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- Nuclear Astrophysics When astrophysicists first realized, in the 1920s, that processes producing enormous amounts of heat and outward radiation pressure must be occurring deep inside the Sun to prevent it from collapsing under its own gravitational field, the study of nuclear physics had only barely begun. The neutron itself was not discovered until 1932, and it was another 6 years before a plausible explanation for the Sun's energy was advanced by nuclear physicists: in a type of reaction called nuclear fusion, four hydrogen nuclei combine to form one helium nucleus, with the release (on a stellar scale) of vast amounts of energy. Since that time, a fruitful symbiosis has arisen between nuclear physics and astrophysics, with progress in each field spurring progress in the other. Studies of nuclear reactions in laboratories on Earth tell us a great deal about the birth, evolution, and death of stars, while astrophysical measurements tell us much about nuclear processes that are difficult or impossible to produce on Earth. Nuclear astrophysics is concerned with the mechanisms of stellar nuclear reactions that generate energy and that lead to the formation of the chemical elements in the process of nucleosynthesis. Some of the most active areas of nuclear astrophysics today are concerned with the mechanisms of supernova explosions, where nucleosynthesis of the heavy elements occurs, and the formation of neutron stars. The latter represent nuclear matter under conditions of high temperature and density, from which a unique insight can be gained on the fundamen 107

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108 NUCLEAR PHYSICS tally important nuclear-matter equation of state. Perhaps most inter- esting of all, however, is the neutron stars' status as a kind of ultimate nuclear laboratory: they are the only known "nuclei" in which the effects of all three of the fundamental forces-the strong force, the electroweak force, and gravitation are intimately interwoven. In this chapter we look at a few of the most active current topics in nuclear astrophysics research, which epitomize the ways in which progress in basic nuclear physics benefits the development of other sciences and, ultimately, of our technological society as a whole. NUCLEI UNDER EXTREME ASTROPHYSICAL CONDITIONS The most extreme condition of matter imaginable existed for only an instant at the beginning of our universe, but a plausible account of this awesome event and its aftermath has been reconstructed from data available today. Among the most important of these data are the known abundances of the chemical elements in the stars and nebulas and in the Earth itself because these values impose certain constraints on the theoretical mechanisms by which nucleosynthesis could have occurred. These constraints are based not only on the nature of nuclear reactions as we know them from terrestrial studies but also on the conceivable dynamical processes by which stars can undergo a spec- tacular death by supernova explosion. Nucleosynthesis of Light Elements In the first seconds after the big bang, there were no nuclei just elementary particles and hadrons. The latter were primarily nucleons, and it was only after about 3 minutes when the temperature of the nascent universe had cooled to about 109 K that these particles could begin to coalesce to form deuterons (2H) and nuclei of helium-3 and helium-4 (3He and 4He); it now seems possible that nuclei of the isotope lithium-7 may also have formed at that time. These four nuclides are thus the big bang nuclides. It took at least half a million years more for the universe to cool sufficiently for these nuclei to capture electrons and become atoms, and a few billion years for stars to form. Only when the stare nuclear fires began to burn did nuclei of the remaining elements begin to form. In the universe today, hydrogen and helium constitute roughly 93 and 7 percent, respectively, of the nuclei, while all the heavier elements make up only about 0.1 percent. Although most of the lighter elements are believed to be produced in

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NUCLEAR ASTROPHYSICS 109 the stellar interiors, a few are too fragile to survive the intense heat and must be formed at cooler sites. These elements are the ones that lie between helium and carbon in the periodic table: lithium, beryllium, and boron. The nuclides in question are 6Li, 9Be, LOB, and SIB, and their observed abundances in the universe can now be accounted for fairly well in terms of a model based on the bombardment of heavier nuclei in the interstellar medium by cosmic rays. In these spallation reactions, a very energetic projectile breaks the target nucleus up into several fragments. Measurements of nuclear spallation reactions at cosmic-ray energies have recently become sufficiently extensive to allow a meaningful test of the astrophysical model, and it has been found that these cosmic-ray nuclides are produced in roughly their observed relative cosmological abundances. The four big bang nuclides mentioned above are the only four that can be attributed to that stage of the evolution of the universe. Remarkably, the modern theory of nucleosynthesis can account for the observed abundances of these four nuclides in terms of a single assumed value of the baryon density of the early universe. In terms of the expanding universe, this primordial density would give rise to a present density between 0.6 x 10-3~ and 11 x 10-3~ gram per cubic centimeter (g/cm3), a range that neatly brackets the observed density of visible matter, 3 x 10-3i g/cm3 (see Figure 5.11. For the universe to be closed i.e., for its own gravitational self-attraction to be sufficient to stop the expansion eventually this density would have to be about 10 times greater. Whether the universe is closed is not known, nor is it known where the missing mass, if any, is to be found. A possible source of the missing mass may be neutrinos if they turn out to have some mass after all. Neutrinos exist in enormous numbers throughout the universe, but a limit can be set on the number of kinds of neutrinos (the three now known correspond to electrons, muons, and tauons) from the observed abundance of 4He produced in the early universe. If there were still another (as yet undetected) kind of neutrino-and if it were present in great numbers it would have added substantially to the overall energy density of the universe during the first 3 minutes, and the universe would therefore have expanded more rapidly. Among other things, this more rapid expansion would have increased the neutron-to-proton ratio, and because most of the neu- trons were eventually incorporated into helium nuclei, the result would have been a greater abundance of 4He than is actually observed. It could be, therefore, that we have already discovered all the kinds of neutrinos that exist in the universe, although a fourth kind cannot be

