PHYSICAL REVIEW C, VOLUME 64, 064604

Thermal excitation-energy deposition in 5–15 GeVÕc hadron-induced reactions with 197Au.II. Relation between excitation energy and reaction variables

L. Beaulieu,* T. Lefort,† K. Kwiatkowski,‡ W.-c. Hsi,§ G. Wang,i D. S. Bracken,‡ E. Cornell,¶ D. S. Ginger,**K. B. Morley,‡ and V. E. Viola

Department of Chemistry and IUCF, Indiana University, Bloomington, Indiana 47405

F. Gimeno-Nogues, R. Laforest,†† E. Martin, E. Ramakrishnan,‡‡ D. Rowland,§§ A. Ruangma, E. Winchester,and S. J. Yennello

Department of Chemistry and Cyclotron Laboratory, Texas A & M University, College Station, Texas 77843

R. G. KortelingDepartment of Chemistry, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

L. PienkowskiHeavy Ion Laboratory, Warsaw University, 02-093 Warsaw, Poland

H. BreuerDepartment of Physics, University of Maryland, College Park, Maryland 20742

B. BackPhysics Division, Argonne National Laboratory, Argonne, Illinois 60439

S. Gushue and L. P. RemsbergDepartment of Chemistry, Brookhaven National Laboratory, Upton, New York 11973

M. J. Huang, W. G. Lynch, M. B. Tsang, and H. XiDepartment of Physics and NSCL, Michigan State University, East Lansing, Michigan 48824

~Received 19 December 2000; revised manuscript received 1 June 2001; published 6 November 2001!

The relation between excitation energy and reaction observables has been examined for (6.0– 14.6)-GeV/cprotons,~5.0–9.2!-GeV p2, and 8.0-GeV/c antiprotons incident on a197Au target. Relative to proton andp2 beams, 8.0-GeV/c antiprotons are found to be the most effective projectile for depositing high excitationenergies in the targetlike residue. For protons andp2 the excitation-energy distributions are nearly identicaland appear to be independent of beam momentum above 6 – 8 GeV/c. It is found that total measuredcharge, total thermal energy, and total charged-particle multiplicity scale most directly with excitation energy,whereas IMF multiplicity and total transverse energy exhibit large fluctuations. Correlations of the observedfragment multiplicity, charge, and kinetic-energy distributions with excitation energy indicate a transitionin the reaction observables nearE* /A'4 – 6 MeV. These experimental signals are consistent with amultifragmentation mechanism that becomes the dominant deexcitation mode above in the rangeE* /A;4 – 6 MeV.

DOI: 10.1103/PhysRevC.64.064604 PACS number~s!: 25.70.Pq, 25.40.2h, 25.43.1t, 25.80.Hp

*Present address: De´partment de Physique, Universite´ Laval, Laval, Quebec, Canada G1R 2J6.†Present address: Laboratoire de Physique Corpusculaire de Caen, F-14050 Caen Cedex, France.‡Present address: Los Alamos National Laboratory, Los Alamos, NM 87545.§Present address: Rush Presbyterian, St. Luke Medical Center, Chicago, IL 60612.i Present address: Epsilon, Inc., Dallas, TX 75240.¶Present address: Lawrence Berkeley Laboratory, Berkeley, CA 94720.** Present address: Department of Physics, Cambridge University, Cambridge, U.K.††Present address: Barnes Hospital, Washington University, St. Louis, MO 63130.‡‡Present address: Microcal Software, Inc., One Roundhouse Plaza, Northampton, MA 01060.§§Present address: Mallinckrodt Institute of Radiology, Washington University, St. Louis, MO 63110.

0556-2813/2001/64~6!/064604~11!/$20.00 ©2001 The American Physical Society64 064604-1

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I. INTRODUCTION

During the past decade many challenging new physquestions have been exposed by the studies of nuclear mfragmentation; i.e., the breakup of highly excited nuclei inmultiple clusters and nucleons. Motivated by the desiredefine the parameters of the nuclear equation of state anunderstand the physics of neutron star condensation@1#, ex-perimentalists have sought to resolve several crucial issrelevant to the properties of hot nuclear matter@2#. Canequilibrated systems be clearly identified? Is there evidefor a liquid-gas phase transition? What can the data telabout nuclear compressibility? Is it possible to relate dfrom finite systems observed in the laboratory to the infinsystems that presumably occur in neutron stars? Manyferent physical effects—heat content, temperature,compression/decompression cycle, rotational and shapegrees of freedom—must be understood in order to arrivemeaningful description of the thermodynamic propertieshot nuclei.

