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Funciamental Forces in the Nucleus Since the early days of nuclear physics, researchers have had considerable success in accounting for the measured properties of nuclei by assuming that the only constituents of nuclei are protons and neutrons. The effects of the other constituents, such as virtual mesons, are present in the strong forces that act between nucleons. However, the mesons and more fundamental constituents are usually hidden from view in experimental measurements. The situation is analogous to the role of the core electrons in the chemical bonding of atoms. The core electrons certainly affect the chemical bonding forces but can for the most part be ignored in describing the chemical bond. In the same way, nucleons are viewed as composite objects made up of quarks, but only a few kinds of experiments are decisive in revealing this underlying structure. Experiments measuring the electromagnetic properties of nuclei are particularly informative. Many of the constituents are charged and thus produce measurable electromagnetic currents. Another kind of exper- iment is to measure violations of symmetry in nuclear transitions. Nuclear states have symmetries that are easy to classify and measure, and any violations can be attributed to fundamental particles that mediate the nuclear forces. In the next two sections, some of the studies that connect nuclear properties with the fundamental particles and interactions are described in more detail. 67
68 NUCLEAR PHYSICS NONNUCLEONIC CONSTITUENTS OF NUCLEI The lightest hadron, the pion, has a prominent role in both nuclear and elementary-particle physics. In nuclear physics, the strong inter- action is mediated at large internucleon distances by virtual pions. The charged virtual pions found in the nucleus make their presence known by the magnetic effects of their currents. The pionic aspects of nuclear states can be studied in many other ways as well, such as the scattering of high-energy nucleons from nuclei. In a grazing collision, the projectile nucleon hardly disturbs the target except for the fleeting effect of the pionic cloud of the projectile, as well as the effects of the other forces. Measurement of the scattering and absorption of pions by nuclei has provided knowledge of the hadronic interactions, supporting the idea that the symmetries embodied in the quark physics apply to the pions in the nuclear medium. The realization that the nucleus contains virtual mesons suggests that it may contain other virtual particles as well. To complicate even further this sharp departure from the simple proton-neutron model of the nucleus, it is now widely accepted that nucleons and mesons are themselves composite objects made up of quarks. The quarks that constitute a nucleon interact strongly by exchanging gluons among themselves. The quarks are strongly bound in the nucleon and have a spectrum of energy states analogous to those of bound electrons in an atom. From this viewpoint, a particular nucleon is only one possible quark state; other excited states correspond to more massive, non- nucleonic members of the baryon family, so that a nucleon changes to a different kind of baryon when the quarks change state. In the five decades since the discovery of the neutron, the picture of the nucleus has changed from a simple cluster of proton and neutron "billiard balls" to a seething mass of nucleons, other baryons, and mesons, all consisting of quarks and gluons. It is natural to ask whether the new, nonnucleonic features in the present model of the nucleus have observable consequences. The success of the proton-neutron model of the nucleus at low to moderate energies implies that nonnucleonic contributions must be looked for in higher energy ranges or in interactions different from the nucleon- nucleon scattering used so widely in the past. In recent years, experimenters have probed nonnucleonic effects in nuclei by going to higher energies, by deliberately creating nonnucleonic constituents in nuclei, and by studying directly the interactions of more exotic particles.
FUNDAMENTAL FORCES IN THE NUCLEUS 69 Scientists have long known that an object is difficult to see unless the wavelength of light is small compared with the object's dimensions; this fundamental wave property limits the useful magnification of optical microscopes, for example. It is one of the stranger aspects of quantum mechanics (also called wave mechanics) that any particle of atomic dimensions or smaller exhibits distinctly wavelike as well as particlelike behavior and has a definite wavelength that is inversely proportional to the particle's momentum. Exploring small structures in the nucleus therefore requires a particle probe with high momentum (and correspondingly high energy) to give a wavelength small enough to enable inner structures to be distinguished clearly. High-energy electrons are a good choice for this type of experiment, because they interact with nuclei through the well-understood electromagnetic force and because they seem to be pointlike particles having no dimensions or inner structure themselves. Another recent approach is to implant nonnucleonic baryon impuri- ties into a nucleus and to study the subsequent response of the system. Using advanced experimental techniques, one can replace a single nucleon in a nucleus by a strange lambda or sigma hyperon (a baryon that differs from nucleons in having a strange quark rather than up and down quarks only) with hardly any disturbance of the nucleon orbits. The result is a hypernucleus, in which a nucleon-nucleon interaction is replaced by the somewhat different hyperon-nucleon interaction. Be- cause the internal motions in the hypernucleus are closely related to known motions in the original nucleus, properties of the nucleon- hyperon interactions can be inferred from the measured hypernuclear structure. A new class of experiments still being developed uses proton- antiproton collisions at moderate energies to bridge the gap between nuclear physics and particle physics. On the one hand, the proton- antiproton system represents a familiar interaction mediated by the exchange of mesons, but from the viewpoint of the quark model it is a system of three quarks and three antiquarks whose interactions are mediated by the exchange of gluons. These experiments should pro- vide challenging tests of both meson-exchange theories and quark models. The three types of experiments outlined here are discussed in further detail below, to bring out the kinds of information that they can provide and to mention some of the exciting surprises that have already been found.