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110 NUCLEAR PHYSICS ' ~' 1 Closed universe Open universe Astronomy 2H 3He 7Li . 1 1 , 1 ; 1 , 1 10-32 10-31 10-3 10-29 10-28 Baryon density (9/cm3) FIGURE 5.1 From the observed abundances of the four big bang nuclides, it is possible to infer the present baryon density of the universe. The shaded bar for each nuclide represents the range of values calculated from its abundance, and the solid vertical line represents the best fit to these data. The inferred baryon density of about 5 x 10-3' g/cm3 is about 10 times less than that which would be required for the universe to be gravitationally closed (dashed vertical line). Thus, this evidence is consistent with an open universe. (After S. M. Austin, in Progress in Particle and Nuclear Physics, Vol. 7, D. Wilkinson, ea., Pergamon Press, Oxford, 1981.) entirely ruled out. Uncertainties in the observed abundances of the nuclides, as well as certain assumptions in the big bang model that have not yet been validated, make various details of the picture unclear. What is clear is that the nucleosynthesis of the light elements is closely connected to fundamental questions of particle physics and cosmology.

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NUCLEAR ASTROPHYSICS 111 Supernova Explosions and Neutron-Star Formation The study of supernovas and neutron stars has opened up a new area of nuclear astrophysics and has motivated theoretical and experimental research leading to a deeper understanding of the rich properties of nuclei and nuclear matter, especially at high densities. In ordinary stars, such as our Sun, the inward force of gravity is balanced by the outward hydrodynamic pressure of the hot gases and, to a lesser extent, by the radiation pressure of photons. When their nuclear fuel is exhausted, however, some stars undergo gravitational collapse and then explode as a supernova (see Figure 5.21; a small, extremely dense neutron star may be left as a remnant of this stupendous event. The physics of neutron-star formation and the establishment of a new equilibrium against gravity are intimately tied to the behavior of nuclear matter under extreme conditions. In particular, it now appears that neutrinos play an important role in the mechanism of supernova collapse. The hydrogen fusion reaction in stars produces two positrons and two neutrinos. Most nuclear matter is almost perfectly transparent to neutrinos, so most of them depart the star, headed for deep space. (Experiments to detect solar neutrinos passing through the Earth are described later in this chapter.) The escaping neutrinos cool the star by carrying away some of its fusion energy, but this energy loss is slight during the middle period of a star's life. As the star reaches old age and the hydrogen in its interior is consumed, its central temperature will rise, causing the outer layers to expand to form a red giant as our Sun is most likely to do. In later stages of its evolution, the star's interior may collapse, with the release of huge amounts of gravitational energy. As the collapse progresses, the heated nuclei are reformed into much heavier, more neutron-rich species than are normally found in stars. Changing a proton into a neutron, however, requires the capture of an electron, a process that releases a neutrino. (The competing reverse reaction of neutrino capture raises new problems in the study of weak-interaction pro- cesses.) The increased neutrino flux produced by the collapsing star increases the rate of energy loss by the star; this, in turn, decreases its internal pressure and hastens the collapse. At a later stage of the collapse, however, neutrinos will become trapped inside the star because of the greatly increased mass density of the star, which decreases its transparency to neutrinos; this trapping inhibits further electron capture and halts the synthesis of heavy elements. As the nuclei become crushed together by the colossal gravitational

