by Walter Greiner and Horst Stöcker

namely about 1,000 degrees, the wa-ter molecules are destroyed by violentcollisions and water becomes a plasmamade up of electrically charged ionsand electrons.

Analogous phases are thought to ex-ist in hot, dense nuclear matter. Theground-state, or normal, nucleus israther like a liquid droplet: individualprotons and neutrons (known collec-tively as nucleons) move about freelywithin the droplet but seldom stray be-yond its surface. In the ground state,where the temperature is effectivelyzero, the density is 2.8 X 1014 gramsper cubic centimeter and the press ureis zero. (The press ure must be zerosimply because the nucleus is uncon-fined: if the press ure were greater thanzero, the nucleus would expand, and ifthe pressure were negative, it wouldcontract.)

The study of heavy-ion collisionshag already given evidence of a tran-sition to a high-temperature vaporlikephase, in which the nucleons move fastenough to overcome the cohesive nu-clear forces. In essence nuclear matteris observed to boil. At still higher tem-peratures the nucleons themselves aretransformed into particles of greatermass. There is speculation that at highdensity but comparatively low temper-ature there may be an ordered phase ofnuclear matter analogous to a crystal-line solid. If even greater compressionor heating can be achieved, the nucle-ons may be destroyed and the nuclearequivalent of a plasma may appear; itwould consist of quarks and gluons,the constituent particles of nucleons.

Even using beams of relativisticheavy ions it is not possible to studythe phase diagram of nuclear matterby means of the deli berate and careful-ly controlled experiments employedwith other forms of matter. A high-en-ergy collision of two nuclei is anythingbut controlled. The nuclei crash intoeach other and interact vigorously,raising the density and the temperature

trolls. The nucleus ac counts für almostall of the mass of an ion, and so Ollecan think of it as simply an acceleratedatomic nucleus.

The capabilities of a heavy-ion ac-celerator depend on how much energyit can impart to a nucleus and on howlarge a nucleus it can accelerate. Theenergy is generally expressed in mil-lions or billions of electron volts (Me Vor GeV) per nucleon; the size of thenucleus is simply the total number ofnucleons, equal to the atomic massnumber. The synchrophasotron at theJoint Institute für Nuclear Research atDubna in the U.S.S.R. can accelerateions of neon (atomic mass 20) to anenergy of 4 GeV per nucleon; at thatenergy the ions move at 98 percentof the speed of light. The Bevalac atthe Lawrence Berkeley Laboratory ofthe University of California reaches 2GeV per nucleon with ions as heavy asuranium (atomic mass 238).

The accelerated nuclei collide withnuclei in a stationary target. The out-come of the collision depends on sev-eral factors: the energy of the acceler-ated ion, the mass of both the pro-jectile and the target nuclei, and the"impact parameter," which indicateswhether the nuclei meet head on orstrike a glancing blow. As might beexpected, the most violent events arehigh-energy, head-on collisions be-tween very heavy nuclei.

A major aim of studying such eventsis to determine the equation of

state of nuclear matter, the equationthat describes how the nucleus re-sponds to changes in temperature,pressure and density. For an ordinarysubstance such as water the equationof state can be found through straight-forward experiments. For example,water at atmospheric press ure goesthrough a familiar sequence of phases:it is asolid below zero degrees C.,a liquid up to 100 degrees and then avapor. At a much higher temperature,

T he nucleus of the atom is a bit ofmatter quite unli~e anything fa-miliar in everyday experience. It

is extraordinarily dense: a thimblefulof nuclear matter would weigh a mil-lion tons. Nevertheless, the substanceof the nucleus can be described interms of the same physical propertiesthat characterize any other form ofmatter. Of particular interest is the re-sponse of nuclear matter to changesin temperature, density and pressure.Water undergoes dramatic changeswhen the temperature is raised fromzero degrees Celsius to 100 degrees.Nuclear matter might be subject toanalogous transformations, hut up un-til now there have been no experimen-tal methods tor inducing them. It is asif water could be studied only at roomtemperature and press ure and nothingwere known of ice or steam.

What has changed this situation isthe development of relativistic heavy-ion accelerators, which bring abouthigh-energy collisions between mas-sive nuclei. The collisions are said tobe relativistic because the nuclei moveat nearly the speed of light, so that ef-fects of the special theory of relativitybecome important. Such collisions of-fer the unique opportunity to com-press nuclear matter to several timesits normal density and to heat it to tem-peratures in excess of 1012 degrees.Comparable conditions ex ist inside aneutron star; the interior of the Süll, incontrast, is at a temperature of only106 degrees. Still more powerful accel-erators may be ahle to create on a nu-clear scale the kinds of matter that ex-isted at the birth of the universe in thebig bang.

