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4 Nuclei Uncler Extreme Conclitions As accelerator technology has advanced, so has our ability to produce nuclei under highly unusual conditions. This has resulted in the discovery of exciting new phenomena and has given us a broader perspective on the properties of nuclei under more normal conditions. Increasingly, nuclear projectiles with heavier and heavier masses accelerated from medium to relativistic energies are being used in collisions with other nuclei to raise nuclear matter to high temperatures and densities, to create new elements and exotic isotopes, and to produce highly excited and deformed nuclear systems. Some projectile fragments that are formed in relativistic nuclear collisions appear to exhibit totally unexpected behavior not explained by current theory. Called anomalous, they were first seen sporadically in cosmic-ray experiments but have now been reported in some laboratory experiments as well. Their appearance has stirred a spirited controversy worldwide, and vigorous efforts are under way to prove- or disprove that they are what they seem to be. As higher projectile energies become available, it may be possible to create from nuclear matter a state of such high temperature and density that it will undergo a transition to a quark-gluon plasma. In this exotic state of matter, individual nucleons will cease to exist, and conditions will be similar to those that existed briefly after the big bang. Recent research that is leading toward this ambitious goal is discussed in the following section. 87

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88 NUCLEAR PHYSICS NUCLEI AT HIGH TEMPERATURE AND DENSITY Some of the nuclear matter in the universe is much hotter and denser than the relatively cold atomic nuclei on Earth. In order to understand the origin and evolution of spectacular celestial objects such as supernovas and neutron stars, we must produce nuclear temperatures and densities comparable with theirs. To do this in the laboratory, a huge amount of energy (on the submicroscopic scale of nuclei) must be deposited instantaneously throughout a much larger volume than that of a single nucleon. As we will see below, this requires the violent collisions of very heavy nuclei in powerful accelerators. Until 10 years ago, no such nuclear collisions could be produced systematically. Although tantalizing glimpses of extremely energetic heavy nuclei were caught in cosmic-ray experiments, these events were rare and uncontrollable. In 1974, however, the Bevalac acceler- ator at the Lawrence Berkeley Laboratory became capable of accel- erating nuclei as heavy as iron to energies as high as 2.1 GeV per nucleon. This achievement marked the beginning of a dedicated research program of accelerator-based relativistic heavy-ion physics, in ~t I/...;;: , , ,.= - .... '~ ~'2,'52 at,, ~,_~, 1 10-4 m 1 ; ~ c ; %, FIGURE 4. l A microprojection drawing of the central collision of a relativistic uranium-238 nucleus, having an energy of l GeV per nucleon, with a heavy nucleus (either silver or bromine) in a photographic emulsion. In this event, the two nuclei were completely destroyed. (Courtesy of H. H. Heckman, Lawrence Berkeley Laboratory.)

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NUCLE! UNDER EXTREME CONDITIONS 89 which a massive projectile (heavy ion) is accelerated to a speed so close to that of light that its kinetic energy becomes comparable with or greater than its own rest energy. At such enormous energies, the effects of special relativity become dominant and must be taken into account in interpreting the experimental results. The Bevalac was further upgraded in 1982 to accelerate all the natural elements of the periodic table to relativistic energies, culminat- ing with uranium at 1 GeV per nucleon (see Figure 4.1~. Thus, a vast new domain of nuclear physics has been opened up, in which nuclear temperatures and densities can be achieved for brief instants that far exceed those existing even in most stars. High Nuclear Temperatures Implicit in the concept of temperature is the assumption of a system of particles in a state of equilibrium-even if only for a very short time, such as 10-22 second (the typical duration of a nuclear collision). In a central (head-on) collision of two heavy nuclei at relativistic energy, a nuclear fireball is created in which hundreds of individual nucleon- nucleon collisions occur very rapidly before the produced particles are blasted outward in all directions. (This fireball is so infinitesimal that, if it exploded in one's eye, it would only appear as a pinpoint flash of light.) The statistical nature of the overall event suggests analysis by means of nuclear thermodynamics. A consequence of thermodynamic equilibrium in such a system would be a uniform distribution (the same in all directions) of the momenta of the emitted particles. To test for this pattern, one needs a detector capable of capturing and identifying hundreds of particles- charged hadrons and light nuclear fragments simultaneously, at all possible angles of emission of the particles. Such a detector, the Plastic Ball/Plastic Wall, has been built by a team from the GSI laboratory (Darmstadt, West Germany) and the Lawrence Berkeley Laboratory (see Figure 4.21. Investigations have been carried out with this detector on collisions of calcium beams with calcium targets and niobium beams with niobium targets, both at 0.4 GeV per nucleon. The measured momenta of all the observed particles were transformed mathematically from the laboratory frame of reference (in which the experiments were done) to the center-of-mass frame (in which the data analysis is easier), and the momentum distribution of particles was calculated and plotted. The markedly nonuniform angular distribution for the relatively light cal- cium system showed clearly that thermodynamic equilibrium had not