70 NUCLEAR PHYSICS Probing Quark Structure with Leptons Leptons-electrons, muons, tauons, and their associated neutri- nos interact with nucleons through the electroweak force rather than the strong force. Thus a lepton interacting with a nucleus does not usually exert enough force on the nucleons to perturb them signifi- cantly from their internal motions, even if the lepton passes directly through the nuclear matter. Leptons are therefore excellent probes for observing the nucleus essentially in its natural state. Moreover, because the electromagnetic force is well understood, the measured scattering of leptons from nuclei can be related to the properties of the scatterers without much uncertainty. Over the past three decades, the scattering of high-energy electrons by nuclei has been the most successful method for providing detailed information on the distribution of electric charge, and also of magne- tism, in nuclei. This charge does not reside in the protons alone, however. Many of the virtual mesons existing momentarily in a nucleus are electrically charged, and even the neutrons and neutral mesons can exert magnetic forces. The technique of high-energy electron scattering is therefore a natural choice in looking for the effects of these me sonic constituents. Relatively high bombarding energies (in the GeV range) are needed to make the electron's wavelength short enough to be able to 'isee" the fine details inside a nucleus. The experimental results of scattering high-energy electrons from the very light nucleus helium-3 cannot be explained satisfactorily using theoretical models that take into account only the ejects of the charge and magnetism of the two protons and one neutron; one must also include the electromagnetic effects arising from the exchange of a pion or rho meson between nucleons. The meson-exchange model gives a strikingly better account of the data (see Figure 3.1~. Such tantalizing results obtained over the past decade have created intense scientific interest. The 4-GeV Continuous Elec- tron Beam Accelerator Facility (CEBAF) proposed for construction by the Southeastern Universities Research Association (SURA) would allow much-improved investigation of meson-exchange contributions in experiments of the kind described above. Electrons, muons, and neutrinos have all been used to investigate the quark structure of hadrons (baryons and mesons). The usual method of studying new particles bombarding a target with sufficient energy to create or release the desired particle~oes not apply here, however. Because of the phenomenon of quark confinement, it is
10° 10-2 o Cal o c' 10-4 ._ - a' ct 10-6 10-8 FUNDAMENTAL FORCES IN THE NUCLEUS 71 1 1 1 \\ _ \\ o 0 MlT-Bates · CEN Saclay Nucleons only \ \2 - Nucleons plus meson \ ~ exchange \ \ I /~- `` 1 b 20 30 Squared momentum transfer (fm~2) FIGURE 3. l Data obtained by the high-energy elastic scattering of electrons from the helium-3 nucleus reveal the superiority of the meson-exchange model in describing the distribution of magnetism in nuclei, compared with the model that considers only the nucleons. All three curves represent theoretical calculations; the two solid ones are based on somewhat different assumptions. [From J. M. Cavedon et al., Physical Review Letters 49, 986 (1982).] apparently impossible to liberate quarks from their hadrons with the means currently at hand. To describe this unique situation, quark models are based on the assumption that the constituent quarks of a hadron are confined in an impenetrable bag or tied together by unbreakable strings, so that they cannot escape. This aspect of quark behavior is based on an astonish- ing characteristic of the strength of their color interaction: it is nearly zero when they are very close together (a condition called asymptotic freedom) and grows stronger as they move apart! This is just the opposite of the gravitational, electromagnetic, and strong interactions
72 NUCLEAR PHYSICS between hadrons, all of which grow weaker as the interacting particles move apart. The size of a quark bag (i.e., the size of a hadron) represents the limit beyond which the quarks are unable to move apart. The standard quark model was developed in order to account concisely for the variety of known hadrons. The model requires quarks to have the spin quantum number 1/2 so that their spins can combine properly to yield the observed spins of the hadrons. Electron-scattering and muon-scattering experiments have yielded results consistent with this requirement. These experiments make use of the magnetism that spinning charged particles inherently possess. Comparison of the fraction of projectiles scattered through small angles with the fraction scattered through large angles allows the erect of electric forces to be eliminated, leaving only the scattering due to magnetism. At the energies where the theoretical model is most accurate, the magnetic erects are consistent with the scattering from pointlike particles (the quarks) having spin 1/2. The standard quark model also assumes that quarks have fractional electric charge (compared with the unit charge of the electron), to make the net charge of a given combination of quarks equal to the observed charge of the hadron that they constitute. The existence of a free fractional electric charge has never been convincingly demonstrated for any macroscopic object; this is explained on the basis of quark confinement. However, electron scattering from hydrogen and deute- rium at the Stanford Linear Accelerator Center and neutrino scattering from a fluorinated hydrocarbon at CERN in Geneva have both pro- duced results