The accelerators employed in workwith relativistic heavy ions are syn-chrotrons, like many of those used inelementary-partic1e physics. Instead ofaccelerating individual particles suchas protons or electrons, however, theycreate a beam of ions: atoms that havebeen stripped of most of their elec-

76

and thereby the pressure. There areno instrumental probes tor measuringthese quantities directly. Moreover,the high-density state is short-lived:in roughly 10-22 second the mergednuclei exp1ode, scattering shards ofnuclear matter in all directions. The

the moderate energy of 70 MeV pernucleon and made to collide almosthead on with a silver nucleus (atomicmass 108). The silver nucleus was in aphotographic emulsion, which servedas both target and detector. In the sub-sequent disintegration of both nuclei

fragments can be detected by instru-ments surrounding the interaction re-gion. Whatever is to be learned fromthe collision must be deduced fromthe distribution of this debris.

In one experiment a carbon nucleus(atomic mass 12) was accelerated to

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trically charged fragment from a nuclear collision enters ODe of thefacets, it passes through the calcium fluoride and then is stopped inthe plastic, causing both materials to scintlliate, or emit a flash oflight. The position of the facet gives the fragment's direction; thetwo scintlliations allow its energy and mass to be determined. Detec-tor systems of ibis complexity are common in elementary-particlephysics, bot untll recently they were rare in nuclear physics. Be-cause they allow a collision to be reconstructed even when hun-dreds of fragments are emitted, they give an exceptionally clear viewof the nature of nuclear matter at high temperature and pressure.

---Plastic Ball, which detects the debris emitted when atomic nn-

of0 ,-. - -- -- --- -- .. c the detector is assembled, a similar hemisphere is

to this one and a target is placed in the beam path at theThe complete sphere has 815 facets, or detector elements.

When an elec-

77

The fragments emittedwere mainly in-dividual nucleons and clusters of twoor three nucleQns. Indeed, the debrisradiating from the site of the collisionincluded more than 130 charged ele-mentary particles, substantially morethan the 100 proton charges in theoriginal nuclei. Where did the extraunits of charge come from? The colli-sion process was violent enough to cre-ate more than 30 new particles, chieflynegative and positive pions [see lowerillustration on page 80].

some 16 electrically charged nuclearfragments were emitted; they were nu-clei of the light elements deuterium,helium, lithium and beryllium, madeup of from tw010 nine nucleons. Theycan be interpreted as particles evapo-rated in the boiling of the nuclear liq-uid [see upper illustration on page 80].

In another experiment the collisiontook place in a streamer chamber,where the passage of a charged particleleaves a bright trail of electrical dis-charges. An argon nucleus acceleratedto an energy of 1.8 GeV per nucleonstruck a stationary target nucleus oflead, again almost head on. At thismuch higher energy the two nuclei,which together comprised almost 250nucleons, were yompletely destroyed.

H ow is ODe to interpret such events?What are the physical processes

ta king place when two heavy nucleicollide at relativistic speed? The mostrigorous method of analysis would be

to calculate the outcome of the col-lision according to the principles ofquantum field theory. That turns outto be impractical. Even tor very smallnuclei such a calculation is a mathe-matical tour de force; tor larger col-lections of nucleons-in the case ofuranium striking uranium there are al-most 500-the task is hopeless.

Although the large number of parti-cles rules out a quantum-mechanicalcalculation, it also opens the possibili-ty of other approaches. After all, phys-ical systems such as macroscopic sol-ids, liquids and gases have an enor-mous number of component particles,and yet they are accurately describedby physical theories. Indeed, a largenumber of particles can aid analysis byadmitting models based on statisticalassumptions.

Two models have taken on primaryimportance in the study of heavy-ioncollisions. In the first model the nucle-us is treated as a drop let of liquid andthe equations of hydrodynamics areemployed to describe the collision oftwo such droplets. The particles of thenucleus do not appear at all in themodel, any more than individual watermolecules appear in a hydrodynamicdescription of a raindrop. Instead nu-clear matter is viewed as an ideal, con-tinuous fluid. The hydrodynamic mod-el was first applied to relativistic nu-lear collisions about 10 years ago byWerner Scheid, Hans J.Müller, JürgenHofmann and ODe of us (Greiner) ofthe University of Frankfort and byGeorge F. Chapline, Michael H. John-gon, Edward Teller and Morton S.Weiss of the Lawrence Livermore Na-tional Laboratory.