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90 NUCLEAR PHYSICS Cat if_ 111 FIGURE 4.2 One hemisphere of the Plastic Ball detector during its assembly. Consist- ing of 815 pyramidal scintillator detector modules, each with its own electronics package, the complete detector covers 96 percent of the total solid angle into which nuclear- reaction products can be emitted. (Courtesy of the GSI/LBL Collaboration, Lawrence Berkeley Laboratory.) been fully achieved-not even in central collisions, where the highest multiplicity of emitted particles occurs. By contrast, the more nearly uniform angular distribution for the heavier niobium system indicated a much closer approach to equilibrium. This demonstrates the need for using the heaviest possible projectiles and targets in relativistic nuclear collisions. To make valid thermodynamic analyses-and hence mean- ingful estimates of nuclear temperature one needs as many nucleon- nucleon collisions as possible within the fireball. Experimental and theoretical results indicate that central nuclear collisions at energies of 1 to 2 GeV per nucleon do indeed produce a fireball at extremely high temperatures: about 100 MeV, or 10~2 K, which is about 60,000 times hotter than the core of the Sun! Much of the kinetic energy of the collision is converted directly to mass in the form of created particles, such as kaons and pions, whose kinetic energies reflect the temperature of the fireball. It has been observed that the kaons emitted by the fireball are appreciably hotter than the

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NUCLE! UNDER EXTREME CONDITIONS 91 protons, which, in turn, are hotter than the pions. This surprising result is thought to mean that the kaons reflect the fireball temperature at an early, hot stage of its evolution, whereas the pions reflect the temper- ature at the final, "freeze-out" stage. Thus, it could be that different kinds of particles produced in the collision serve as nuclear "clocks" in their record of the event. High Nuclear Densities Measuring the nuclear density in fireballs that last about 10-23 second is very difficult. First, the average mass of the fireballs is not known accurately (although it can be estimated), because none of the collisions that produce them are perfectly central. Most are sufficiently off center that some of the nucleons in the projectile and target nuclei do not participate in the fireball formation; they are merely spectators (see Figure 4.3~. [Furthermore, the volume into which the participating nuclei are compressed by the energy of the collision is not known either. Surprisingly, however, an indirect way of measuring this it. 3 ':' ~ all/:...... ....,.,,..... ...... ,~ ''/ 1 , ~ .. 1 ~ i' FIGURE 4.3 The participant-spectator model of relativistic nuclear collisions. The participant (overlapping) regions of the two nuclei coalesce to form an intensely hot, dense nuclear fireball, which explodes in a shower of high-energy particles. The spectator fragments, meanwhile, remain relatively cold, at normal nuclear density.