Isolation of the thermal component of the multifragmetation process is basic to these studies and is achievedtransparently via systems prepared with GeV hadron be

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@3–9#. Transport calculations indicate that the internal heing in hadron-induced reactions is created byp-N andN-Nscattering andD(N* ) resonance excitation/ pion reabsortion, which heat the targetlike residue on a time scalet&30 fm/c, at the same time leaving it in a state of depletdensity@10–14#. Further, hadron beams suppress the colltive effects of the compression/decompression cycle, rotion, and the shape degree of freedom. Boltzmann-UehlUhlenback calculations@14# indicate that the average entropper nucleon becomes nearly constant after about 30 fmc,suggesting that at least quasiequilibrium is achieved overy fast time scale. Schematically, it is possible to performseparation of the reaction into fast cascade and subseqstatistical deexcitation stages, providing a rationale for inpretation of these reactions in terms of hybrid two-stnonequilibrium/equilibrated decay models@15#. However, itis clear that time evolution of the targetlike residue cannotignored in these processes@15,16#.

Hadron-induced reactions on heavy nuclei (h1A) alsopresent several experimental advantages for the studmultifragmentation and the possible relation of such eveto a nuclear liquid-gas phase transition. First, only a sin

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FIG. 1. ~Color! Contour plot of longitudinalv i vs transversev' velocity of hydrogen~left! and carbon~right! fragments from the

8.0-GeV/c p21 197Au reaction for several bins inE* /A. Solid lines indicate geometrical acceptance of the ISiS array; dashed line givethermal cutoff velocity@34#, not corrected for source velocity.

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TABLE I. Percent of events with at least one thermal particle of chargeZ. Trigger requires at least threcharged particles including one thermal particle withZ>2, in silicon detectors.

Beam Events analyzed%(Z51) %(Z52) %(Z53) %(Z>3)

5.0 GeVp2 1.03106 94.6 96.2 18.9 38.48.0 GeVp2 a 2.53106 93.3 95.2 21.4 42.28.2 GeVp2 2.43106 94.0 96.3 19.5 38.79.2 GeVp2 1.43106 95.1 96.3 20.9 41.5

6.2 GeVp 2.43105 94.9 96.3 18.9 38.110.2 GeVp 1.73106 94.8 96.3 20.8 41.512.8 GeVp 1.43106 95.2 96.4 22.0 39.214.6 GeVp 1.13106 92.5 96.2 20.0 39.2

8.0 GeVp a 5.53104 91.6 95.2 21.4 42.4

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source of thermal-like fragments is produced, as illustraby the invariant cross-section plots in Fig. 1 forZ51 and 6fragments as a function of source excitation energynucleon,E* /A. Further, the hot residues formed inh1Areactions are characterized by low velocities (v i&0.01c),permitting the breakup of the system to be studied in a fravery close to the center of mass. The comparison betwZ51 andZ56 invariant cross sections in Fig. 1 also illutrates another important feature; i.e., the thermal-like frments~enclosed by dashed lines! are emitted nearly isotopically, in contrast with the energetic forward-focuscomponent observed forZ51 particles, which we attributeto fast nonequilibrium processes. These features of the rtion observables play an important role in evaluating thecitation energy/nucleon,E* /A of the hot residue.

Excitation-energy distributions for hadron- and3He-induced reactions have recently been investigated byexperimental groups. At beam energies below 2 GeVBerlin-neutron-ball/silicon-ball@17# array has been used tstudy stopped- and 1.2-GeVp-induced reactions at thCERN LEAR facility @7,18,19# and the ORION neutron balhas been employed at LNS Saclay to study proton-3He-induced reactions@20,21#. These measurements hademonstrated that Au-like nuclei can survive as self-bousystems up toE* ;800– 1000 MeV, subsequently decayinvia the classical low-energy mechanisms of evaporationfission. The highest excitation energies in these experimroughly correspond to the threshold for opening of the mtifragmentation channel, as predicted@22–24# and shown ex-perimentally@16,25,26#.

At higher incident energies the Indiana silicon sphe~ISiS! array @27# has studied~1.8–4.8!-GeV 3He-inducedreactions at LNS Saclay@28–30# and (6.0– 14.6)-GeV/cproton, 8.0-GeV/c antiproton, and~5.0–9.2!-GeV/c p2

reactions at the Brookhaven AGS@6,8,9,31#. These lattermeasurements have shown that at higher beam momabout 100 mb of the cross section goes into events wE* .1000 MeV, which decay primarily via multiple lighcharged particle~LCP: H and He isotopes! and, IMF(3<Z&20) emission and exhibit features consistent w

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statistical multifragmentation models@22–24#. The ISiS re-sults also show many characteristics in common withALADIN peripheral Au and Au studies@32# and the EOS197Au1 12C measurements@33#, although some differenceexist.

The primary objective of this paper is to investigate trelationship between the excitation energies derived in@34#and experimental observables. The data were taken atBrookhaven National Laboratory AGS accelerator usingISiS array, details of which are described in@34#. The num-ber of events that met the hardware trigger of three silicfast signals, at least one of which is a thermalZ.1 frag-ment, are summarized in Table I for each beam. For all prabilities quoted in the text, the total number of eventsTable I is normalized to a unit probability,( i Pi(Ni)51.

