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7 Approaching the Quark-Gluon Plasma About 20 billion years ago, the universe began in a stupendous explosion called the big bang. At that instant, all matter is believed to have had a temperature corresponding to about 10'9 GeV, or 1032 K. During the earliest moments (much less than 1 second) after the big bang, the fundamental forces that we know today strong, electroweak, and gravitation were all comparable in strength, accord- ing to present theories. None of the many composite particles the mesons and baryons existed, since they could not have survived such unimaginable heat. Only the elementary leptons, quarks, gluons, photons, and intermediate vector bosons could have existed. As time progressed during the first second, the nascent universe expanded and therefore started to cool. About 10-' second after the big bang, with the universe at a temperature corresponding to about 103 GeV (10~6 K), the unity between the weak force and the electromag- netic force began to disappear. The quarks (and their antiquarks) were still free, however, not yet bound up in hadrons. Later, at about 6 x 10-6 to 7 x 10-6 second, when the universe had cooled down to a temperature corresponding to 100 to 200 MeV (1 x 10'2 to 2 x 10'2 K), the quarks and antiquarks started to coalesce into the strongly inter- acting particles (mesons and baryons). As the universe continued to cool, the nucleons themselves coalesced to form light nuclei. This nucleosynthesis started about 3 minutes after the big bang; the process leading to the formation of stars and galaxies had begun. 137

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138 NUCLEAR PHYSICS Today we find ourselves in a relatively cold universe at an overall temperature of 3 K. To investigate the universe during its first few microseconds, therefore, we need, in a sense, to go back in time and try to recreate the conditions that existed then. The tools at our disposal are the descendants of the big bang itself: the abundant heavy nuclei all around us, which were formed long ago in stars. Our goal is to accelerate such nuclei to extreme relativistic energies and then smash them together. At a high enough collision energy, the tempera- ture and pressure will become so great that the nucleons will disinte- grate into a dense, blazing fireball of quarks and gluons. This process, called quark Reconfinement, has never been seen on Earth but may occur in the cores of neutron stars. The study of quark Reconfinement will thus provide insight into questions of great cosmo- logical interest and at the same time give us a stringent testing ground for some of the fundamental ideas of quantum chromodynamics (QCD). During quark Reconfinement, a new state of matter, the quark-gluon plasma, will be created. In this state, quarks and gluons are no longer bound inside individual hadrons but are contained inside a much larger volume; this will allow the long-range behavior of QCD, which is at present very poorly understood, to be examined. This chapter deals with the various states of nuclear matter, the values of temperatures or densities that are required for achieving quark Reconfinement (based on present theoretical models), and the detectable signatures expected to be left behind by the quark-gluon plasma. It concludes with a brief discussion of other frontiers in relativistic heavy-ion physics. STATES OF NUCLEAR MATTER Let us first consider an everyday form of matter and see what happens as we heat it up by providing energy to its internal constitu- ents. If an ice cube is placed on a hot plate, it first melts to water, which represents a higher energy state than ice. After further heating, the water evaporates to a still higher energy state water vapor. These changes are called phase transitions. In each change of phase, the internal energy of the matter (per molecule) is increased, and a different aspect of its structure is revealed to us. In an analogous fashion, we expect to heat ordinary nuclear matter to temperatures sufficiently high that an extreme energy state, the quark-gluon plasma, will be created. What are the possible phases of nuclear matter? Previous research using nuclear collisions below 100 MeV per nucleon has dealt primarily with the ground-state properties of cold nuclear matter. Even the

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a) - ct APPROACHING THE QUARK-GLUON PLASMA 139 Path of early universe during first few microseconds after the Big Bang - Quark-gluon plasma Excited ~ hadronic matter Liquid-gas Pion phase Normal nuclei condensates Relative baryon density FIGURE 7.1 Some of the phases of nuclear matter that are expected to exist at high temperatures and low-to-high relative baryon densities are shown in this phase diagram, which is described in detail in the text. The shaded band schematically represents the transition region for quark Reconfinement, beyond which lies the quark-gluon plasma. The scope of known nuclear physics is confined almost entirely to nuclei under normal conditions. highest-energy heavy nuclear beams currently available are not thought to be sufficiently energetic to produce a fully developed quark-gluon plasma. Now let us see what happens as we heat ordinary nuclei. Figure 7.1 illustrates some of the possible phases of nuclear matter in terms of two variables: temperature and relative baryon density (the number of baryons mainly protons and neutrons per unit volume, compared with this number for ordinary nuclei). Normal nuclei, of which