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92 NUCLEAR PHYSICS infinitesimal volume has been found in a technique borrowed from the science that deals with the largest sizes imaginable: astronomy. The technique, intensity interferometry, was developed in 1956 for measuring the sizes of galaxies, but it can be applied in nuclear physics as a means for measuring the sizes of the fireballs formed in relativistic nuclear collisions. These events produce many pairs of identical particles, such as protons or positive or negative pious. From mea- surements of such particle pairs, correlations are determined that depend on the spatial and temporal properties of the source. The results of these correlations indicate source sizes 2 to 4 fermis in radius, which are typical of most atomic nuclei and hence plausible. Theoretical calculations using an intranuclear cascade model in which the nuclei are treated as collections of independently interacting particles for central argon-on-argon collisions at energies of 1 to 2 GeV per nucleon yield mean nuclear densities of about 4 times normal, or about 10~5 grams per cubic centimeter. This value is within the range of densities believed to exist in the cores of neutron stars. Similar results are obtained from hydrodynamic models, in which the nuclear medium is treated as a fluid. Extrapolations of the cascade calculations to heavier nuclear systems predict mean densities of about 5 to 6 times normal. With some knowledge of high nuclear temperatures and densities finally in hand, the stage is set for seeking the solution to a very important problem: the determination of the equation of state of nuclear matter. Nuclear-Matter Equation of State Equations of state are among the most valuable tools in science, because they describe the behavior of a physical system over a wide range of conditions, on the basis of a few measurable quantities, called state variables (for ordinary gases, these variables include the pres- sure, volume per molecule, and temperature). If all but one of their values are known for a given state, then the unknown one can be calculated. To determine an equation of state, the appropriate state variables must be identified and their values measured over wide ranges. Until the advent of relativistic nuclear collisions, there was almost no direct experimental evidence on which to base a nuclear-matter equation of state for conditions of high temperature and density,

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NUCLEI UNDER EXTREME CONDITIONS 93 although a great deal of theoretical work had already been done. However, recent experiments on the interaction of argon with argon at bombarding energies of 0.36 to 1.8 GeV per nucleon may be a major new step toward understanding hot, dense nuclear matter. One inter- pretation of the surprisingly low pion yields in these experiments is that much of the kinetic energy that was expected to be transformed into pions was used for nuclear compression instead. When the results were combined with those from an intranuclear cascade calculation, a tentative equation of state was extracted for nuclear matter at about 2 to 4 times normal density. If confirmed, this development would be a major advance for at least three reasons: It would buttress the bridge between the hydrodynamic models that are used to explain many experimental observations and the more detailed (but difficult) many-body calculations that seek to relate observed nuclear properties to various aspects of the underlying nucleon-nucleon force. It could provide a testing ground for the growing list of theoretical ideas such as the existence of extraordinary forms of nuclear matter called density isomers and pion condensates" that have been among the foremost stimuli for experimental work in relativistic nuclear collisions in the past decade. It would be progress toward the determination of such global nuclear properties as viscosity and thermal conductivity, which are important indicators of otherwise hidden aspects of the internucleon force. The behavior of these quantities as functions of the temperature and density is expected to reveal aspects of many-body behavior that are not accessible in simple scattering experiments. With the relatively light argon-on-argon system described above, the compressional energy produced in the collisions increases smoothly with bombarding energy, showing no sign of a discontinuity that could be associated with a new state of matter or a phase transition. With a very heavy nuclear system at very high relativistic energies, on the other hand, it is very likely that there will be a transition from hot hadronic matter to the quark-gluon plasma, the state of matter believed to have existed briefly at the moment of creation of the universe the big bang. This prospect, surely one of the most exciting that nuclear physics has ever contemplated, is discussed in Chapter 7.