The approach of the paper is as follows. In Sec. II tcollision stage of the reaction is examined as it relatesexcitation-energy deposition as a function of hadron typebeam momentum. In Sec. III, the relationship between frment observables and excitation energy is presented. InIV, the conclusions, we discuss the correspondence of thresults with the expected charactistics of a nuclear liquid-phase transition.

II. COLLISION DYNAMICS: PROJECTILE DEPENDENCE

Excitation-energy deposition in GeV hadron-inducedactions follows a much different path than in low-tointermediate energy heavy-ion reactions due to the stronforward-focused nature of theN-N collisions, formation-zone effects, and the significant transparency of nuclear mter in the GeV energy regime@35#. As a consequence of thenergy dissipation mechanism, a broad range of excitaenergies is populated at a single projectile incident eneThus, in a single reaction it is possible to study a spectrumexcited nuclei that extends from low excitation energy upvalues well in excess of the total nuclear binding eneunder identical experimental conditions.

Few theoretical predictions of excitation-energy depotion are available for (5 – 15)-GeV/c hadron-induced reac

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L. BEAULIEU et al. PHYSICAL REVIEW C 64 064604

tions with heavy nuclei. Two major complications encoutered in such calculations are, first, the need to incorporatrelevant scattering cross sections~many unknown! in thismomentum regime, and second, the inclusion of the nucphysics assumptions necessary to fix the amount of enstored in the residual nucleus at the end of the fast cascOne such model is the intranuclear-cascade~INC! codeQGSM @13#, which we examine here. In Fig. 2 INC calculations of the average excitation energy^E* & imparted to Au-like residual nuclei are shown as a function of momentfor proton,p2, and antiproton beams.

The qualitative features of the INC predictions cansummarized as follows. For protons andp2 the average ex-citation energy is predicted to be nearly the same. In contrthese same calculations predict a significant increase in^E* &for antiprotons relative to other hadrons, presumably duethe rescattering and reabsorption of some fraction of thetiproton annihilation pions (np&'5). For the most centracollisions (b<2 fm, or .100 mb!, the calculations show amarked enhancement of high excitation-energy events foprelative top2 beams~see inset in Fig. 2!. Above a momen-tum of about 5 GeV/c the code also indicates a saturationthe amount of excitation energy that is deposited in thegetlike residue, a consequence of the decrease in densithe residue after shower particle emission and the hadrontion time. For comparison with the INC predictions, in Fig.we show the reconstructed excitation-energy and resmass distributions for several of the systems measured inwork. Values ofE* below 250 MeV are uncertain due to thunmeasured neutrons and the requirement of three chaparticles in the ISiS trigger@34#. Data for 6.2-GeV/c and12.8-GeV/c protons~not shown! are similar to other protonand pion data in all figures.

The results in Fig. 3 confirm the qualitative behavior pdicted by the INC code. Specifically, the largest populat

FIG. 2. INC predictions@13# of the average excitation energfor events withE* .50 MeV are shown as a function of mometum for p, p2, and p beams incident on197Au. Inset compares theexcitation-energy probability distributions for 8-GeV/c p2 and pbeams for central collisions (b<2 fm).

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of high excitation-energy events is achieved with t8.0-GeV/c p beam and the lowest with the 5.0-GeV/c p2

beam. In addition, the proton andp2 beams produce nearlidentical E* distributions at the same beam momentuwhile the 8.0-GeV/c antiproton beam produces significantmore high excitation-energy events than does the 8.0-Gecp2 beam. Finally, the predicted saturation inE* depositionis reflected by the relative insensitivity of theE* distribu-tions to beam momentum above about 6 GeV/c.

The residue massAres distributions in Fig. 3 show asomewhat different pattern. In this case the 14.6-GeV/c pro-ton beam produces the lightest residues and the 5.0-Gecp2 the heaviest. This trend can be understood as a coquence of the initial fast cascade, which produces an incring number of fast shower particles as the beam momenincreases~@14# and references therein!. It is this process thatproduces the approximate saturation in average excitaenergy shown in the INC calculations of Fig. 2 and the din Fig. 3.