In the second model, called the cas-cade model, the nucleons do appearexplicitly; indeed, the nucleus consistsof nothing else. A direct calculation oftheir trajectories is made possible bythe simplifying assumption that eachnucleon is free-moving and travels in astraight liDe except when it hits anoth-er nucleon. The complex forces thatbind the nucleons together are ignoredentirely; colliding nuclei are like col-liding bags of marbles. In the cascademodel the outcome of a collision is de-termined by simulating the paths ofthe nucleons with the aid of a com-puter; the simulation must be repeat-ed thousands of times with differentinitial configurations of the nucleons.The cascade model was developed byZeev Frankel of the Weizmann In-stitute of Science in Israel, VladislavD. Toneev of the Joint Institute torNuclear Research in Dubna, JosephCugnon of the State University of Li-ege in Belgium and their colleagues.

The predictions of the two modelscan be compared by following the pic-

PLASTIC BALL is installed at the Bevalac, a heavy-ion accelerator at the Lawrence Berke-ley Laboratory of the University of California. The sphere of detector elements is obscuredby the photomultiplier tubes that register scintillations and by the cables that supply powerto and receive data from the photomultipliers. The heavy-ion beam travels in the alumi-num vacuum liDe that euters the detector at the bottom of the photograph. At the far end ofthe hall is an additional detector system called the Plastic Wall, which supplies informa-tion about the numerous high-energy fragments emitted at a small angle to the beam axis.

78

through the target. In the hydrody-namic model, in contrast, the nucleistop each other. As a result of the highpress ure developed there is a strongsideward peak in emission, perpendic-ular to the beam axis.

The nature and the origin of the side-ward emission in the hydrodynamicmodel can be seen more clearly by ob-serving what happens when an argonprojectile strikes a target nucleus oflead [see illustration below). The pro-jectile, with an energy of 800 MeVper nucleon, moves at about 80 per-cent of the speed of light, wh ich issome tour times the speed of sound innuclear matter at the ground-state den-sity. As the projectile burrows into thetarget, a supersonic shock wave formsahead of the collision region. Theshock wave is analogous to the ODecreated by a supersonic aircraft in theearth's atmosphere. At first the wave isdirected predominantly forward, butas it pushes matter out of its way itbegins propagating outward as weIl. In

the late stages of the collision, whenthe system has reached a low densityand has- begun breaking up into frag-ments, the collective flow of mattercaused by the shock wave leads to apreferential sideward emission of there action products.

Model calculations of the kind dis-cussed hefe have been düne by J. Ray-ford Nix and Daniel Strottman andtheir colleagues at the Los AlamosNational Laboratory and by GerdBuchwald, Gerhard Graebner andJoachim Maruhn of the Universityof Frankfort working with uso

ture that each yields of a niobium-nio-bium collision [see illustrations on page82]. In both cases the first stage is thepartial interpenetration of the two nu-clei, forming an ellipsoid al re,gion ofhigh density. As the collision proceedsmore matter enters the region of com-pression, until all the nucleons arewithin a volume no larger than that ofOlle of the original nuclei. The fusedand compressed nuclei then beg in toexpand aga in, and they soon greatlyexceed their original volume. Explo-sive dis integration folIows.

The major difference between themodels is observed in the later stagesof the reaction. In the cascade mod-el most of the nucleons are emittedroughly parallel to the be am axis, inthe "forward" direction in the labora-tory frame of reference. In spite of thehigh compression achieved and thethousands of individual nucleon-nu-cleon scatterings, the nuclei are com-paratively transparent, so that many ofthe projectile nucleons effectively pass

W hat does nature say about thediffering predictions of the two

models? Do nuclei stop one another orare they transparent? First it should benoted that interpretation of the experi-mental results has been hampered bytechnologicallimitations. Until recent-ly most experiments in nuclear physicswere düne with rather simple and inex-pensive instruments. As the focus of

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...".\"of sm all volumes of the fluid and contour liDes indicate density. Inthe early stages of the collision the nuclear fluid is heated and com-pressed only in the region of interpenetration. The shock wave thendevelops, moving forward at first and later to the side. Ultimately,when the fused nuclei disintegrate, many fragments are emitted tothe side. Times shown are in units of the time needed for light totravel ODe fermi, or 10 -13 centimeter. The model calculations werecarried out by Gerhard Graebner of the University of Frankfort.