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1 12 NUCLEAR PHYSICS FIGURE 5.2 The Crab nebula, about 5 light-years in diameter with a neutron star at its center, is believed to be the remnant of a supernova explosion that was observed and recorded by Chinese and Japanese astronomers and also, perhaps, by North American Indians July 4, 1054. It remained visible.to the naked eye, in the constellation Taurus, for almost two years. Why there is little evidence of its having been chronicled by European or Arabic astronomers is a matter of conjecture. (Courtesy of the Lick Observatory, University of California.) field, the supernova collapse is eventually halted by the repulsive part of the strong force at very short internucleon distances. One effect of this compression to about twice normal nuclear density is an intense, rebounding pressure wave that forms a gigantic, outward-moving shock wave. The shock wave is believed to be principally responsible for the supernova explosion that blasts the outer mantle and envelope of the star into space. Understanding the propagation of the shock

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NUCLEAR ASTROPHYSICS 113 wave is complicated, however, by the dissociation of nuclei as the shock passes through them a process that dissipates some of its energy. Many other aspects of this model are not yet clear. The ability of the shock wave to blast away the outer layers, for example, depends critically on the temperature, density, and composition of the original star; these factors are, in turn, highly sensitive to the rates of electron capture by the various nuclei present and to the rate of cooling by the accompanying neutrino emission. Refining the model is hampered by inadequate knowledge of the properties of nuclei and of the equation of state of hot, dense nuclear matter. Predicting the amount of energy transmitted to the outer layers, for instance, requires an accurate equation of state. A key parameter, the compressibility of nuclear matter, is letdown for ordinary nuclear density (2.5 x 10'4 g/cm3) from observations of the giant monopole resonance, as discussed in Chapter 2. Relativistic heavy-ion collisions can reach the regime of densities (up to BOOS g/cm3) existing in supernova collapse, but such experiments have only recently begun (see Chapter 41. The supernova shock wave forms outside a central core of about one solar mass, so the explosion of a very massive star leaves behind only a small fraction of its mass as a remnant. If the mass of the remnant is less than about 2.5 solar masses, the remnant becomes a small, dense, rapidly rotating neutron star, of the order of 10 km in diameter; more massive remnants become black holes and disappear from direct view. A neutron star can make its presence known to us by electromag- netic radiation as a pulsar or compact x-ray source. Neutron stars can also be detected indirectly, if they perturb the motions of a visible star with which they are associated in a binary system. To date, well over 300 neutron stars have been identified in our neighborhood of the galaxy, and some black holes may also have been detected indirectly. Weak-Interaction Processes in Supernovas As far as we know, the conditions required for the nucleosynthesis of heavy elements occur only in supernovas. All the gold and uranium found on the Earth today, for example, may have come from a single supernova whose cast-off outer layers were swept up into the interstel- lar gas cloud that eventually evolved into our solar system. Although the nuclear reactions in supernovas are dominated, as in all other forms of nuclear matter, by the strong force, it is also crucial to a description of supernova dynamics to understand the key weak-interaction pro

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114 NUCLEAR PHYSICS cesses that occur there. One such process is electron capture, or inverse beta decay. Electron-capture rates by nuclei under conditions of high tempera- ture and density appear to be dominated by excitation of the Gamow- Teller giant resonance (see Chapter 2) in the product nucleus; here the values of both the spin and the isospin of the nucleus are simulta- neously flipped as a proton is transformed to a neutron upon capturing the electron. Calculated rates based on this picture provide not only information necessary for constructing supernova models, but also a self-consistent analysis of the electron-capture process through the region of moderate atomic mass numbers from 21 to 60. To supplement this work experimentally will require high-energy neutron beams having a narrow spread in energy. The purpose of such beams would be to excite and study the Gamow-Teller resonance in those nuclei that result from electron capture in the corresponding stellar reactions. The extremely neutron-rich nuclei produced in supernovas can be far from the relatively narrow valley of nuclear stability described in Chapter 4; indeed, the last neutron may be bound so weakly that it is almost ready to "drip" from the nucleus. Recent theoretical work on beta decay of nuclei far from stability has emphasized the role of the spacing of highly excited energy levels in the product nucleus. The half-life for beta decay is quite sensitive to this quantity, and the half-lives are a crucial ingredient for calculating the production of heavy elements in supernovas. Recently refined beta-decay calculations lead to relative nuclear mass abundances that match measured values extremely well. The abundances of these heavy elements and their decay products can also be used to estimate the age of the universe (actually, the age at which heavy-element production began), using the calculated beta-decay half-lives and updated beta-delayed fission rates. The result obtained is about 20 billion years, which is not inconsistent with the value of 15 billion to 18 billion years, derived for the age of the oldest globular clusters (using the theory of stellar evolution), or with the value of 13 billion to 18 billion years, derived from the rate of expansion of the universe. NUCLEAR REACTIONS IN STARS Modern experimental and theoretical techniques have provided a great deal of information on many of the nuclear reactions that generate energy and synthesize elements in the stars. In our own Sun, for example, the main path to hydrogen fusion starts with the pep reaction,