Quantitatively, however, the INC calculations predictE*distributions that extend significantly beyond the data. Tis shown in Fig. 4, where we compare the experimentalE*distributions for 8-GeV/c p and p2 with the INC code~stopped aftert530 fm/c). The calculation assumes randoimpact parameters and uses values of the code paramthat reproduce other cascade results at lower beam mom(<3 GeV/c) @37#. The two left-hand frames compare thexperimentally derived excitation-energy distributions fp2 ~top! and p ~bottom! beams. Both the thermal definitioadopted in our work@34# and the uniform spectrum cutofof Ei /AIMF,30 MeV of @33# are shown. Although theexcitation-energy enhancement withp beams relative toother hadrons is qualitatively reproduced, the INC predictis seen to overestimate the experimentally derived excitaenergies for both projectiles. In this regard, the cutoffsumption of @33# agrees better with the calculation. Thagreement can be explained in terms of the inclusion osignificant number of nonequilibrium LCPs with the cuto

FIG. 3. Excitation-energy~left frame! and residue mass probability ~right frame! distributions for several systems studied in thwork, as indicated on figure. The distributions are normalizedunit probability, relative to the total number of events~Table I!.

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assumption of@33#, which are also included in the cascadcode excitation energies.

On the right-hand panel of Fig. 4, the mass distributioof the reconstructed residues for the 8-GeV/c p2 and preactions are compared with the cascade code. The mpredicts slightly less mass loss than deduced from theusing the thermal assumption, but is in relative accord wthe results of@33#, which assumes a much higher eneracceptance for thermal particles and therefore larger rdues. The success in describing the residue mass while asame time overpredicting theE* distribution may indicatethat the probability for pion rescattering and reabsorptionthe residual nucleus is too high in the code and/or the fortion time too short.

In order to emphasize the probability for forming highexcited systems, in Table II we examine the ratio of toevents withE* greater than a given value to that for evenwith E* >400 MeV. The normalization atE* 5400 MeV is

FIG. 4. Left: distribution of excitation energy in targetlike resdues for p2 ~upper! and p ~lower! beams. Open circles denotthermal particles only, solid circles include all energies up toE/A<30 MeV and lines give INC prediction@13#. Right: residue massdistributions; all symbols are the same as for left-hand panels.distributions are normalized to unit probability.

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chosen because the sensitivity to the ISiS trigger is minimabove this energy. Table II confirms that the 8.0-GeV/c an-tiproton beam produces a significant enhancement of hexcitation-energy events. In addition, the table showsyield of events with excitation energy above the predicmultifragmentation threshold for Au-like nuclei~a range thatspans 800–1000 MeV or about 5 MeV/nucleon! relative tototal events aboveE* .400 MeV (E* /A* 2 MeV!. Theenhancement for thep beam is approximately 25% greatethan the next most effective beam, 12.8-GeV/c protons.Since an increase in hadron beam momentum ab5 – 6 GeV/c has little effect on the amount of energy depsition, the observed enhancement of excitation energy wantiprotons suggests that the dependence of temperaturexcitation energy~nuclear caloric curve! @36# could be ex-tended to excitation energies that approach the nuclearporization limit by using an antiproton beam in this mometum range.

In order to convert the probabilities shown in this paperthe cross-section observed in the ISiS detector, we havetempted to estimate the missing cross section for eventslow E* ,300 MeV as follows. We have scaled our resultsboth the INC predictions and the experimental resultsPS208@7#. The INC code predicts that 33% of the crosection falls below 300 MeV; when our distributions are nomalized to these predictions, the value increases to 3since the cascade-code overestimates the highest excitenergies. For the PS208 results 49% of the cross sectionbelow E* 5300 MeV. When normalized to our data, thnumber becomes 26%, since our data extend to much hiexcitation energies. We adopt a value of 37% for the misscross section and use a geometric cross section of 2100assumingr 051.20 fm. This gives an estimated measurcross section ofs'13006200 mb, which can be used tconvert unit probability into cross section.

In summary, these studies show that, using the reconsttion procedure described in@34#, excitation energies well inexcess of 1 GeV can be reached in hadron-induced reactThis translates into values up toE* /A'9 MeV ~12 MeV!for all but the highest 1%~0.1%! of the observed events

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TABLE II. Ratio of the integrated events beyond the multifragmentation threshold for three assconditions (E* 5800 and 1000 MeV;E* /A55 MeV) to total events withE* .400 MeV (E* /A.2 MeV).

Beam p(GeV/c) T(GeV)P~E*.800 MeV!

P~E* .400 MeV!

P~E* .1000 MeV!

P~E* .400 MeV!

P~E* /A.5 MeV!

P~E* /A.2 MeV!

E900ap 8.0 7.2 0.30 0.097 0.27E900 p 14.6 13.7 0.23 0.067 0.21E900 p 12.8 11.9 0.25 0.076 0.22E900 p 10.2 9.3 0.23 0.066 0.19E900 p2 9.2 9.1 0.21 0.058 0.17E900ap2 8.0 7.9 0.21 0.056 0.18E900 p2 8.2 8.1 0.20 0.054 0.17E900 p 6.2 5.3 0.19 0.045 0.13E900 p2 5.0 4.9 0.17 0.036 0.11

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Increasing the proton beam momentum beyondEbeam.8 GeV does not lead to a significant increase in theseues because of the nature of the energy dissipation menism for relativistic hadrons. Thus, the bulk of the observcross section in these studies~90–95 %! falls below the mul-tifragmentation threshold ofE* '800– 1000 MeV for target-like residues formed from197Au. In the next section we fo-cus on the highest 5–10 % of the excitation-enedistribution.