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140 NUCLEAR PHYSICS everything on Earth is made, are found only in one small region of this phase diagram. There are much larger regions of the diagram, each corresponding to a different phase in which nuclear matter can exist. We will refer to these phases as hadronic matter (which encompasses normal nuclei) and the quark-gluon plasma, or simply quark matter (on the far side of the diffuse boundary region in which quark deconfine- ment occurs). At normal nuclear density and low temperature (close to 0 MeV- cold nuclear matter), we find the nuclei that make up the everyday world. As we start to heat the nuclei through collisions at ever higher energies, the individual nucleons gain more energy and try to move apart. The nuclear system becomes larger, and its density necessarily decreases. Thus, at slightly elevated temperatures, but at subnormal densities, a liquid-gas phase transition from nuclei to nucleons may occur. Heavy-ion collisions below 100 MeV per nucleon and high- energy proton-nucleus collisions, in which the incident proton deposits a local hot spot in the nucleus (which then propagates through the nucleus, heating it up), are currently being used for probing this phase transition. At high baryon densities, on the other hand, but still at relatively low temperatures, new and unusual phases of nuclear matter are postulated to exist. One of these, called a pion condensate, would be a highly ordered form of nuclear matter, analogous to the atoms in a crystal lattice. No positive evidence for its existence has yet been found, but it might exist deep in the interiors of neutron stars. At the highest densities, we enter a region that is characteristic of neutron stars. It seems ironic that in order to gain information on some of the most massive objects that we know about stars we must study some of the tiniest objects known nuclei. At high temperatures (20 to 100 MeV) in the nuclear medium, we produce many new excited levels of the individual nucleons them- selves. Nuclear matter at such temperatures is referred to as excited hadronic matter. If there were no internal structure to the individual nucleons, this state of matter would continue indefinitely, since in principle there can be an infinite number of excited states. But there is an internal structure. The nucleons are composed of confined quarks and gluons, and as the temperature or density is raised sufficiently, we expect to experience a transition in which hadronic matter becomes Reconfined: the nucleons decompose into a quark- gluon plasma similar to the one from which mesons and baryons condensed a few microseconds after the big bang.

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APPROACHING THE QUARK-GLUON PLASMA 141 ACHIEVING QUARK DECONFINEMENT Relativistic nuclear beams will be used for the production and study of the quark-gluon plasma. What are the appropriate physical param- eters and critical values needed to achieve and describe this state? The only currently conceivable method is to accelerate heavy nuclei to enormous energies and cause them to collide head-on. In this cata- strophic impact, we expect high temperatures and densities to be created throughout a volume of space comparable with the size of the nuclei themselves. The larger the nuclei that are used, the more individual nucleon-nucleon collisions will occur, each helping to heat and, to some extent, compress the system. Ideally, therefore, the facility for such experiments should be able to accelerate heavy nuclei such as the uranium nucleus. Estimates of the critical values of the temperature and baryon density needed for quark Reconfinement have been made. Simple calculations based on compressing nuclei until the space between individual nucleons disappears predict that Reconfinement could occur when a critical baryon density only a few times that of normal nuclear matter is exceeded at sufficiently high temperatures. (Normal nuclear density is 0.16 nucleon per cubic fermi.) Other calculations, reflecting a different view of the effective size of the nucleons, yield substantially higher values for the critical baryon density. One still expects, how- ever, that a fundamentally important change in the nature of nuclear matter will occur at a relatively low baryon density, as the nucleons are squeezed together. An alternate approach is based on filling the space between the nucleons by creating mesons (for example, pions and kaons) and other particles, such as proton-antiproton pairs, in the collision process. Such an argument leads to the prediction that a critical energy density (the amount of energy per unit volume residing in the system), again as low as a few times that of normal nuclear matter, would be sufficient to initiate the Reconfinement of quarks from hadrons. [The energy density of normal nuclear matter is 0.15 GeV per cubic fermi (GeV/fm31.] Sophisticated theoretical calculations support these simple estimates and predict the following critical values for the transition to a quark- gluon plasma: a temperature between 140 and 200 MeV and an energy density in excess of 0.5 GeV/fm3. The requirement for much higher bombarding energies than are available with today's heavy-ion accel- erators lies in the fact that only with such higher energies will we be able to achieve the extreme temperatures and energy densities needed to Reconfine hadronic matter and produce the plasma.