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94 NUCLEAR PHYSICS THE HEAVIEST ELEMENTS New Transfermium Elements Ever since the infancy of nuclear science, chemists and physicists have tried to discover new elements beyond uranium (atomic number Z = 921. With the advent of particle accelerators and nuclear reactors, rapid progress was made, culminating with the synthesis of lawrencium (Z = 103) in 1961. For the next 13 years, the only proven method of synthesizing transfermium elements (Z greater than 100) was the bombardment of radioactive targets heavier than uranium with nuclear projectiles as heavy as neon, to produce compound nuclei. Since heavy-ion accelerators are required for this research, the efforts have been concentrated at the Lawrence Berkeley Laboratory, the Joint Institute for Nuclear Research (JINR) at Dubna, USSR, and, most recently, the GSI laboratory at Darmstadt, West Germany. Although these searches have succeeded in producing transfermium elements through atomic number 105, their already very low yields have been steadily decreasing with increasing atomic number. In 1974, element 106 was produced and unambiguously identified at Berkeley by this method. The bombardment of californium-249 (Z = 98) with oxygen-18 (Z = 8) yielded the unnamed nuclide 263106, which decayed by emitting alpha particles, with a half-life of 0.9 second, to known daughter-granddaughter nuclei that decayed in turn by alpha emission with distinctive energies and half-lives. The reaction yield was only about one atom produced per 10' nuclear collisions. At about the same time, however, another isotope of element 106 may have been observed at JINR in the bombardment of a somewhat lighter target, lead-208 (Z = 82), with a much heavier projectile, chromium-54 (Z = 241. These experiments were of great interest because the excitation energy of the compound nucleus with 106 protons was much lower (one can say that the fused system was colder) when produced with the chromium-54 projectile, so that fewer low- energy neutrons had to be emitted in order to stabilize the system; this resulted in a greater yield of the specific isotope of interest. More recently, the Darmstadt group has brought an exquisitely sensitive new technique to the search for elements 107 and higher, adding new dimensions to these cold-fusion reactions. They coupled their 12-m-long recoil velocity selector to an elegant solid-state detec- tor system installed at its focus. This carefully tuned filter is able to reject essentially all of the bombarding beam while transmitting a high

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NUCLEI UNDER EXTREME CONDITIONS 95 percentage of the final reaction products to the detector system' in times of the order of a microsecond. An array of seven detectors made of single-crystal silicon is used to record the time of flight of a reaction product, its energy, and where it stopped in the detector array. Subsequent alpha-decay or spontaneous fission events can then be correlated by their positions. For an alpha-decay daughter- granddaughter chain stemming from the implantation of a single heavy nuclide, such correlation evidence can be extremely power- ful. With this impressive system, the bombardment of bismuth-209 (Z = 83) with titanium-50 (Z = 22) was found to produce a new alpha- emitting nuclide, 257105, which in turn decayed to new alpha-emitting nuclides of elements 103 and 101. Similarly, the nuclide 258105 was identified, along with new or known descendants, by alpha emission or electron-capture decay. With their basic work on element 105 completed, the Darmstadt group then bombarded bismuth-209 with chromium-54 to look for element 107. In 1981 they found 262107, with a half-life of 4.7 millisec- onds (msec); the assignment was proved by the nuclide's decay to its by-then-known descendant 258105. The most elegant experiment of all in this extensive series was that which appears to have produced element 109, one single atom of which was observed in August 1982. In a 12-day experiment, bismuth-209 was bombarded with iron-58 (Z = 26) to produce a single chain of events in one of the detector crystals. The only observed candidate for complete fusion of the projectile and target nuclei had a calculated mass of 264 + 13, from its time of flight and energy. Five milliseconds after its implantation, it decayed by emitting an 11.1-MeV alpha particle. A second alpha particle emitted from the same spot 22.3 msec later escaped from the detector after depositing only 1.14 MeV. Finally, 12.9 seconds after that, a spontaneous fission event was observed, releasing an energy of 188 MeV. This sequence of events is compatible only with a decay series starting with the nuclide 266109 and proceeding via two successive alpha emissions and one beta capture to the nuclide 258104, which then undergoes spontaneous fission. If corroborated, this event will represent the first identification of a new element through the characteristics of a single atom. In March 1984, the gap between elements 107 and 109 was closed: the Darmstadt group presented convincing evidence for the dis- covery of element 108, based on the observation of three distinctive events.