SHOCK WA VE propagates through nuclear mat-nuclei. The projectile, anapproach es from the Jett

79

interest moves to higher energy, moreelaborate detectors are needed to pro-vide more informatjon about the reac-tion products. In this case it is vital todistinguish between head-on, or cen-tral, collisions, which feature a strongsupersonic shock wave, and peripheral

collisions, which do not. A good crite-rion für making the distinction is thenumber of fragments emitted, hut withcrude detectors the selection of suchhigh-multiplicity events can be onlyapproximate.

Early experiments düne by Hans-

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Georg Baumgardt and Erwin Schop-per of the University of Frankfortseemed to cenfirm the hydrodynamicmodel's prediction of sideward emis-sion. Baumgardt and Schopper ex-posed solid-state detectors to beamsgenera ted by the Bevalac and by theDubna synchrophasotron accelerator.They then selected für analysis onlythe high-multiplicity events and meas-ured the angular distribution of theemitted helium fragments. They founda sideward peak above a backgroundof isotropic, or directionally undiffer-entiated, emission.

~-,.,- To gather data of greater statistical

reliability a detector based on elec-. tronic particle counters was built as a: joint undertaking by a group of work-

.' ers from the Gesellschaft für Schwe-rionenforschung (GSI) at Darmstadtin West Germany, headed by Hans

, H. Gutbrod and Reinhard Stock, anda group from the Lawrence BerkeleyLaboratory (LBL) headed by Arthur M.Poskanzer. In high-multiplicity events(corresponding to central collisions)particles with low kinetic energy ex-hibited a sideward peak. The results

, . were in agreement with hydrodynamiccalculations düne by Maruhn and uso

The collective sideward flow pre-dicted by hydrodynamic calculationshas been established unambiguouslyonly in recent experiments düne byHans-Georg Ritter, Gutbrod, Poskan-zer and their colleagues in the GSI-LBLgroup. The -experiments were dünewith a new detector system called theplastic ball. More than 800 plasticdetector elements are mounted in a

I spherical shell surrounding the target;they register not only the number offragments emitted hut also their mass,charge and energy. The plastic ballwas first employed to study central col-lisions between nuclei of equal mass,where the hydrodynamic model pre-dicts the strongest sideward emission.In collisions of calcium on calcium(atomic mass 40) no sideward peakwas detected. With niobium on niobi-um (atomic mass 93), however, a defi-nite pattern of sideward emission wasfound, in agreement with the hydro-dynamic calculations made by Buch-wald, Graebner, Maruhn and uso

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NUCLEAR FRAGMENTATION follow-ing a beavy-ion collision is recorded in apbotograpbic emulsion (above), wbicb actsas target and detector. A carbon nucleus ac-celerated to 70 MeV per nucleon bas strucka silver nucleus in tbe emulsion. At tbis mod-erate energy some 16 fragments of nuclearmatter (labeled in the diagram at feit) radi-ate from tbe site of tbe collision. Tbey arenuclei of deuterium, helium, lithium and be-ryllium, witb from two to nine nucleons. Tbeevent was recorded by Bo Jakobsson &11'-bis colleagues from tbe University of Lund.

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As the situation stands now the sim-.f1.. plest version of the cascade modelseems to be limited to describing inter-actions of lighter nuclei. The hydrody-namic model has much broader sup-port as a description of central colli-sions between more massive nuclei. Itssuccess establishes the key mechanismtor creating hot, compressed nuclearmatter in the laboratory, namely thepropagation of nuclear shock waves.Having such a mechanism on hand

MORE VIOLENT IMPACT of larger nuclei at high er energy leads to the complete dis-integration of nuclear matter. An argon projectile at an enfrgy of 1.8 billion electron volts(GeV) per nucleon and a lead target are broken up info individual nucleons and clustersof two or three nucleons. More than 130 fragments are emitted. In the photograph, madeby Robert T. Poe and his colleagues from the University of California at Riverside, thepaths of charged particles are traced by trails of electrical discharges in a streamer chamber.

