 (1988) 120

2) K.G. Doss & al ; Phys. Rev. Lett. 59 (1987) 2720C.F. Bertsch, W.G. Lynch, M.B. Tsang ; Phys. Lett . B189 (1987) 384

4) V. De La Mota, F. S6bille, M. Farine, B. Remand, P. Schuck ; Preprint Nantes 91-01,Proc. of XXIX Meeting Bormio (1991) to be published.

5) G. Bizard & al ; Nucl . Inst. & Meth. A244 (1986) 4836) A. Wghaire & al ; Nucl . Inst, & Meth. A299 (1990) 3657) j . Mer& al ; Nucl. Phys . A519 (1990) 6118) 1 Nter & 3 ; Phys. Lett . B237 (1990) 1879) J.P. Sullivan & al ; Phys. Lett . B249 (1990) 810) Q W&a& al ; Communication to Nikko meeting (june 1991) and to be published .I i) C.A. Ogilvie & al ; Phys . Rev. C40 (1989) 259012) IP. Sullivan &I Pdttr ; to be published13) F. S6bille & al ; Communication B-06 at this conference14) A. Ohnishi, T. Maruyama, H. Horiuchi ; communication B-02 at this conference15) 1 Cosset & al ; Phys. Rev. Len. 62 (1989) 1251