consistent with those predicted by a quark model based on pointlike particles having charges of -1/3 and + 2/3 (in units of the electron charge). Furthermore, the experimental results are in excel- lent agreement with each other. Taken as a whole, the lepton-scattering experiments provide strong support for the quark model. Nuclei provide the only available system for hunting for complex multiquark states, in which more than three quarks are confined in the same bag. Finding multiquark states would be of great interest in developing our understanding of quark confinement. The European Muon Collaboration at CERN has recently obtained exciting results in collisions between muon projectiles and deuterium or iron targets. The experiments have been interpreted to show that the distribution of quarks in iron nuclei is slightly, but significantly, different from the distribution in isolated nucleons (see Figure 3.21. (The deuteron is so loosely bound as to be essentially two free nucleons.) Possible explanations based on the notion that quarks are less strongly confined within the environment of a nucleus have been
FUNDAMENTAL FORCES IN THE NUCLEUS 73 1.2 ._ 0 4 ~ _ 1. 1 Q ._ .° 1.0 Cal to C' ~ 0.9 en CO o C) ' O.8 ~ ~ ~ ~ ~ ~ I _ ~ - ~ ~ ~ ~ _ ~ I I I ~ I 1 1 ~ I I I _ o European Muon Collaboration, CERN · Stanford -~-~-- ~--~! T~ 0 0.2 0.4 , , 1 , , , 1 1 1 1 0.6 Momentum fraction, x 1,,, 0.8 1.0 FIGURE 3.2 Inelastic scattering data from experiments with high-energy muons and electrons can be interpreted as showing that the distributions of quarks in iron nuclei and deuterium nuclei are substantially different, as discussed in the text. If they were not different, the data points would be expected to fall along the dashed line. (New electron data courtesy of R. G. Arnold, American University, Washington, D.C.) advanced. The nucleons may expand as a result of their mutual interactions, or the quarks may "percolate" from one nucleon to another. An alternative explanation is that the additional quarks are part of the virtual pions in the nucleus; the lepton scattering, in eject, provides a "snapshot" of the nuclear constituents. The progress of these experiments is being closely watched by nuclear physicists and elementary-particle physicists, all of whom have much to gain from a deeper understanding of the role of quarks in nuclear structure. The Physics of Hypernuclei The presence of surrounding nuclear matter can drastically modify the properties of a particle. A free neutron, for example, has a half-life of about 10 minutes for decaying into a proton, but the neutrons in ordinary atomic nuclei have existed throughout the age of the universe. In turn, the interactions of an embedded particle can modify the properties of nuclear matter. The possibility of studying nonnucleonic particles and nuclear matter in the same system has stimulated both
74 NUCLEAR PHYSICS experimenters and theorists alike since the discovery of the first hypernucleus about three decades ago. For several reasons, much of the work in hypernuclear physics has concentrated on the lambda-nucleus interaction. A lambda hyperon implanted in a nucleus does not modify the nucleus drastically, because a lambda is very much like a neutron: it has zero charge, about 20 percent greater mass, and only somewhat weaker interactions with nucleons. Thus a lambda hypernucleus is different from the original nucleus, but not so different as to preclude understanding. Another useful property of this hyperon is that, compared with other unstable particles, it has the enormously long lifetime (on the nuclear time scale) of about 10-~° second. The lambda's lifetime is long enough for the details of its interaction with nucleons to be studied precisely. The general technique for making hypernuclei is to produce the hyperon in situ by allowing a suitable projectile to react with a nucleon in the target nucleus. The usual projectile is the negative kaon, which is produced in accelerators at such institutions as CERN (Switzerland), Brookhaven National Laboratory, and KKK (Japan). The kaon reacts with a neutron to produce a lambda and a negative pion; the pion is ejected from the system and provides a signal that a hypernucleus has been formed. For the cleanest experiments, the nonnucleonic baryon should be created nearly at rest in the nucleus, to avoid depositing a burst of energy that could boil nucleons out of their orbits or even out of the nucleus entirely. With the appropriate choice of experimental param- eters, this condition can be achieved in the kaon-induced reactions, and the created baryon will be moving not much more rapidly than the nucleons already present in the target nucleus. The baryon will be left in essentially the same state as the nucleon it replaced; this is called a substitutional state of the nucleus. Experimentally, substitutional states can be studied by programming the measuring equipment to accumulate data only when the detectors spot an exiting pion moving nearly parallel to the projectile beam direction. The kaon beams required for producing substitutional states are difficult to produce with high quality. Kaons, which are unstable, are generated as a secondary beam in a multi-GeV proton accelerator. The kaons produced in the initial proton reaction with a selected target have a wide spread in energy and angle and are mixed with a large proportion of pions. Considerable sorting is necessary before the kaons can be isolated for the production of substitutional states in hypernuclei. The research is greatly hampered at present by the lack of intense kaon beams having a narrow energy spread.