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142 NUCLEAR PHYSICS The basis for the calculations mentioned above is a mathematical technique called lattice gauge theory, which has provided new insights into many areas of theoretical physics. It is based on the hypothetical concept of a regular lattice of points in a four-dimensional space-time. On each point, and along each link between points, some physical property of the system (in this case, a system of strongly interacting particles) is defined. Using the concepts of group theory (the mathe- matics of symmetry operations) and sophisticated numerical methods of computation, the values of these properties can be calculated for a given spacing of the lattice. As this spacing is successively reduced, i.e., as the lattice is "shrunk" indefinitely, the calculated values of the physical properties converge to those that QCD would predict for them in the continuum limit of real space-time. Thus it has been possible for a number of theorists, through the artifact of the lattice, to perform a wide range of calculations that would otherwise be impossible. Such calculations have led to the prediction of quark Reconfinement. At present there are at least two pieces of experimental evidence suggesting that we can indeed achieve quark Reconfinement. The first of these is provided by high-energy cosmic-ray events from the Japanese-American Cooperative Emulsion Experiment (JACEE) col- laboration. In this experiment, nuclear emulsions (similar to ordinary photographic film) are carried by balloons to the top of the Earth's atmosphere to intercept high-energy, heavy cosmic-ray nuclei before they are destroyed through interactions with the nuclei of air mole- cules. A few cosmic rays collide with silver or bromine nuclei in the emulsion, and their tracks and those of the interaction products can be seen and measured after the emulsion stack is processed (developed like film from a camera). In one such event the most violent one ever seen-an incoming silicon nucleus is estimated to have had an energy of 4000 to 5000 GeV per nucleon. It triggered an explosion for which the number of particles produced (about 1000, mostly pions) indicates that the energy density in the collision was about 3 GeV/fm3, several times the estimated value required for quark Reconfinement. It is impossible from just one event, however, to tell whether Reconfinement actually occurred. Detailed investigations of this phenomenon will require accelerator beams, which, unlike cosmic rays, can be controlled. For the results of this kind of accelerator experiment to be interpretable and statistically meaningful, a large number of similar events must be recorded, and an event rate of the order of one head-on collision per second would be required. (By contrast, cosmic-ray events of the kind described above are so rare that they are individually named.)

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APPROACHING THE QUARK-GLUON PLASMA 143 The second piece of evidence comes from recent European Muon Collaboration/Stanford Linear Accelerator Center experiments on lepton-nucleus deep-inelastic scattering, which probed the quark struc- ture of nucleons bound in nuclei (this work was discussed in Chapter 31. The results seem to indicate that the quarks are freer to move about in nucleons inside nuclei than in a free nucleon. If this is true, then quark Reconfinement might occur at even lower values of temperature and energy density than those currently estimated. What are the energies of the nuclear beams needed to Reconfine quarks from hadronic matter, i.e., what energies will produce sufficient temperatures or densities? The answer depends on whether one tries to maximize the baryon density or to achieve a very-high-energy density in the collision process. To maximize baryon density, the energy should be such that the colliding nuclei stop each other with maximum mutual compression (see Figure 7.2~. Present theoretical estimates suggest that this will occur at laboratory bombarding energies near 10 GeV per nucleon. If very-high-energy density is desired, on the other hand, higher bombarding energies are needed. The most efficient route to this goal is to build a heavy-ion colliding-beam accelerator (as opposed to a fixed-target machine). To achieve the desired energy density will require a relativistic nuclear collider with an energy of the order of 30 GeV per nucleon in each beam. Here the impact of a head-on collision is so great that the two nuclei exhibit nuclear transparency: they interpenetrate explosively. Three separate regions are created in such an event: the two baryon-rich regions (vestiges of the two projectile nuclei, consisting of recondensed nucleons), which speed away from the collision zone in opposite directions, and the central region, where the high-energy density will occur in the form of created mesons, baryon-antibaryon pairs, quark-antiquark pairs, and gluons. DETECTING THE QUARK-GLUON PLASMA The entire process of formation and recombination of the quark- gluon plasma will take about 10-22 second, which is comparable with the time it takes light to cross a single nucleus. During this period, the initially hot plasma will expand and cool (by the emission of particles), eventually recondensing to a normal hadronic phase, i.e., the usual mesons and baryons observed in accelerator experiments. To detect the presence of the plasma, we can look for particles that either originate in the early, hot, dense stage or appear at a later, cooler, more rarefied stage. If we wish to see into the fiery heart of the