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96 NUCLEAR PHYSICS The Search for Superheavy Elements In the mid-1960s, the interest of many nuclear scientists was aroused by theoretical calculations that showed the strong possibility of a magic island of superheavy elements in the region around proton number Z = 114 and neutron number N = 184. This island would be characterized by a relatively high stability associated with the closed nucleon shells predicted by the shell model of the nucleus. The calculations, which were based on logical extrapolations of properties of ordinary nuclei, indicated that some half-lives might even be long enough for superheavy elements to be found in nature. Since that time, many unsuccessful attempts to find such elements have been made throughout the world, using a great variety of techniques and covering many possibilities including primordial ores, meteorites, and lunar rocks. The effort has recently become focused on the use of heavy-ion accelerators to make nuclear species as close as possible to N = 184 in the general vicinity of Z = 114. The most direct way to make superheavy elements in accelerators is by the complete fusion of a projectile nucleus and a target nucleus. Even under optimal conditions, however, the resulting compound nucleus contains substantial internal excitation (tens of MeV) and angular momentum, which must be quickly dissipated by the emission of light particles (mostly neutrons), followed by the emission of gamma rays, before the ground state of the final reaction product is reached. At each step in the de-excitation process, there is a much better chance for fission to occur instead, so the final probability of producing a superheavy element may become minuscule. At Berkeley, Darmstadt, and Dubna, complete fusion has been pursued vigorously, using reactions such as the bombardment of curium-248 (Z = 96) with calcium-48 (Z = 20) and detection methods sensitive to lifetimes as short as 1 second. However, nothing has been seen that can be attributed to superheavy elements. The most promising ideas at present seem to be those involving the bombard- ment of heavier and very exotic short-lived radioactive targets, such as 276-day einsteinium-254 (Z = 99) or even 40-day einsteinium-255, in that bombarding these targets with a calcium-48 beam brings one closer to the goal of 184 neutrons. (Perhaps, as another tool, acceler- ated beams of radioactive nuclei such as calcium-50 will become available in the future.) The available amounts of these materials are very small, however, and the experiments are extraordinarily difficult to perform. Also, it may simply be that even the best projectile-target combination does not produce a nucleus close enough to the center of

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NUCLE! UNDER EXTREME CONDITIONS 97 the magic island to take advantage of the expected higher stability there. The focus of research in this area now is on trying to understand why these elements have not yet been identified. Is it because such nuclei cannot be made with the tools we have available, or because they cannot exist at all? HIGHLY UNSTABLE NUCLEI Theoretical models of nuclear structure suggest that some 8000 different nuclides of the chemical elements should exist and be observable in the laboratory, but only about 2700 have been discovered so far. Of these, about 300 are the well-known stable nuclides. The other 2400 are radioactive ones that, for the most part, have been artificially produced in particle accelerators or nuclear reactors; about 30 to 40 new ones are discovered each year. Studies of these unstable nuclides provide a wealth of valuable information about exotic nuclear decay modes, about the behavior of the nuclear ground state (mass, shape, and angular momentum) as the neutron-to-proton ratio shifts into highly abnormal regimes, and about the spectroscopic properties of nuclei so strangely composed. When a nucleus is formed, a small amount of the mass of its constituent nucleons is converted to energy. This becomes the binding energy of the nucleus, which overcomes the electrostatic (Coulomb) repulsion between the protons. The more nucleon mass is converted to binding energy, the more stable and less massive, for a given number of nucleons is the resulting nucleus. Thus less stable nuclei have proportionally more mass than more stable ones, and the difference is called the mass excess. Figure 4.4 maps the mass excess for the ground states of the lighter nuclides; the most stable ones, with minimal mass, occupy the valley of stability. Nuclides some distance from the bottom of the valley are radioactive, typically decaying by beta decay but also by alpha decay or spontaneous fission. Farther up the slopes, near the edges of stability, it becomes energetically possible for exotic new radioactivi- ties to appear, and several new decay modes have been discovered in recent years. Exotic Radioactivities Beta-delayed particle emission in which a nucleus beta-decays to an excited state of its daughter, which then emits a neutron, proton, or