FUNDAMENTAL FORCES IN THE NUCLEUS 75 About two dozen distinct types of lambda hypernuclei have been produced, mainly from among the light elements (up to oxygen). Analysis of the binding energy data of the lambda in the nuclear ground state (i.e., the amount of energy required to break the lambda free) shows that the spin-independent part of the lambda-nucleon interaction is only about two thirds as strong as the nucleon-nucleon interaction and that the spin-dependent interaction is much weaker for the lambda. If an excited state of a lambda hypernucleus is produced, it may decay to a lower state by emitting a gamma ray. Measurement of the gamma-ray energy therefore gives the energy spacing between the states the same method commonly used to study the energy levels of ordinary nuclei and thereby to test theories of nuclear structure. Researchers at Brookhaven National Laboratory have been especially active in this field, and they are currently performing experiments with high-resolution gamma-ray detectors to measure the energies more precisely. The sigma hypernucleus has also been studied to a small extent. The sigma is a hyperon that decays to the lambda a process that is expected to be very fast. Workers at CERN and at Brookhaven were therefore surprised recently to discover quite long-lived substitutional states in sigma hypernuclei. The data are sparse, and it is not yet known whether the slow decay of a sigma to a lambda in hypernuclei represents a special inhibiting effect limited to light nuclei or a general property of nuclear matter. Quantum Chromodynamics at Low Energies It is now widely believed that quantum chromodynamics will be- come established as the correct theory of the strong interaction. For the region of asymptotic freedom, where the quarks are close together and interact very weakly, QCD calculations produce results in good agreement with experiment. At larger distances, however, where the confined quarks interact strongly, the calculations become so compli- cated that reliable results are difficult to obtain, although considerable progress is being made through the use of lattice gauge theory (see page 142 for an explanation of this term). Because the region of asymptotic freedom can be probed in the laboratory only in experiments at very high energies, theory and high energy have gone hand in hand in the development of QCD. At lower energies, however, the experiments performed so far do not seem to bear on QCD in a way that would facilitate extending the theory to the domain of strong quark interac
76 NUCLEAR PHYSICS Proton Antiproton Virtual muon Lambda + ~ Antilambda FIGURE 3.3 Annihilation of a u quark and a u antiquary in a proton-antiproton collision. The annihilation produces a high-energy virtual gluon, which disappears with the creation of an s quark and an s antiquary in the respective nuclei, which have thus become a lambda hyperon and an antilambda hyperon. lions. Physicists have therefore tried to conceive lower-energy exper- iments directly relevant to QCD. Prime candidates for studying quark properties at lower energies (less than 1 GeV) are the proton-antiproton interaction or the proton- kaon interaction. According to the quark model, a proton has the quark structure uad (two up quarks and one down quark). An antiproton has the analogous structure uad, made with antiquarks instead of quarks. During a proton-antiproton collision, one u quark may annihilate its antiquark u to form, for example, the strange quark s and its antiquark s (see Figure 3.31. After the collision, the system separates into two three-quark hyperons: uds (a lambda) and uds (an antilambda). The precise study of such processes over a range of energies is expected to provide important data for guiding the development of QCD. Studies of proton-antiproton interactions are already under way at CERN's new Low-Energy Antiproton Ring (LEAR), an accelerator facility that is a nearly ideal source of low-energy antiprotons. It provides a copious, essentially pure beam of antiprotons over a wide energy range, with a very small energy spread. Although it could profit from the additional ability to produce polarized (spin-aligned) antiprotons for the investigation of spin-dependent forces, the LEAR facility offers opportunities for exciting research that make it singularly attractive to many user groups from the United States.