80

PHASE DIAGRAM OF NUCLEAR MATTER shows transformations predicted by vari-ous theories and conjectures. The normal, liquidlike state of nuclear matter occupies thetower Jett-hand corner of the diagram. At elevated temperature and density the liquid evap-urates, forming a gas made up not only of nucleons bot also of pions and of heavier par-ticles known generically as hadrons. With further heating and compression the hadronsthemselves could break down info their constituent particles, the quarks and gluons, creat-ing a plasmalike mixture called quagma. At high density bot comparatively low tempera-tore nuclear matter could be frozen info a lattice structure analogons to a crystalline sol-id. Protons and neutrons with oppositely oriented spins would alternate in the lattice. Inthe pictorial representation of the phases shown here density is not indicated accurately.

is an important stimulus to the ex-perimental search für new, abnormalstates of nuclear matter.

ODe indicator of a transition fromthe liquid to the vapor phase it;l nucle-ar matter is an increase in entropy, themeasure of the disorder in a system.As the colliding nuclei are compressedthe temperature rises; the nucleonsare more violently agitated by theirrandom motions. It follows that they-become more disordered and the en-tropy increases. When the compressedmatter expands again, the tempera-ture falls, but the entropy generat-ed in the collision cannot (according tothe second law of thermodynamics) bedissipated. In other words, once the nu-cleon motions have become more cha-otic they cannot be restored to theirformer order.

The production of entropy in a colli-sion has definite effects on the debristhat ultimately appears in a detector.In general as the entropy increases, thenuclear matter breaks up into a largernumber of smaller fragments. This ef-fect was seen in the two collisions dis-cussed above. The effect of entropyon the mass spectrum has been ex-ploited by Barbara V. Jacak, GaryD. Westfall, Konrad Gelbke, DavidScott and their colleagues at MichiganState University to measure the entro-py produced in collisions. At interme-diate impact energies they find theentropy is considerably higher thanwould be expected from calculationsbased on the properties of normal nu-clear matter.

Among various candidate explana-tions of the entropy excess, ODe possi-

.. The ex-a product of the

transition from a liquid to a va-

adopt a new, denser geometric config-uration, that of diamond. At low pres-sure diamond is metastable: it is notthe lowest-energy form of carbon, butan energy barrier greatly inhibits itsdecay into graphite.

Lee and Wick sugges~d that if nu-clear matter could be compressedenough to create a high-density iso-mer, it might form superdense "abnor-mal nuclei" consisting of from 300 to100,000 nucleons. The nucleons them-selves would give up nearly all theirmass to a thick soup of pions (the par-ticles that embody the nuclear forcefield) in which they would be embed-ded. Another mechanism that mightlead to the formation of a density iso-mer was proposed by lohn Boguta ofthe University of California at Berke-ley. In the strong nuclear field generat-ed by a dense assemblage of nucleons,he pointed out, the effective mass ofvarious excited states of the nucleonmight be reduced to a value not muchhigher than that of the ground-statenucleon itself. Many excited statescould then be produced by thermalfluctuations even at low temperature.

A third mechanism, called pion con-densation, is based on calculations ofthe interaction between nucleons and

University of Minnesota, the se-of events could be as foliows.

stage of the

the phase transition. In- same of the

evaporate, becoming freelyparticles of agas. As the nu-

--- - - - -"' ~" however, the nuclear matter con-

- into a liquid again, releasinglatent heat of vaporization. It isliberation of this energy that givesto the excess entropy; indeed, the.. the entropy from the

. could be greater thanfrom the original heating and

together, and when the compressiveforce is released or dissipated, thenuclear matter immediately expandsagain. What this means in mathemati-cal terms is that the curve described bythe equation of state rises with increas-ing density. There is no law of nature,however, that requires the curve tocontinue rising indefinitely. It couldhave a secondary minimum, corre-sponding to a stable high-depsity con-figuration of nucleons. Once thatcon-figuration wasestablishedestablished, itmaintained without applied press ure.Speculations about the existence ofsuch stable "density isomers" of nu-clear matter were first discussed byArnold R. Bodmer of the ArgonneNational Laboratory, T. D. Lee andG. C. Wick of Columbia Universityand A. B. Migdal of Moscow StateUniversity.