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98 NUCLEAR PHYSICS 60 ~0 O '20 ~0 Valley of f stabi i NU: ~5 /1Li FIGURE 4.4 A computer-graphic plot of the mass excess for nuclides of the elements up to titanium. The greater the mass excess, the less stable the nuclide, so the nuclides on the upper slopes of the valley in this diagram are extremely unstable. Conversely, the nuclides along the bottom of the valley are the most stable of all. The nuclides "Li and 22Al are discussed in the text. (After J. Cerny and A. M. Poskanzer, Scientific American, June 1978, p. 60.) alpha particle has been known for several decades. Within the past decade, however, as developing techniques have permitted the obser- vation of predicted nuclides at or near the edge of stability, decay modes have been observed that involve the emission of more than one particle after the beta decay namely, beta-delayed two-neutron, three-neutron, and two-proton emission. Consider two representatives of these exotic nuclei, each of which lies at a limit of stability for the element in question. First, on the neutron-rich side of the valley, is lithium-11 (3 protons, 8 neutrons, and a half-life of 8.7 msec). This nuclide's decay energy is so high (greater than 20 MeV) that a great variety of decay modes are open, and decays

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NUCLE! UNDER EXTREME CONDITIONS 99 by both beta-delayed two-neutron and three-neutron emission have been observed. Since these studies require the detection of neutrons, which is difficult because they are neutral, the parent lithium nuclide is first separated and identified by an ingenious technique developed at the Laboratory for Nuclear and Mass Spectroscopy at Orsay, France. In this technique, the target for the accelerator beam also acts as a preferential collector of product alkali metal nuclei, which in turn- owing to their particular surface-ionization properties-act as the ion source for an attached mass spectrometer. Second, on the neutron-deficient side of the valley, is aluminum-22 (13 protons, 9 neutrons, and a half-life of 70 msec). Here the decay energy is again extremely high (greater than 18 MeV), and a number of decay modes are open, including beta-delayed two-proton emission. A particular beta-decay channel produces the daughter nucleus magne- sium-22, which emits two protons that are detected simultaneously. The mechanism for this decay is of considerable interest: is it actually an extremely fast two-step sequential emission of the protons, or does the decay occur by the predicted mode of diproton (helium-2) emis- sion? (The diproton is considered a transient nuclear species.) The angular correlation of the two protons in the aluminum-22 decay has been measured. The mechanism is complex and appears to be largely sequential; however, some component of helium-2 emission cannot be ruled out. Beta-delayed fission, which is analogous to beta-delayed particle emission, is another exotic form of radioactivity. It allows "ordinary" spontaneous fission studies to be extended to regions far from beta stability, because the beta-delay effect makes these nuclides suffi- ciently long-lived for experimental measurements. A knowledge of the energy barriers to fission in nuclei far from stability is useful in understanding the production of heavy elements in the astrophysical reprocess, one of the principal mechanisms of stellar nucleosynthesis. In neutron-deficient nuclei at the limits of particle stability, decay by the direct emission of a proton (similar to alpha decay) is possible. This decay mode, direct proton radioactivity, was originally observed in an unusual, long-lived excited state of cobalt-53, a nuclide close to the valley of stability. Ground-state proton radioactivity has recently been observed in two rare-earth nuclides, thulium-147 and lutetium-151. The proton-decay results can provide valuable empirical tests of nuclear models that predict both the masses and the half-lives of the parent nuclei. A surprising exotic radioactivity was just discovered in 1984. Using a relatively simple laboratory setup, a team of physicists at Oxford