III. THE EVOLUTION OF FRAGMENT OBSERVABLESWITH E* ÕA

Two central questions must be addressed in order to cstruct an argument for a nuclear phase transition:~1! has thefragmenting system attained at least quasiequilibrium?~2! is the evolution of the fragment observables as a funcof excitation energy consistent with the expected properof such a phenomenon? The first question can be addreby referring to the invariant cross-section plots for hydrogand carbon in Fig. 1. ForZ51 the existence of two components is evident, one consisting of fast, forward-focused pticles and a second characterized by thermal-like, isotroemission. The fast component decreases systematicallyincreasing fragment charge, so that for carbon~and allheavier! fragments it is negligible, as seen in Fig. 1. Tslow component, bounded by the dashed lines, exhibits Mwellian behavior and behaves similarly for all charges. Whtransformed into the source frame, this component is isopic. Thus, the basic criteria for quasiequilibrium are metthe subset of events within the bounded area, which are idtified as thermal particles in this text.

In the remaining section we address the second quesby comparing the reconstructedE* /A distributions from theE900 and E900a data with direct experimental observafrom ISiS. Many of the examples shown here are for8.0-GeV/c p11 197Au reaction, but other systems are neaidentical.

A. Gauges of heat content

Studies of hot nuclear matter have frequently employvarious experimental observables as a measure of excitaenergy deposition ~centrality! in the collision@8,20,26,30,38–43#. The choice has usually been dependon experimental conditions, since no existing detector aris capable of simultaneously measuring all reaction produand their kinetic energies.

To examine the correlation between these observablesexcitation energy, in Fig. 5 two-dimensional contour ploare shown for the 8-GeV/c p21 197Au reaction in whichE* /A is plotted as a function of: observed IMF multiplicityNIMF ; observed light-charged-particle multiplicity,Nlcp ; to-tal transverse energy,Etr ; total thermal energy,Eth as de-fined in @34#; total observed charge,Zobs, and total boundcharge,Zbound5( i(Zi>2). Superimposed on each plotthe average value of the observable as a function ofE* /A.The plots for NIMF , Nlcp , Eth , and Zbound include onlythermal-like particles, inside the dashed boundary of Fig

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For each of the average observables, a nearly linearcrease withE* /A is found up toE* /A'8 – 9 MeV. Thedeviation from linearity above this value is most likely duto the skewing of the distributions toward lowerE* /A, aconsequence of the exponentially decreasing cross sewith E* /A, as discussed in the preceding paper@34#. How-ever, considerable variation in the extent of the fluctuatiois observed for the various parameters. As evidenced bynarrow widths of the contours, the tightest correlations ocfor the total thermal energy and the total observed chaSince the thermal energy is a significant part of the recstructedE* value and the total observed charge influencthe reactionQ value strongly@34#, a close correlation musresult for these two observables. The multiplicity of lighcharged particles exhibits somewhat larger fluctuatioWhile the Q-value contribution associated with LCP emision is large, gating on LCPs alone permits consideravariation in the reconstruction from which the total eventQvalue is calculated. The correlation can be improved if olooks at the total charged-particle multiplicityNcp by includ-ing the IMFs in the sum, thereby constraining theQ values.Thus, these results are consistent with the use ofEth , Zobs,andNcp as excitation-energy measures of hot nuclei.

The largest fluctuations are found for the frequently usE* markers,NIMF , andEtr . The IMF multiplicity appears tobe a particularly poor experimental indicator of excitatienergy@44#, as might be expected due to the small mu

FIG. 5. Two-dimensional cross-section contours of variousservables for the 8-GeV/c p21 197Au reaction as a function ofE* /A. Solid points are average values for each variable at a giE* /A. Each contour line indicates a decrease of 10% in crosstion and the dotted line on each graph indicates theE* /A valueabove which the last 1% of the cross section is contained.