In understanding density isomers ananalogy with ordinary matter is againhelpful, in this instance an analogywith the solid phases of carbon. Atroom press ure the stablest crystallineform of carbon is graphite; it can becompressed, but when the pressure isremoved, it returns to its original den-sity. If the applied press ure exceeds athreshold, however, the carbon atoms

--- known high-density forms ofnuclear matter are unstable. Theybe created only by supplying en-to squeeze the nucleons closer

81

HYDRODYNAMIC MODEL describes a heavy-ion collision as the fusion of two liquiddroplets. Here, in calculations done by Gerd Buchwald of the University of Frankfort, twoniobium nuclei collide almost head on. The collision is shown in the center-of-mass coor-dinate system, so that the nuclei seem to be moving with equal speed in opposite directions.The ßow of matter has an important component perpendicular to the original axis of motion.

pions düne by Migdal and by GeraldE. Browri and Wolfram Weise of theState University of New Yorkat StonyBrook.Their results show that at fromtwo to three times the normal nucleardensity pions can bind nucleons into alatticelike structure comparable to acrystalline solid. Protons and neutronswould alternate in the lattice, as wouldthe orientation of the particles' intrin-sic spins.

Is there any experimental evidenceof these peculiar high-denSity forms ofnuclear matter? With Scheid we haveconsidered (by means of hydrodynam-ic calculations) what events might sig-nal the formation of the abnormalstates, if they exist. We find that asthe threshold für making superdensenuclei was crossed there would be anabrupt increase in the number of pionsemitted. The additional pions wouldbe given off by a nucleus as it sur-mounted the energy barrier and de-scended to the secondary minimum inthe energy curve.

lohn W. Harris, Andres Sandovaland Stock in the GSI-LBL streamer-chamber group have recently meas-ured the pion multiplicities resultingfrom collisions of argon nuclei. Theyhave found that the pion yield increas-es smoothly and linearly with bom-barding energy and has no abruptjumps. They were ahle to extract fromtheir data a nuclear equation of statethat rises steadily with density andshows no sign of abnormal, secondaryminimums.

From these findings one might con-clude that the abnormal states do notexist in nature. It is also possible, how-ever, that the accelerators of the cur-cent generation are not ahle to assem-ble a large enough collection öf nucle-ons and maintain the required densitylong enough für them to cross the en-ergy barrier, if it exists.

T he several successes of the hydro-dynamic model of heavy-ion col-

lisions are in some respects surpris-ing. The model relies on thermody-namic concepts such as temperatureand press ure, which can properly beapplied only to a system near thermalequilibrium. To be specific, tempera-ture measures the vigor of the randommotions of the particles in a system,but the measurement is valid only ifthe motions are in fact random. It is byno means obvious that this condition issatisfied in nuclear matter.

In a fluid, motion becomes randomand the system reaches thermal equi-librium if the mean free path-the av-erage distance a particle moves be-tweeD collisions-is small comparedwith the overall dimensions of the sys-tem. Calculations of the me an free

CASCADE MODEL of a niobium-niobium collision calculates the path of each nucleon.The model adopts the simplifying assumption thai the nucleons do not interact except intwo-body collisions. As in the hydrodynamic model, there is an initial stage of compression,followed by disintegration. The distribution of fragments, however, is more nearly uniformin the cascade model. Calculations are by Joseph Molitoris of Michigan State University.

82

the particles designated N* resonances.There are many such particles, whichcan be arranged in aseries of progres-sively higher mass. They all have thesame b~sic properties as the proton orthe neutron and are made up of thesame constituent quarks; indeed, theycan be viewed as mere excited states ofthe nucleons, analogous to the excitedstates of an atom, in which the quarkshave taken on additional energy andangular momentum.

At still higher energy other mesonsand baryons can be formed. Severalhundred varieties of hadrons havebeen discovered, with masses as highas 10 GeV. In most cases the massivehadrons decay in about 10-23 second,so that there is ample time during anuclear collision (lasting 10-22 second)für repeated cycles of creation and de-cay. For any given energy an equilibri-um distribution of hadron types andmasses is established; nuclear matteris converted into hadron matter. Thisis what constrains temperatures in thehighest-energy experiments. Collisionenergy that in the absence of hadroncreation would contribute to the kinet-ic energy of the nucleons is divertedinto the mass of the excited hadrons.Instead of producing raster particlesthe collision forms heavier Olles.