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100 1 1 1 1 1, 1 1 . w--N o ._ _ cn cn - Q o Q o a c m I- . . _. ~\ .-o cn .m CD 3 a) o Q cn o a) 23 Q C5) ~ C ._ o .= O C~ o 1 a) ~Z y i \ ~ ~ a 0 a -O cn - ~ o Q. ~ O O a) . _ - I 11 c .-o cn CO . _ a) ~_ a) cn a) _ ~:\ Ct a) - o o Q o c ~0 - . _ U) o >% U ~Ct C: _ a) O ~ Q ~: 1 1 1 1 1 1 O a . _ ~, cn c CD a) - c o ._ - a) m 1 _ - o - a' c o O _ \ _ 0 0 0 ~C ~0 _ 0 _ C~ _ C~ o 0 o _ Co~ ,= C 0 0 _ 0 ~a) o 0 o 0 C~ 0 0 00 CD z~Jeqwnu U010Jd O O CM ~ O O O ~ ~ ~ ~ ~Z O U~ O (~- O O ~ . _ . _ _ ~> ~ U' X ._ ~ _ ~ O._ Ct ~ O ~ U, ~ 50= 0 ~ ~ (L) - Ce ~L~ 3 ~z o ~) ~ ;^ .= ,.~: ; ~ o ~ . _ ~ U, ~ ~ o t4 s: ~ ~ 3 == O ~ _ ~ s: Ce ._ .= ~ ~ - 3 ~ ~ O - c: Ct O s._ ~_ O O ~ << ~ V, . ~o _ ~ oo C~ ~ .=

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NUCLEI UNDER EXTREME CONDITIONS 101 University found that radium-223, which ordinarily decays by alpha emission with a half-life of 11.4 days, occasionally emits a carbon-14 nucleus instead; this occurs about 2 times in every 109 decays. That such a novel decay mode should be observed in a naturally occurring nuclide (radium-223 is a member of the radioactive decay series that begins with uranium-235) is particularly significant because it suggests that many other decays by the emission of relatively large nuclei might also be found in nature. Searches for such massive, highly charged decay products (neon-24, for example) are now under way at many laboratories around the world. Long Isotopic Sequences One of the best ways to learn about a physical system that can be characterized by two quantities is to change the value of one of them while holding the other one constant. If we vary the proton number Z or the neutron number N while holding the other one constant, we can examine a long series of nuclides whose properties change more or less smoothly from one extreme to another (any of the columns or rows in the map shown in Figure 4.51. This allows models of nuclear structure to be tested critically by their predictions of changes in behavior as Z or N is varied. Certain values of Z or N are called magic numbers because they correspond to the completion of nucleon shells in the shell model of the nucleus. Any nucleus that has a magic (or near-magic) number of protons or neutrons will be slightly more stable than one would otherwise expect, and if it is near stability, it will be spherical. In regions of the chart of nuclides away from the magic numbers, on the other hand, the nuclei will be deformed by varying amounts into a variety of shapes. It is most interesting and fruitful to follow a long isotopic sequence through the spherical and deformed regions and across the magic numbers; every such sequence crosses the valley of stability in one direction or the other. Generally, deformations in the ground states of nuclei agree rather well with theoretical calculations; the few observa- tions of discrepancies have led to refinements in the theory. Among the most significant developments in the study of nuclei far from stability has been the increasing use of atomic-beam and laser techniques, which provide extremely accurate determinations of such quantities as the nuclear spin and the magnetic moment. The sensitivity of these methods permits measurements to be made on very small quantities of relatively short-lived isotopes, and long sequences of