FUNDAMENTAL FORCES IN THE NUCLEUS 77 THE NUCLEUS AS A LABORATORY FOR FUNDAMENTAL SYMMETRIES Much of our physical understanding of nature is embodied in conservation laws and in the symmetry principles from which they stem. Conservation laws make powerful statements of great generality that apply even if the details of a system are unknown. The classical laws of electric-charge conservation, energy conservation, and mo- mentum conservation are routinely applied to the analysis of nuclear reactions because of their complete reliability. From the opposite viewpoint, the fact that conservation laws inferred from everyday physics can be applied to nuclear systems represents a great extension of these laws to new realms of size and energy. The study of nuclear systems has also revealed new symmetries and conservation laws not apparent in the behavior of macroscopic objects. As theory pushes on to examine the nature of the fundamental forces at energies far beyond the reach of the largest manmade accelerators, searches for symmetry violations in the precisely calibrated environment of the nucleus may be the only viable approach for seeing the subtle residual effects predicted to occur at energies that are accessible. There are several reasons why the nucleus is an excellent laboratory for the study of fundamental symmetries. The nucleus readily displays the effects of both the strong and electroweak forces, and the dimen- sions of the nucleus place it only one or two steps away from what we believe is the ultimate structure of matter. Furthermore, the wide range of proton and neutron numbers available in nuclei helps to illuminate differences and distinguish the general from the specific. Strange particles such as the lambda hyperon can be implanted to form hypernuclei, thereby extending the variety of nuclei even further. Finally, nuclei have definite quantum states, so that the systems studied have well-defined properties. An added advantage is the large amplification of small effects that can occur when two nuclear states with specific properties happen to have nearly the same energy; as physics has advanced to more and more comprehensive theories, experimental sensitivity to small effects has become increasingly important. The weak force has been an extraordinarily fruitful source of information about the underlying symmetries of nature. It is exposed for convenient study in the more than 2000 known nuclei that undergo beta decay a manifestation of this force. The attention of physicists was refocused on the question of symmetry laws by a famous experi- ment carried out in 1956 at the National Bureau of Standards. The beta
78 NUCLEAR PHYSICS decay of parallel-spin (magnetically oriented) cobalt-60 nuclei was shown not to give the same result as the corresponding mirror-image experiment- a most astounding result at the time. In terms of symme- try, this result is described by saying that the weak force does not behave symmetrically under reflection; in terms of conservation laws, it is described by saying that weak-force interactions do not conserve parity. The strong, electromagnetic, and gravitational forces do not appear to violate parity; why the weak force does is not understood. In familiar examples of the phenomena of classical physics-collid- ing billiard balls, for example the physical laws that govern the interactions of objects appear always to be the same, regardless of whether one considers time to be running forward or backward. This independence of the direction of time's arrow is a symmetry principle called time-reversal invariance, which was long thought to be abso- lutely valid in all physical systems. In 1964, however, a violation of time-reversal invariance was discovered in a decay process involving the weak force. The particle in question was the neutral K meson (kaon), which can undergo beta decay by two modes, to give in part either positive electrons (positrons) or negative electrons. If time- reversal invariance held, the two rates of decay would be exactly equal; instead, their ratio is found to be 1.0067. Although the effect is small and occurs in an obscure submicroscopic system, it may have important cosmological implications: it may be related to the preponderance of matter over antimatter in the known universe or to the preponderance of radiation over matter. Along with other cases of symmetry-principle violations, time-reversal-invariance violation has forged unexpected links between nuclear physics and cosmology, connecting the unimaginably small with the unimaginably large. Finding other examples of time-reversal-invariance violation in processes simpler than that of kaon decay would help greatly in understanding the origin of this surprising phenomenon. Theorists have therefore tried to predict observable effects of such a violation in nucleons and nuclei for instance, a nonzero electric dipole moment (slight separation of internal positive and negative charges) for the neutron. Searches for such effects are being conducted in phenome- nally precise studies that are a tribute to the ingenuity of experimen- talists. Because symmetry principles can apply even when the detailed interactions in a system are unknown, modern theory building often starts by postulating certain symmetries suggested either by experi- mental data or by beauty of design in the theory. Some symmetries can