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plicities. This width is also related to the small effect thIMF emission has on theQ value@34# and the large numbeof open channels at very highE* /A. The large fluctuations intransverse energy are likely due to the inclusion of noneqlibrium light-charged particles in the sum. These particoriginate in the cascade process during energy dissipaand are subject to the fluctuation introduced in subsequknockout collisions. Thus, whileNIMF& and ^Etr& correlatewith E* /A, their large widths must be kept in mind wheusing these parameters in relation to the heat contenhighly excited nuclei. Although the ISiS array does not dtect heavy recoils and therefore is not ideal for determinZbound, we still find a nearly linear correlation withE* /A;the fluctuations in this case are part of experimental orig

B. Fragment charge distributions

The predicted opening of the multifragmentation chanin the vicinity of E* /A'5 MeV @22–24# indicates that mul-tiple IMF emission should appear above this excitationergy. In Fig. 6, this prediction is examined in terms of taverage IMF multiplicity, the probability for emitting a givenumber of IMFs, and the probability for emitting threemore IMFs relative to events with two or less. The unmesured heavy residue is not included in these probabilitHereN refers to the measured multiplicity andM to the truemultiplicity derived from a Monte Carlo reconstruction thtakes into account detector geometry and thresholds. Intop frame, the values ofNIMF& and^M IMF& increase mono-tonically, with no apparent deviations nearE* /A'5 MeV.However, when the averages are decomposed into the p

FIG. 6. Top: average number of observed IMFs~closed circles!and corrected for geometry~solid triangles! and for both geometryand fragment energy thresholds~open triangles! as a function ofE* /A for the 8-GeV/c p21 197Au reaction. Middle: probability forgiven number of detected IMFs as a function ofE* /A. Bottom:probability for IMF multiplicity M>3 ~circles! and M,3 ~tri-angles!.

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ability for emitting a specific number of IMFs~middle frameof Fig. 6!, then a different picture emerges. It is observed tasE* /A increases, the probability forNIMF50, 1 decreaseswhile the channels forNIMF>2 open up systematically withE* /A.

In the bottom frame of Fig. 6, the probability for emittinthree or more IMFs~the classical definition for multifrag-mentation @22#! is seen to grow rapidly aboveE* /A;4 MeV, while that forM IMF50 – 2 IMFs decreases correspondingly. AboveE* /A>6 MeV, fragmentation into threeor more IMFs becomes the dominant IMF decay channelthis context, it should be stressed that the growth of the Imultiplicity with E* /A is accompanied by a correspondingrowth in the light-charged-particle multiplicity, so that thfractional contribution of each to the total excitation enerremains nearly constant, as shown in the preceding pa@34#. Thus, the results of Fig. 6 demonstrate that aboE* /A'5 – 6 MeV, the principal decay channel involvebreakup into three or more IMFs. Below this value, the crosection is assumed to go into fission and evaporation-resformation~the latter measured inefficiently with ISiS!, as hasbeen shown in Refs.@7,19#. These changes coincide withrapid decrease in the relative emission time, which becomconstant at 20– 50 fm/c aboveE* /A*5 MeV for this sys-tem @16#.

Another important aspect that must be considered ininterpretation relative to the multifragmentation mechaniis the relative charges of the emitting source and the cosponding fragments. In the top frame of Fig. 7 we showaverage fraction of source charge~mass! relative to the targetcharge~mass! as a function ofE* /A. The values are ex-tracted from the data by subtracting from the target chathe total charge of all shower/nonequilibrium particles, i.those above our thermal cutoff energy@34# and outside thedashed boundary in Fig. 1. At the highest excitation energthe effect of nonthermal particle emission is quite stronleading to average source charges ofZ;60, i.e., a decreaseof 20–30 % relative to the target.

The middle frame of Fig. 7 shows the average misscharge in our reconstruction procedure, assumed here tosingle fragment. The missing charge is obtained by subtring the total observed chargeZobs ~corrected for efficiency!from the charge of the thermal-like source. This differencethen identified asZmax1 in Fig. 7. These values should bconsidered upper limits, since there is a finite probability tthe missing charge consists of more than a single residespecially as the excitation energy increases. Nonethecomparison with the statistical multifragmentation mod~SMM! @45# indicates that this is a resonable assumption@46#.The solid line in the center panel of Fig. 7 is the missicharge predicted bySMM after passing through the ISiS filteand the dashed line is the maximum fragment charge frSMM. In addition, because ISiS does not detect the smnumber of fast shower particles above 350 MeV, our soucharge in the top frame would be slightly lower if this corection could be made. Nonetheless, the results showaboveE* /A'6 MeV, the missing mass corresponds toIMF, indicating that on the average the source has distegrated completely into IMFs and LCPs.

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The bottom frame of Fig. 7 shows the average chargethe two heaviest observed IMFs as a function ofE* /A, or inthe context of the missing charge, the second (Zmax2) andthird (Zmax3) heaviest fragments in an event. It is apparthat the average charges of the fragments evolve contously toward similar, although not completely symmetricvalues as the heat content increases. This is consistentthe behavior predicted by multifragmentation models@22–24# and with the data of@47#. The charges of the second anthird largest fragments predicted by theSMM model are alsoshown in Fig. 7. Up toE* /A&7 – 8 MeV, the model anddata are in relative accord. At higher excitation energiesSMM model predicts decreasing charge for the largest frments. The version ofSMM shown here stores excess excition energy in the emitted fragments, enhancing seconddecay asE* /A increases and increasing the relative yieldlighter fragments. The data suggest that this version ofSMM model may overestimate secondary decay effects.