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102 NUCLEAR PHYSICS isotopes can thus be studied. Here, on-line mass separators, as employed by the ISOLDE collaboration at the European Center for Nuclear Research (CERN) in Geneva, have made great progress possible. Nuclei with Extremely High Spin Nuclear reactions between heavy nuclear projectiles and heavy- element targets often produce compound nuclei that are spinning extremely fast, i.e., they have high angular momentum. Studying these compound nuclei as they de-excite, or relax, to the ground state helps us to understand the interplay among the various forces that control nuclear behavior under such extreme conditions. Among these forces are the centrifugal and Coriolis forces, which are familiar from classical physics. As they increase in magnitude, they affect the nuclear structure in major ways. The centrifugal force tends to stretch the nucleus out into nonspherical shapes involving collective rotations of the nucleons. These deformations, which can be ablate (doorknob-shaped) or prolate (football-shaped), eventually result in nuclear fission. It is the onset of fission, in fact, that generally limits the amount of angular momentum that a nucleus can support. On the Earth, the Coriolis force, arising from the Earth's rotation, causes east-west shifts in north-south winds. In a rotating nucleus, the Coriolis force tries to align the spin of an individual nucleon with the axis about which the collective rotations occur, much as a gyrocompass tries to align itself with the Earth's rotation axis. These alignments of the single particles tend to weaken the collective rotations, while the centrifugal stretching tends to stabilize them. It is the interplay between these two opposing effects that makes high-spin phenomena so richly varied. One such phenomenon, discovered in 1971, came as a complete surprise. In measuring the rate of decrease of the nuclear rotation rate as certain rare-earth nuclides were relaxing from high-spin states, physicists found that the otherwise smooth curves had occasional sharp kinks, or backbends. Every such backhand signifies an abrupt increase in the rotation rate, followed by a resumption of its steady decrease. This is caused by a sudden internal rearrangement of the nuclear structure that decreases its moment of inertia (the ratio of angular momentum to angular velocity) and hence increases its rotation rate. (A spinning skater, pulling the arms in close to the body, spins faster for exactly the same reason the law of the conservation of angular momentum.)

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NUCLEI UNDER EXTREME CONDITIONS 103 c) a) co o0.8 - g . _ Q ~0.6 a) an 0.0892095 _` a' co - o Q0.0892090 co cl) 0.0892085 1.0 1 ~.rbium-158 1 1 / - / 1 / / 1 / 1 ~L' _ _ 0 0.5 1.0 1.5 Time (10-" see) ~ Vela '' i / ~ I / / Jan. Feb. Time (months) March 1969 FIGURE 4.6 Plots of the rotation period (the time required for one complete rotation) versus time, for the nucleus of erbium-158 and for the Vela pulsar. (The nucleus is initially in a high-spin state.) In each case, the rotation period increases with time, i.e., the rotation slows down except when a backbend occurs, as described in the text. (Courtesy of R. M. Diamond and F.S. Stephens, Lawrence Berkeley Laboratory.) The sudden internal rearrangement of the nucleus could be called a nucleusquake. As tiny as it is, it mimics a similar (though unrelated) phenomenon on a colossal scale the starquakes that were first de- tected in the Vela and Crab pulsars in 1969. A pulsar is a rapidly spinning neutron star that, like a high-spin nucleus, is slowing down as it loses energy and angular momentum; it is, in fact, very much like a giant nucleus in many ways. Backbends ("glitches" in the jargon of astrophysics) that resemble those of nuclei appear in its rotational decay curve when sudden internal rearrangements in its structure cause the starquakes (see Figure 4.61.

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104 NUCLEAR PHYSICS Although the effects of nucleusquakes and starquakes are the same, the causes are not. Nucleusquakes are related to the pairing correla- tions of nucleons in nuclei (i.e., the tendency of like nucleons to form pairs with oppositely directed spins) and are proportionally much larger than starquakes. The latter are poorly understood but are now thought to be caused by vortexes in the internal flow pattern of the star. Nonetheless, the similarity between these two phenomena from oppo- site ends of the cosmic scale provides a striking example of the universality of physical laws and of their power to extend our intellec- tual grasp of events far beyond ordinary experience.

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II Impacts of Nuclear Physics

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