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NUCLEAR ASTROPHYSICS 115 in which two protons react to form a deuteron by emitting a positron and a neutrino. Our Sun, being the nearest star, is naturally the most thoroughly studied. An indirect way of checking the validity of models of solar structure and dynamics is to compare calculated results with measured physical properties of the Sun or with measured abundances of the elements. The Solar-Neutrino Problem About 25 years ago, an improved understanding of neutrino interac- tions led to the suggestion of a relatively direct way of observing nuclear reactions taking place in the Sun's core: use an earthbound detector to measure the flux of neutrinos released by these reactions. Because neutrinos interact only via the weak force, they stream relatively unimpeded from the Sun's center and offer us a glimpse of the processes occurring there. Photons, by contrast, undergo the much stronger electromagnetic interaction with the solar material, and it takes them about 107 years to wend their way from the Sun's center to its surface. In 1970 a solar-neutrino detector built by Brookhaven National Laboratory began operating in a South Dakota gold mine, a mile underground to help shield against cosmic-ray background counts. In experiments carried out during the past 14 years, the average counting rate has been about three neutrino captures per week, roughly one fourth the rate predicted by solar models. The discrepancy, which is still unresolved, is called the solar-neutrino problem. Solar-neutrino detectors are based on a nuclear process, related to beta decay, in which a nucleus absorbs a neutrino and transforms to a daughter nucleus by emitting an electron. In the Brookhaven radiochemical detector (see Figure 5.3), the target nucleus is chlorine-37 (37Cl), in the form of 100,000 gallons of perchloroethylene cleaning fluid. The daughter nucleus, argon-37 (37Ar), is a gas, which is relatively easy to sweep out of the liquid and measure. The reaction in question, however, requires a minimum neutrino energy of 0.81 MeV. Unfortunately, this restriction makes the detector insensitive to the pep reaction, which provides 90 percent of the total solar-neutrino flux but whose neutrinos have a maximum energy of only 0.42 MeV. An analysis of relevant nuclear reactions shows that 80 percent of all the neutrinos that should be detected by the 37Cl come from a minor solar reaction (about 0.01 percent of the total) in which a proton reacts with beryllium-7 to produce boron-8, which then decays to beryllium-8 by emitting a positron and a neutrino with a maximum energy of 14

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1 16 NUCLEAR PHYSICS 3.8 x 108 cm3C2CI4 2 2 x 103 37CI atoms ~ .. =-q l 3.86 x 1026 watts 1.8 x 1038 neutrinos/sec - - - 6.6 x 101 neutrinos/sec~cm2 _ __. _ . \ /_ \\ \ ( 037CI ~ ~37Ar/week l FIGURE 5.3 The solar-neutrino experiment being conducted in a South Dakota gold mine (see the text for details). Of every 1022 neutrinos that pass through the 100,000- gallon tank of perchloroethylene, fewer than one interacts with a 37C1 nucleus. Each such interaction produces a 37Ar atom, which can be extracted and counted. The counting rate of about three neutrino-produced events per week is about one fourth the expected rate.