FUNDAMENTAL FORCES IN THE NUCLEUS 79 be readily visualized, such as the symmetries of space and time that underly the conservation laws for momentum, angular momentum, parity, and energy. But symmetries can also apply to abstract quanti- ties such as the isospin concept that merges individual proton and neutron identities into the more general nucleon description. Present-day theorists have set themselves the ambitious task of unifying the "fundamental'' forces of nature into one comprehensive description from which everything else can be rigorously derived. Their achievements to date have been impressive. The theory showing that electromagnetism and the weak force both spring from a com- mon electroweak force has been a triumph of successful predic- tions, including the existence of the charm quark and the recently discovered W+, W-, and Z° bosons. These last three particles are crucial because their exchange (as virtual particles) is at the origin of the weak force. Despite these triumphs, the new electroweak theory-which, to- gether with QCD, is now referred to as the Standard Model-is incomplete. It does not explain (but does allow) the violations of parity and time-reversal invariance, it does not unify the strong force or the gravitational force with the electroweak force, and it does not predict, a priori, the observed relative strengths of the electromagnetic and weak forces. Theorists are still striving for a Grand Unified Theory that would unite all the forces and that would include all the symmetry laws and their violations. The following sections give some examples of how nuclear physics is providing guideposts along the dimly outlined road to grand unification. Right-Handed Bosons in Beta Decay Parity is found to be violated to the maximum possible extent by nuclear beta decay; i.e., the mirror-image decays are never observed. Suppose that the neutrino emitted in a beta decay is represented by a partially closed left hand, with the thumb in the direction of the neutrino's motion. The curl of the fingers represents the direction of the classical rotation analogous to the neutrino's spin. If this model is viewed in a mirror parallel to the thumb, the direction of motion is unchanged, but the mirror-image spin is in the opposite direction. Mirror reflection changes a left hand to a right hand, a complete reversal of parity. The hypothesis that neutrinos are strictly left- handed therefore successfully accounts for parity violation. The Standard Model assumes that the W+ and W- bosons are left-handed (strictly speaking, it is their interactions that are left
80 NUCLEAR PHYSICS handed) and that the Z° boson is partly left-handed, which leads automatically to the left-handedness of neutrinos. Other theories consider the more symmetric possibility that there are right-handed as well as left-handed W and Z bosons. If the right-handed bosons were significantly more massive than the left-handed ones, their force would have a shorter range, and left-handed neutrinos would dominate in present experiments. The situation is somewhat like that of the electroweak force, where the constituent electromagnetic and weak forces are fundamentally the same yet manifest themselves to us with very different strengths. Several different kinds of experiments have shown that if right- handed W and Z bosons do exist, they must be extremely massive. Some experiments have searched for small right-handed effects in muon decay or in the beta decay of neon-19 nuclei; other experiments infer the properties of neutrinos from the measured spin and motion of the much more easily observed decay electrons. It will be some time before accelerators large enough to permit a direct search for the massive right-handed bosons themselves can be constructed. The Mass of the Neutrino If an observer could overtake and pass a left-handed neutrino, the neutrino's direction of motion (but not its spin direction) would appear to reverse, the way cars seem to fall behind when we pass them. The observer's motion alone could thus change a left-handed neutrino into a right-handed one, so that left-handedness would no longer be an intrinsic oronertv of the neutrino. The way out of this paradox is to r - - ~ - - - ~ assume that neutrinos move with the speed of light, too fast for any observer to overtake. The theory of relativity shows that particles moving with the speed of light must have zero mass. The Standard Model admits only massless neutrinos, but in most proposed Grand Unified Theories, electron neutrinos, for example, can have a very small mass, typically between 10-8 and 1 eV. (By comparison, the mass of the electron is 511,000 eV.) Whether a neutrino has zero or nonzero mass bears directly on neutrino handedness and parity, and on the structure of Grand Unified Theories. The neutrino mass also has important implications for cosmology. The universe still contains so many neutrinos formed during the big bang that if the neutrinos have even a very small mass, their gravitational force could eventually brake and reverse the universe's current outward expansion. Because the density of ob- served stars and galaxies appears to be too low to accomplish this, the
FUNDAMENTAL FORCES IN THE NUCLEUS 81 neutrinos could represent the additional "missing mass" needed to hold the universe together. Indeed, arguments from cosmology have set a rough upper limit of 30 eV on the electron neutrino mass, based on the observation that the universe is still expanding at present. In 1980, researchers in the Soviet Union reported that the electron neutrino from nuclear beta decay probably has a mass between 15 and 50 eV, just within the interesting range for cosmology. Their experi- mental method was to study the beta decay of hydrogen-3. The decay electron and the neutrino (actually an antineutrino in this case) are emitted simultaneously and share the available decay energy between them, so that in different decays, the electron may receive anywhere from nearly zero energy to the maximum. The probability of the electron's receiving a particular energy within this range is a charac- teristic of the decay and is called the shape of the electron spectrum. The object of the Soviet experiment was