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T he creation of hadron matter is akind of phase transition, and it hag

a latent heat, just as the liquid-vaportransition does. When liquid water isheated, the temperature rises at first,then it remains constant at 100 degreeswhile additional heat supplies the en-ergy needed foryaporization; the tem-perature rise resumes only when all thew~ter hag been converted into vapor.The temperature curve tor nuclearmatter could have a similar shape.With initial heating the temperaturewould rise, then the rate of increasewould diminish as nucleons were con-verted into higher-mass hadrons; thetemperature would asymptotically ap-proach some maximum value. Therapid temperature increase could re-stirne only when all the particles in thesystem were in the form of the highest-mass hadron.

The trouble with this formulation isthat there may not be a "highest-masshadron." The number of hadron typesseems to increase exponentially withenergy. If the trend continues indefi-nitely, further heating will never raisethe temperature of matter much be-yond what hag already been attained inheavy-ion collisions. There would bean absolute limiting temperature in na"ture. This idea was introduced by RolfHagedorn of CERN (the European lab-oratory tor particle -physics), who sug-gested the limiting temperature should

path of a nucleon show that normalnuclear matter just barely qualifies: themean free path is a fermi or two (onefermi is 10-13 centimeter), whereas thediameter of a large nucleus is betweeneight and 14 fermis. In a heavy-ion col-lision compression and certain subtiereffects further reduce the mean freepath. On the other hand, the interac-tion is exceedingly brief. Does the sys-tem stay together long enough für theenergy of impact to be randomly dis-tributed among the nucleons?

The justification für describing col-lisions of nuclei in thermodynamicterms is that the predicted tempera-tures are in accord with experimentalresults. The temperature reached in acollision can be estimated from the en-ergy distribution of the emitted frag-ments. The temperatures deduced inthis way agree with those calculated byhydrodynamic methods over a rangeof three orders of magnitude. Only atthe highest impact energies does a dis-crepancy appear: the temperature doesnot increase as fast as the model sug-gests it should.

The flattening of the temperaturecurve is not a mystery; it comes aboutbecause a full description of the colli-sion process must take into accountnot only nuclear physics but also el-ementary-particle physics. Nucleonsare not inert hard spheres: at sufficient-ly high energy they are subject to in-ternal transformations, much as at-oms and molecules undergo chemicalchanges at high temperature.

The proton and the neutron aremembers of the large class of particlescalled hadrons. They are the particlesthought to consist of the more elemen-tary constituents called quarks. Thereare two basic groups of hadrons: thebaryons, made up öf three quarks, andthe mesons, made up of a quark and anantiquark. The nucleons are the low-est-mass baryons and the pions are thelowest-mass mesons. It is the creationof higher-mass hadrons that limits thetemperatures attained in violent nucle-ar collisions.

Pions are the first hadrons to appear.The rest mass of a pion is about 140MeV, which is the threshold für pionproduction in proton-proton colli-sions. In nuclear collisions pion emis-sion has been observed even at ener-gies as low as 25 MeV per nucleon.Under those conditions the mecha-nism of pion creation clearly requiresthe cooperative action of many nucle-ons, whose total energy exceeds thethreshold.

When the collision energy is greaterthan about 1 GeV per nucleon, had-fons heavier than pions are also creat-ed. One important process is the trans-formation of a nucleon into one of

84

be about 1.5 X 1012 degrees. This tem-perature is not rar beyond what hasbeen observed a1ready in heavy-ion ex-periments.

The last of the possible phases ofnuclear matter we shall consider is theone analogous to a plasma of chargedparticles. In it the nucleons and thehigher-mass hadrons lose their identi-ty as individual particles. The matter

HYDRODYNAMICMODEL

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in such a nucleus consists of quarksand the particles that bind them to-gether, the gluons; it is a quark-gluonplasma, or quagma.

In the la bora tory the usual way tomake an ordinary plasma is to heat agas to the point where collisions be-tweeD atoms are energetic enough tostrip away the outermost electrons.The electrons are thereby "decon-fined": they are not bound to a particu-lar atom hut can roam throughout thevolume of the plasma. There is anoth-er method of achieving the same end,which operates in the interior of stars.Extreme compression of agas candrive the atoms into close contact andeven make their outer shells of elec-trons overlap. Under these conditionsthe electrons are again deconfined andcan move freely from ODe atom to an-other. As in a metallic solid, a sea ofdeconfined electrons is shared by allthe atoms.