Additional insight into the breakup process can be gainfrom studies of the fragment charge distributions, of revance to discussions of critical phenomena and the nucliquid-gas phase transition@4#. The results of a power lawanalysis,s(Z)aZ2t are nearly identical for all projectileand momenta, as shown in the bottom panel of Fig. 8. Atlowest excitation energies, values oft'3 are found, consis-tent with lower-energy proton-induced reaction studies@48–50#. As the system is heated and particle multiplicitiescrease,t values decrease steadily~larger clusters!, reaching a

FIG. 7. Dependence of fractional source charge and Icharges as a function ofE* /A for the 8 GeV/c-p21 197Au reac-tion. Top: fractional source charge of residue. Middle: misscharge in ISiS, assumed to be the largest fragment; and SSMdiction for missing charge~solid line! and for largest fragmen~dashed line!, both passed through the ISiS filter. Bottom: chargetwo largest observed fragments, solid line is theSMM prediction forsecond largest fragment (Zmax2) and dashed line for third largesfragment (Zmax3).

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minimum neart'2 in the vicinity of E* /A56 MeV, justabove the multifragmentation threshold. This behavior is pdicted by the multifragmentation models@22–24#. At stillhigher excitation energies, where multiplicities are large anearly all charged particles correspond to LCPs or IMFstvalues begin to increase. This reversal in trend towardformation of smaller fragments at the highest excitationergies most likely reflects the influence of the excess eneabove the multifragmentation threshold, due to the dissotion of large clusters in the heat bath and/or emissionhighly excited clusters that subsequently undergo secondecay.

The average number of IMFs per residue mass is founbe nearly independent ofE* /A @9#, as shown in the top paneof Fig. 8. This systematic behavior is in good agreement wresults from heavy-ion studies@32,51# and suggests a comparable breakup probability for hot nuclei at a givenE* /A,regardless of formation mechanism.

C. IMF kinetic-energy spectra

Finally, an important probe for estimating the breakdensity in multifragment emission is provided by the IMkinetic-energy spectra, due to the sensitivity of this obseable to the Coulomb field of the emitting source. In Fig. 9 tkinetic-energy spectra for oxygen nuclei are shown at fangles for three excitation-energy bins for the 8.0-GeV/c p2

and 197Au reaction. These spectra are representative oZ>6 fragments observed in all systems studied here. FoZ<6 fragments at the lowest excitation energy, a break inslope at high kinetic energies indicates the presence oweak nonequilibrium component at forward angles@52#.Above E* /A54 MeV, the kinetic-energy distributions foall Z.5 IMFs can be described by a single spectral shthat is nearly independent of angle. The systematic evolu

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FIG. 8. Top: average ratio of observed and geometry-correcIMFs per residue nucleon as a function ofE* /A; symbols are de-fined in bottom frame. Bottom: power law parameterst from fits tothe charge distributions as a function ofE* /A of the residue.

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of the spectra withE* /A shows that the energy of thCoulomb-like peak decreases with increasing excitationergy, as can be seen also in Fig. 1 forZ56 fragments. Thisbehavior is consistent with the measured decrease of

FIG. 10. Fragment mean kinetic energy as a function of IMcharge calculated in the source frame for four bins of excitatenergy, as indicated on the figure. Data are from the 8.0-Gecp2-induced reaction.

FIG. 9. Kinetic-energy spectra of oxygen nuclei at four anglesthe laboratory system for three bins of excitation energy8 GeV/c p21 197Au reaction; open circles are forE* /A52 – 4 MeV; closed triangles forE/A54.6 MeV; and open tri-angles forE* /A56 – 9 MeV. The lines correspond toSMM calcu-lations for breakup volumeV53V0 with extra expansion energyequal to zero~solid line! and 0.5A MeV ~dashed line! @53#. For eachbin in excitation energy, the simulated spectrum is normalized tomaximum of the experimental one. Data are for the 8.0 GeVcp2-induced reaction.

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hesource charge~see above! and emission from an expandedilute system. As expected for a hotter source, the specslopes become flatter with increasing excitation energy.

In Fig. 10 the mean kinetic energy of fragments from t8.0-GeV/c p2 reaction is plotted as a function of fragmecharge for several excitation-energy bins, transformed ithe source frame. The data are found to increase monoticwith charge, as expected from Coulomb effects. But the mdistinguishing feature of Fig. 10 is the near independencethe average kinetic energies on excitation energy ovebroad range ofE* /A. This behavior can be interpretewithin the context of Fig. 9. It results from a compensatibetween competing factors in which the decrease ofsource charge and density~shown by the decrease of thlocation of the Coulomb peak! is offset by the increase intemperature of the system~flatter slope! at high excitationenergy.