to determine the shape (by measuring the energies of the decay electrons), because it depends on the neutrino mass in a known way. The experiment is far from easy, and certain systematic effects can distort the shape in a way that mimics the effect due to neutrino mass. Conclusions from this experiment are not universally accepted, and refined versions are now being carried out in the United States and other countries. Neutrino Oscillations A mass hanging from a spring is a favorite demonstration in physics lectures. The system has two modes of oscillation: the mass can vibrate up and down, or the whole system can swing like a pendulum. With proper design, the system can pass alternately from one mode to the other, with swinging changing gradually to springing, and back again. A quantum-mechanical system may exhibit a similar alternation of mode, as a kind of swelling and ebbing "beat" of the quantum- mechanical wave oscillations. In some cases, the beats can even manifest themselves as alternations in the identity of a particle. There are three apparently distinct neutrinos emitted during beta decays: a different neutrino is associated with electrons, muons (essentially, heavy electrons), and tauons (very heavy electrons). The Standard Model strictly maintains the separate identities of electron neutrinos, muon neutrinos, and tauon neutrinos, in accord with the currently accepted lepton-family-number conservation laws: the total number of electrons and electron neutrinos in the universe minus the total number of antielectrons (positrons) and electron antineutrinos is
82 NUCLEAR PHYSICS constant. Similar laws hold separately for the muon family and for the tauon family. However, Grand Unified Theories generally allow a neutrino of one kind to transform gradually into another kind. An electron neutrino from a nuclear decay, for example, could gradually become a muon neutrino or a tauon neutrino as it sped along its way. The rate of change as the quantum-mechanical beats ebb and swell depends on the mass differences between the various neutrinos; equal-mass or zero-mass neutrinos retain their identities. If neutrino oscillations were observed experimentally, it would imply that at least one kind of neutrino has nonzero mass. Also, an observed change in identity would be the first known violation of the lepton-family-number conservation laws. The beta decay of fission products in a nuclear reactor produces a copious flux of antineutrinos, and experimenters at the Savannah River, Grenoble (France), and Gosgen (Switzerland) reactors have set up detectors to see if the number of electron antineutrinos diminishes along their flight path. The most sensitive experiments to date have produced no evidence of the disappearance of electron antineutrinos. Similarly, accelerator experiments at Fermilab, Brookhaven, and CERN have not revealed any oscillation of muon neutrinos to other kinds, or any oscillation of electron neutrinos or muon neutrinos to tauon neutrinos. The sensitivity of the reactor experiments to small neutrino-mass differences increases as the flight path is lengthened; small mass differences make the oscillations very slow, so that neutrinos could travel great distances before undergoing observable transformations. The flight paths in the reactor experiments so far have extended up to 46 m, which sets an upper limit on the possible neutrino oscillations. Using neutrinos produced in the Sun would give a flight path of 1.5 x 108 km, increasing the sensitivity dramatically. As discussed in Chap- ter 5, the counting rate in present solar-neutrino detectors is roughly one fourth the theoretically expected value. One proposed solution to this vexing disparity is that oscillation decreases the number of solar-electron neutrinos arriving at the Earth. However, present neu- trino detectors are sensitive only to the small fraction of the Sun's neutrinos that result from a rather minor nuclear-energy-generating process, so the theoretical uncertainties in the expected number may be large.
FUNDAMENTAL FORCES IN THE NUCLEUS 83 Double Beta Decay The energy for the decay of a radioactive nucleus comes from the mass difference between the initial nucleus and the decay products. Accurate mass data are available from many different experimental methods, so the energy available for decay can be predicted quite well. Study of these mass data shows that certain nuclides for example, selenium-82 and tellurium-13~are stable against ordinary beta decay but are allowed by energy considerations to undergo double beta decay. In this process, the decaying nucleus simultaneously emits two electrons instead of one, thereby raising the proton number of the nucleus by 2; double beta decay would therefore change selenium to krypton, and tellurium to xenon. In ordinary beta decay, the decaying nucleus emits an electron and an antineutrino, a process that conserves lepton family number, as discussed earlier. The analogous process for double beta decay would be the emission of two electrons and two antineutrinos, again conserv- ing lepton family number. The more particles that are to be emitted in a given decay process, the smaller the probability that the decay will occur. Because four particles are emitted in this two-neutrino mode of double beta decay, the half-lives are expected to be extremely long, typically 102° to 1025 years. On the other hand, double beta decay might possibly proceed by emitting only the two electrons and no antineutrinos. This neutrinoless mode of double beta decay would be expected to have a shorter half-life than the two-neutrino mode, because only two particles need be emitted, instead of four. However, the neutrinoless mode is opposed by the conservation law for lepton number it involves the creation of two leptons (the two electrons) uncompensated by antileptons (the two antineutrinos). If neutrinoless double beta decay were observed, it would imply a violation of lepton-number conserva- tion. Certain conditions in addition to the violation of lepton-number conservation must also be satisfied to allow neutrinoless double beta decay to occur. The neutrinoless mode is described as a two-step process: the decaying nucleus first emits one electron and a virtual antineutrino, a reaction analogous to ordinary beta decay. In the second step, the daughter nucleus instantaneously absorbs this antineutrino and emits the second electron. The second step is analo- gous to a known process, except that nuclei absorb neutrinos, rather than antineutrinos, to emit electrons. For neutrinoless double beta decay to occur, therefore, the antineutrino and the neutrino must in