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144 NUCLEAR PHYSICS (a) Approaching (b) Stopping (c) Nuclear transparency FIGURE 7.2 Quark Reconfinement in relativistic nuclear collisions may occur in either of two possible regimes, shown in (b) and (c). (b) In a head-on collision at lower energies (on a relative scale), the two nuclei stop each other, producing a quark-gluon plasma under conditions of maximum nuclear compression and, therefore, of maximum baryon density. (c) At higher energies, the nuclei are transparent as they interpenetrate, producing, in the central region, a quark-gluon plasma under conditions of extremely high energy density and relatively low baryon density. plasma, we must detect particles that can exit such a hostile environ- ment unscathed. The only viable candidates are charged leptons- which are not subject to the strong force and therefore interact only electroweakly with the hadrons in the plasma and photons. On the

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APPROACHING THE QUARK-GrUON PLASMA 145 other hand, the "frozen" phase of the collision (i.e., when the quarks and antiquarks have recondensed to hadrons) offers a number of possible signatures among the hadrons, including strange particles (hadrons containing the strange quark) and antibaryons, which reflect the quark-antiquark composition of the plasma. Unusual fluctuations in particle numbers could also signal the formation of the quark-gluon plasma. Finally, it should not be overlooked that the observation of free quarks or unusual combinations of quarks would surely indicate the formation of the quark-gluon plasma and would initiate the study of quark chemistry. Some of the interactions occurring in a relativistic nuclear collider will spew forth hundreds~ven thousands-of particles in a single event. These particles will materialize out of the energy made available in the violent collisions. (An example of the particle multiplicities observed in current fixed-target experiments at near-relativistic ener- gies is shown in Figure 7.3.) The capabilities of the detectors needed for such experiments will have to be greater than those of the detectors used in even the highest-energy proton-proton or proton-antiproton colliders. Consider, for example, a head-on collision of two uranium nuclei, each having an energy of 30 GeV per nucleon. If all the available energy were converted to mass, up to 100,000 pions could be created an unprecedented number of particles in the final state. More realistically, if we assume that these particles are emitted with a characteristic average energy of 200 MeV, the total number of pions drops to the range of a few thousand still a huge number for future detectors to cope with. Because of such high particle multiplicities, many detectors will have to resort to techniques based on calorimetry, where the total energy flow rather than the total number of particles is measured. At the same time, some detectors will be constructed that are "blind" to the vast majority of particles but are able to see and record a specific kind (for example, a lepton-only detector) in tractable numbers. Experiments will undoubtedly entail the use of combinations of these two types of detectors. The path to the quark-gluon plasma will require a state-of-the-art accelerator, and large detector arrays will be needed to unravel its mysteries. These scientific tools will enable us to look across the ages, back to the moment of creation and to a new (to us) state of matter, the quark-gluon plasma. Confirming its existence would have a major impact on fundamental questions common to nuclear physics, particle physics, astrophysics, and cosmology, and this achievement would surely be one of the most exciting in the history of science.

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146 NUCLEAR PHYSICS FIGURE 7.3 A computer-graphic reconstruction of an individual event, shown in the colliding-beam frame of reference, from a fixed-target experiment in which a beam of niobium-93 nuclei at 650 MeV per nucleon bombarded a niobium target. The short arrows represent the projectile and target nuclei approaching each other. The length of each arrow emanating from the point of collision is proportional to the momentum per nucleon of the particle it represents. Altogether, 61 charged particles were observed in this event. (Courtesy of the GSI/LBL Collaboration, Lawrence Berkeley Laboratory.) ADDITIONAL RELATIVISTIC HEAVY-ION PHYSICS Although a major focus of research with the relativistic nuclear collider will be the quark-gluon plasma, there are many other important physics questions that can be investigated with such an accelerator. Indeed, some of these questions must be addressed in any program whose goal is to establish and classify the properties of the quark-gluon plasma. As such, they will form the basic physics of the program of