There is an important difference be-tweeD the binding of electrons in anatom and the binding of quarks in ahadron. With a finite investment of en-ergy an electron can be removed en-tirely from an atom. The attractiveforce between quarks, on the otherhand, cannot be overcome no matterhow much energy is supplied; the forcegrows stronger without limit as thequarks are separated. For this reasonthe quarks in a quagma cannot actual-ly be set free; they are merely given alarger cage. In forming a quagma theaim is not to separate the quarks hut tobring the hadrons closer together, as inthe second me!hod mentioned abovefür forming an ordinary plasma. Whenthe hadrons are close enough to over-lap, their constituent quarks can wan-der throughout the nuclear volume likeelectrons in a metal.

ODe obvious way to achieve the nec-essary density of hadrons is to com-press nuclear matter until the nucleonsare driven into close contact. It turnsout extreme heat can also serve to cre-ate a quagma, although not by rippingquarks loose in violent collisions in theway electrons are freed in a high-tem-perature plasma. The mechanism issubtier: high temperature leads to thecopious production of pions and otherhadrons, which fill all the space be-tweeD the nucleons.

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ANGULAR DISTRIBUTION of emittedfragments discriminates between the hydro-dynamic (top) and cascade (bottom) mod-els. Hydrodynamic simulations yield manyfragments at a sharp angle to the beam axis;in the cascade model emission is more near-ly parallel. The contrast is strongest in head-on collisions, which produce large numbersof fragments at sharp angles to the beamaxis (colored curves). Data for the GSI-LBL Plastic Ball collaboration (center) sup-port the hydrodynamic model. Head-on col-lisions (colored curve) produce more than50 fragments at the sharpest angle; othercollisions scatter 40 to 50 fragments at apronounced angle (middle block curve).

n

H ow densely must nucleons or had-fOnS be packed together to create

a quagma? What beam energy wouldbe needed to reach this density inheavy-ion collisions? We and othershave estimated these quantities by sev-eral methods. Perhaps the simplestmethod proceeds from the observationthat quarks seem to move freely insidea hadron. Thus if an entire blob of nu-

86

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HIGHEST TEMPERATURES ATTAINED in nuclear collisions signal the creation ofmassive hadrons and may give evidence of a maximum temperature thai cannot be ex-ceeded in nature, According to the simplest theoretical calculations (colored curve), temper-ature should increase exponentially with collision energy. Experimental data are in agree-ment up to about .5 GeV per nucleon, bot thereafter the temperature rise is slower thanexpected because energy thai might have heated the nuclear fluid instead goes into makinghadrons of greater mass. If hadrons can have an arbitrarily large mass, it may be impos-sible to reach temperatures beyond some finite limit in nucleus-nucleus collisions. Temper-atures based on two possible limiting values (black curves) were calculated by the authors.

clear matter could be raised- to theof matter inside a hadron, the

.0 Thecrit-

density calculated in this way is

nuclear matter. This degree ofbe readily attain-

; indeed, experiments with existingat a beam energy of 1

nucleon, probably reach den-from three to five times the

- - density.Other estimates of the density need-

quagma formation are in goodwith these. It therefore

the required collision energyjust beyond the reach of the

operating today. A ma-that could accelerate the heavi-

to an energy of from 10 toGeV per nucleon should be welf

to an investigation of the prop-. . The construction ofthis class is under way or

consideration at several labo-including CERN, Dubna, GSI,

National Laboratory

regroup to form hadrons, but at pres-ent little is known aboutthis process,even from theoretical calculations.The mechanisms of regrouping couldreveal much about the nature of theforce betweenquarks. Perhapsa quarkwith high moment um can escape thequagma by pulling other quarks with itto form a hadron. Pairs of quarks andantiquarks might be created spontane-ously in the wake of an escaping quark,ultimately appearing as a stream ofmesons. Alternatively, the entire massof quagma might segregate, or frac-türe, into quark clusters. Some of theclusters could represent unusual formsof hadronic matter.

Up to now the properties of quarkshave been studied only in the interac-tions of individual hadrons, where thenumber of quarks taking part is strictlylimited. Heavy-ion collisions offer thepossibility of observing many-bodyquark interactions. By bringing togeth-er several hundred quarks and gluons,quagma can be studied not as a collec-tion of independent particles but as aform of matter. It is the form of matterwith which the universe began, in thefirst instants after the big bang, and sothe highest-energy heavy-ion reactionscould weIl reenact at small scale theearly evolution of the universe.

-~ LBL.

Some of the most interesting ques-work with theto do with the

of quagma. As the density falls

87

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