Also shown in Fig. 9 areSMM predictions that show theeffects of extra expansion energy, as discussed in@53#. Theextra expansion energy is defined here as the differencetween the observed kinetic-energy spectrum and thatdicted by SMM. Two reference calculations are given, owith no extra expansion energy~solid line! and another withan additional 0.5 A of energy. In Fig. 11 the extra expansenergy that must be included in theSMM in order to providea best fit to the data is shown as a function ofE* /A. The

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FIG. 11. Dependence onE* /A for the following quantities,from bottom up: relative IMF emission timet, extra radial expan-sion energyEexp/AIMF , charge distribution power law exponenZ-t, and probability for a given IMF multiplicity.

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results indicate that the extra expansion effect increamonotonically with excitation energy, but is much smalthan in heavy-ion-induced reactions.

IV. SUMMARY AND CONCLUSIONS

In experiments E900 and E900a the collision dynamand multiple fragment breakup features have been invegated for GeV hadron-induced reactions on197Au. Directobservables have been correlated with excitation energiestermined from high statistics data obtained with the ISiSray, which measures exclusive charged-particle spectra1<Z&16 fragments with excellent spectral definition alarge dynamic range.

The reconstructedE* distributions indicate that relativeto protons and pions, 8.0-GeV/c antiprotons provide thehighest-energy deposition values for the same beam momtum. For proton andp2 beams the excitation-energy distrbutions are nearly identical, indicating an independencehadron type onE* deposition. Above beam momenta6 – 8 GeV/c, the E* distributions show little change, presumably due to increasing transparency, formation-zonefects, and depleted density of the residue. However,E* /Avalues increase slightly with beam momentum due todecreased residue charge associated with increased paknockout at the higher momenta. The observed trends agood qualitative agreement with the intranuclear-casccodeQGSM, although quantitatively the code overpredictsE*deposition.

As signatures ofE* deposition, the total thermal energtotal observed charge, and total charged-particle multipliccorrelate most strongly withE* /A, while rather large fluc-tuations are observed for the IMF multiplicity and total tranverse energy. While the number of IMFs is not a good gaof deposited excitation energy, multiple IMF emissionnonetheless an important signature of the multifragmentamechanism@22–24#. Further, on average 4–5 LCPs aemitted per IMF. Thus, when total charged-particle emissis taken into account, multiple IMF events represent a pcess in which the nucleus has undergone a high degrefragmentation. The excitation energy above which multiIMF emission (MIMF>3) begins to dominate the yields occurs nearE* /A;5 MeV. The decreasing amount of missincharge~assumed largest fragment! also supports the concepof a multifragmentation mechanism, e.g., the missing chafrom our reconstruction procedure corresponds to an IMF

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excitation energiesE* /A*7 MeV. Further consistency isevidenced by the fragment charge distributions, whevolve systematically toward larger fragments up toE* /A;5 – 6 MeV, but at higher excitation energies lighter framents are again favored, presumably due to the secondecay of hot primary fragments.

The IMF kinetic-energy spectra suggest an evolution froemission at normal density to a decay scenario consiswith a system at lower than normal density. This behaviomost apparent in the broadening of the spectra peaks towlow energies~lower Coulomb field! and flattening of theslopes asE* /A increase~higher temperature!. As a result,the average IMF kinetic energies show little change afunction of E* /A.

In Fig. 11 several features of the E900/E900a resultscompared to illustrate the evolution of the disintegration pcess with increasing excitation energy. Both the IMF muplicity data ~top frame! and charge distribution parametrization ~second frame! suggest a transition in the reactiomechanism in the regionE* /A54 – 6 MeV. The third frameshows the deduced extra thermal expansion energy derfrom the fragment spectra@53#, indicating an onset neaE* /A.5 MeV. Finally, in the bottom frame time scale results from an IMF-IMF correlation analysis@16# show a rap-idly decreasing relative emission time up toE* /A'4 MeV,after which a constant value oft;20– 50 fm/c is reached.These very short relative emission times correspond tnear-simultaneous breakup of these highly excited systeThese features of the data aboveE* /A*5 MeV coincidephenomenologically with a process that is suggestive oliquid-gas phase transition@22–24#.

ACKNOWLEDGMENTS

The authors thank R. N. Yoder, R. T. de Souza, J. Vandwerp, W. Lozowski, and K. Komisarcik, at Indiana Univesity and P. Pile, J. Scaduto, L. Toler, J. Bunce, J. Gould,Hackenberg, C. Woody, W. McGahern, F. Kubasiuk, andMruczkowski at AGS for their assistance with these expements and V. Toneev, A. Botvina, and D. Durand for usetheir model simulations. This work was supported by tU.S. Department of Energy and U.S. National Science Fodation, the National Sciences and Engineering ReseaCouncil of Canada, the Polish State Committee for ScientResearch, and the Robert A. Welch Foundation.

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