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NUCLEAR ASTROPHYSICS 117 MeV. The selectivity of the 37C1 detector for this minor reaction is actually an advantage for solar diagnostics, however, because the reaction (unlike the pep reaction) sensitively reflects conditions at the core of the Sun. The solar-neutrino problem represents the only major failure of the otherwise extremely successful standard solar model, and this discrep- ancy between the predicted and measured neutrino counting rates has prompted critical re-examinations of various aspects of solar physics and nuclear physics. The nuclear-reaction rates in question have been substantiated by new results in many laboratories. It has also been suggested that the electron neutrinos, on their way to the Earth from the Sun, may undergo neutrino oscillations to their muon or tauon counterparts, as discussed in Chapter 3. There is no real evidence for this, however, and the problem remains under investigation. The next logical step would seem to be the construction of detectors having target nuclei that could respond to other parts of the predicted solar-neutrino spectrum. The proposed detector currently receiving the most attention is based on gallium-71 (alga), which produces germa- nium-71 (age) upon reacting with a neutrino. The 7'Ga detector has the advantage that most of its counts (63 percent of the total) would be due to neutrinos from the pep reaction, which is the basic reaction responsible for the Sun's luminosity. The neutrino flux from the pep reaction is relatively insensitive to detailed conditions inside the Sun. Therefore, if the measured counting rate in the Olga detector were still less than the predicted rate, we would be left with only two possible explanations: either (1) some form of neutrino oscillation or decay occurs between the center of the Sun and the Earth, or (2) the Sun is producing energy through some nonequilibrium process (so that it is currently producing less energy than it is radiating). Conversely, if the measured and predicted counting rates were in agreement, we could infer a limit on the neutrino mass differences of approximately 10-6 eV or less, and we could verify that the Sun is currently producing energy at a rate consistent with its observed luminosity, although this fact alone could not rule out the possibility of nonequilibrium processes. Tests on a pilot detector made with 1.8 tons of gallium have shown an efficiency of 95 percent or better for collecting the age reaction product; at present, it is estimated that a full-scale detector would require between 15 and 30 tons of gallium. Meanwhile, various other possible detectors are under consideration, including two that would be able to measure the solar neutrinos directly. One of these would be able to measure both the energy and time of interaction of a given neutrino,

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118 NUCLEAR PHYSICS and the other would be able to measure these quantities as well as the direction of arrival of the neutrino. Stellar Evolution As a star evolves from youth to old age, its primary energy- generating reactions shift from hydrogen fusion to other processes involving progressively heavier elements. An understanding of stellar evolution therefore requires a thorough study of the corresponding nuclear reactions. Recent interest in stellar energy generation and nucleosynthesis has been focused on these later stages of stellar evolution. In a red giant star, for example, a primary process is the fusion of three 4He nuclei (alpha particles) to form carbon-12 (TIC), a process called helium burning. Some of the '2C nuclei can react further with 4He to form oxygen-16 (~60), so that the ratio of ~60 to ~2C from nucleosynthesis depends on the reaction rate of '2C with 4He relative to its rate of formation through helium burning. There is currently a discrepancy by a factor of 2 between different laboratory measure- ments of the 4He plus '2C reaction, which needs to be resolved by further experiments. Considerable work has been done recently on stellar nuclear reac- tions involving aluminum and magnesium, triggered by the discovery in 1976 that aluminum mineral inclusions in the Allende meteorite contain an excessive proportion of 26Mg relative to the other magnesium isotopes. The excess 26Mg is directly proportional to the amount of aluminum present; this leaves little doubt that the excess 26Mg is the decay product of radioactive 26Al, which has a half-life of only 7.2 x 1Os years. Recently, gamma rays from the decay of 26Al in the interstellar medium have been identified with high-resolution detectors in orbiting satellites. These observations point to the presence of a substantial amount of 26Al distributed in the plane of our galaxy and suggest that the most likely source of this material is from nova explosions. This is consistent with recent nuclear-physics measure- ments that suggest that red giant stars and novas are more likely sources of 26Al than are supernovas. Another example of the value of nuclear physics in furthering our understanding of stellar evolution is that of very hot stars, such as white dwarfs. Here certain radioactive nuclear species both ground states and long-lived excited states are important in nucleosynthetic reaction cycles even though their half-lives are relatively short. For example, the reaction of a proton with nitrogen-13 (half-life 9.97 minutes) to give oxygen-14 (half-life 70.6 seconds) forms part of the

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NUCLEAR ASTROPHYSICS 119 rp process / / 2sSj ~ 27sf is, ~` JUDAIC 24AI- 20N~; , ~ Hot CNO cycle /~, . O , O IN FIGURE 5.4 Series of nuclear reactions such as the hot CNO cycle and the rp (rapid proton capture) process occur on time scales that are short compared with the half-lives of nuclides such as '3N (10 minutes) and i9Ne (17 seconds). These explosive phases of nucleosynthesis are thought to occur on the surfaces of white dwarfs and neutron stars that are accreting fresh hydrogen on their surfaces. They may be responsible for novas, which occur at a rate of about 25 per year in our galaxy. so-called hot CNO cycle (carbon, nitrogen, oxygen; see Figure 5.41. Studying such reactions experimentally is technically very challenging, requiring the production of intense secondary beams of radioactive nuclides. At least four different methods have been proposed for producing the required beams. This technical capability would provide important information for astrophysical processes, and it would also open up the possibility of investigating otherwise inaccessible nuclear reactions.