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APPROACHING THE QUARK-GLUON PLASMA 147 relativistic nucleus-nucleus collisions, spanning a broad range of studies. A few examples will serve to illustrate this point. From the phase diagram of nuclear matter, we see that there is a large domain of unexplored matter in addition to the quark-gluon plasma. Investigations of excited hadronic matter have just begun, in the last few years, with studies of proton-nucleus and nucleus-nucleus collisions at very high energies. In central relativistic nucleus-nucleus collisions, it should be possible to create nuclear-matter temperatures high enough to produce large numbers of baryon resonances: massive, very-short-lived baryonic states that decay to other baryons and mesons. Chief among these would be nucleon resonances, or N* states, which are highly excited states of nucleons, and delta reso- nances, which are also excited baryonic states. Each of the delta resonances exists in four distinct varieties having electric charges of -1, 0, + 1, and +2, owing to their different quark configurations. Creating and studying such N* or delta matter is important both because it is inherently interesting and because it represents a transi- tional phase of matter between normal nuclear matter and the quark- gluon plasma. Although single baryon resonances can be made in existing accelerators-either as free species or as bound states in nuclei-it is only by means of central nucleus-nucleus collisions at relativistic energies that one could produce large numbers of them simultaneously and in very close proximity. The consequences of this unique situation are difficult to predict. Conceivably, one could form metastable systems of such exotic nuclear matter that would be analogous to ordinary nuclei: a delta-16 state, for example, in analogy with oxygen-16. It has also been suggested that in the de-excitation of N* or delta matter a sudden burst of pions might be observed, possibly in the form of a pion laser. This and many other ideas about excited hadronic matter are admittedly highly speculative, but they do suggest a stimulating and potentially fruitful experimental research program. In recent heavy-ion experiments at energies of a few hundred MeV per nucleon (in the center of mass), the number of created pions is observed to be significantly lower than expected. One interpretation is that this is evidence of compressional effects, i.e., much of the kinetic energy of the colliding nuclei apparently becomes manifest as a compression of the nuclear matter rather than in the creation of pions. Does this effect persist at higher energies, and if so, is nuclear compression the correct explanation? To investigate thoroughly this and other questions of the physics ot excited hadronic matter will require not only that the accelerator be capable of delivering the full spectrum of nuclear beams but also that

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148 NUCLEAR PHYSICS it be tunable in energy. This is necessary in order to see how a given physical process changes with increasing energy, which provides an experimental basis for extending the theory of nuclear matter. In addition to its colliding-beam mode of operation, the accelerator should be capable of fixed-target operation, because of the advantages this offers for many kinds of experiments. This mode of operation could be accomplished either by extracting one of the two countercirculating beams of the collider or by using a booster synchrotron (albeit at a lower effective energy), which would also act as the injector for the collider. An important feature of fixed-target experiments at relativistic energies is that the particles produced in the collisions become localized within an increasingly narrow forward-projecting cone about the beam axis. This strong collimation of the beam of produced particles can be used to advantage in many nuclear-physics experi- ments. One example is in the production of nuclei far from stability- exotic forms of conventional nuclear matter. The primary interest here is in peripheral, or grazing, nuclear collisions, in which only a few nucleons in the target and projectile nuclei participate. In such colli- sions, a few of the projectile nucleons may be chipped off, leaving a high-energy nuclear system moving in the forward direction. In a small proportion of the interactions, the nucleons that are removed can be either mostly protons or mostly neutrons, thus producing very neutron- rich or proton-rich nuclei, respectively. In the last few years, more than 20 new nuclides have been discovered in such reactions. This technique promises to provide physicists with an expanding array of radioactive nuclides whose properties (for example, masses and lifetimes) are of intrinsic interest. Furthermore, they can be used as projectile beams in their own right for studies of nuclear-reaction mechanisms in processes that are important for cosmic-ray propagation and the observed abundances of the elements in the cosmic radiation. They also have potentially valuable applications in radiobiology and nuclear medicine. A few final examples-outside the arena of nuclear physics but accessible with a fixed-target relativistic nuclear accelerator are found in atomic physics. By accelerating partially stripped ions to sufficiently high energies, one can selectively remove most or all of the remaining orbital electrons. For example, by accelerating a uranium- 238 beam in the 68 + charge state (238U68+) to a few hundred MeV per nucleon and then passing it through a thin foil, one can produce mostly 238U9~+, which has only one electron left, i.e., it is hydrogenlike uranium. Having prepared this beam, one can then study the atomic

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APPROACHING THE QUARK-GLUON PLASMA 149 decay schemes of these most unusual heavy ions, providing powerful new tests of the accuracy of quantum electrodynamics. Other possi- bilities include scattering a beam of laser radiation from an oncoming, very parallel, and very intense beam of partially stripped ions. Theo- retical calculations seem to suggest that, under the right conditions, an x-ray laser action might result from such an interaction. The studies outlined above merely suggest the great potential for scientific gain to be realized from a relativistic nuclear collider beyond its use in producing the quark-gluon plasma. The extent of its capabil- ities will be defined by the imagination and ingenuity of many physi- cists from a wide variety of disciplines.