84 NUCLEAR PHYSICS ·~ ~ Electron - ~ tracks 1 MeV FIGURE 3.4 Computer simulation of the two-neutrino double beta decay of a sele- nium-82 nucleus in a particle detector called a time projection chamber. In this hypothetical event, the strong magnetic field in the detector causes the two emitted electrons to spiral away from the nucleus along separate paths. The computer-generated helical tracks of the electrons have been projected onto a plane in this cross-sectional view, producing a figure-8 pattern. (The energy scale gives the track diameter of a 1-MeV electron emitted in the plane of the figure.) Finding such a pattern in an actual experiment might signal the occurrence of this extremely rare event. (Courtesy of M. K. Moe, University of California, Irvine.) fact be one and the same particle. Furthermore, the neutrinoless mode requires the virtual neutrino to be partially right-handed. Although the necessary conditions described above stack the cards heavily against the neutrinoless mode, a single observed instance would shatter many currently held ideas. Meanwhile, considerable effort has been put into the search for two-neutrino double beta decay, despite the experimental difficulties imposed by the very long half-lives and the consequent low rates of decay. Such difficulties make the computer simulation of possible events a valuable design tool (see Figure 3.4~. The search for the presumably even rarer neutrinoless double beta decay is made extremely difficult by cosmic rays, which can create background ejects in the experimental apparatus that mask the true signal. For increased sensitivity, therefore, the experiments must be moved deep into the Earth, under a thick shield of rock. The Soviet Union has recently completed a large underground laboratory at Baksan for physicists who require very high sensitivity in such
FUNDAMENTAL FORCES IN THE NUCLEUS 85 experiments as the search for neutrinoless double beta decay, the search for decay of the proton, and the measurement of the solar- neutrino flux. A similar dedicated facility, the National Underground Science Facility, has been proposed in the United States. Several experiments are already under way in deep mines and mountain tunnels in the United States and Europe. Parity Violation in Nuclei According to the Standard Model, nucleons are made of two different combinations of three up and down quarks. In this picture, all the properties of nuclei spring ultimately from quark interactions, but only recently have the first attempts been made to relate nuclear properties to quark behavior. The strong quark interaction (and the resulting strong force) is believed to conserve parity strictly, but quarks also take part in the parity-nonconserving weak force, in which charged W+ or W- bosons or neutral Z° bosons are exchanged. The quark model predicts that the exchange of charged W+ or W- bosons will add to the nucleon-nucleon force a small weak-force component that does not conserve parity and that chiefly causes the isospin of a pair of interacting nucleons either to remain the same or to change by two units. The neutral Z° exchange gives rise to a weak-force compo- nent that also does not conserve parity and that changes the isospin of a pair of nucleons by zero, one, or two units. A great many states of different parities and isospins are available among the known nuclei, and careful selection of the test nuclei allows the two different weak-force components (from W and Z exchange) to be distinguished experimentally. The strong force in nuclei conserves parity, so that each nuclear state can be assigned a definite parity value (even or odd). However, the parity-nonconserving weak force mixes the parities of the states, so that they are actually neither purely even nor purely odd. The nuclei fluorine-19 and neon-21 both exhibit the favorable circumstance of having two closely spaced energy levels of the same angular momen- tum but opposite parity; this close proximity increases the usually tiny effects of the weak force in mixing the parities of these states. Furthermore, the isospins of the states in question are such that both the charged and neutral boson-exchange components are able to influence the mixing in fluorine-l9 and in neon-21. Experimentally, the parity-nonconserving mixing is observed in fluorine-19, where the charged and neutral components add. However, it is not seen in neon-21, where the charged and neutral components
86 NUCLEAR PHYSICS tend to cancel. Higher sensitivity should soon allow the pure neutral- component contribution in a nearby nucleus, Huorine-18, to be mea- sured. Comparing the experimental results with theory allows two important conclusions to be drawn. First, the Z° boson exchange between nucleons is definitely present (the Z° boson has recently been detected directly as a free particle). Second, the dynamic masses of the up and down quarks in a nucleon are very close to the values originally predicted.
