Subatomic Physics

The following sections are included:

• Dedication
• Acknowledgments
• Preface to the First Edition
• Preface to the Third Edition
• General Bibliography
• Contents

The exploration of subatomic physics started in 1896 with Becquerel's discovery of radioactivity; since then it has been a constant source of surprises, unexpected phenomena, and fresh insights into the laws of nature.

In this first chapter we shall describe the orders of magnitude encountered in subatomic physics, define our units, and introduce the language needed for studying subatomic phenomena.

One of the most frustrating experiences in life is to be stranded without proper tools. The situation can be as simple as being in the wilderness with a broken shoe strap but no wire or knife. It can be as simple as having a leaking radiator hose in Death Valley and no tape to fix it. In these instances we at least know what we miss and what we need. Confronted with the mysteries of subatomic physics, we also need tools and we often do not know what is required. However, during the past century, we have learned a great deal, and many beautiful tools have been invented and constructed. We have accelerators to produce particles, detectors to see them and to study their interactions, instruments to quantify what we observe, and computers to evaluate the data. In the following three chapters we sketch some important tools.

• Why Accelerators?
• Cross Sections and Luminosity
• Electrostatic Generators (Van de Graaff)
• Linear Accelerators (Linacs)
• Beam Optics
• Synchrotrons
• Laboratory and Center-of-Momentum Frames
• Colliding Beams
• Superconducting Linacs
• Beam Storage and Cooling
• References

In everyday life we constantly use our understanding of the passage of matter through matter. We do not try to walk through a closed steel door, but we brush through if the passage is only barred by a curtain. We stroll through a meadow full of tall grass but carefully avoid a field of cacti. Difficulties arise if we do not realize the appropriate laws; for example, driving on the right-hand side of a road in England or Japan can lead to disaster. Similarly, a knowledge of the passage of radiation through matter is a crucial part in the design and the evaluation of experiments. The present understanding has not come without surprises and accidents. The early X-ray pioneers burned their hands and their bodies; many of the early cyclotron physicists had cataracts. It took many years before the exceedingly small interaction of the neutrino with matter was experimentally observed because it can pass through a light year of matter with only small attenuation. Then there was the old cosmotron beam at Brookhaven which was accidentally found a few km away from the accelerator, merrily traveling down Long Island…

What would a physicist do if he were asked to study ghosts and telepathy? We can guess. He would probably (1) perform a literature search and (2) try to design detectors to observe ghosts and to receive telepathy signals. The first step is of doubtful value because it could easily lead him away from the truth. The second step, however, would be essential. Without a detector that allows the physicist to quantify his observations, his announcement of the discovery of ghosts would be rejected by Physical Review Letters. In experimental subatomic physics, detectors are just as important and the history of progress is to a large extent the history of increasingly more sophisticated detectors. Even without accelerators and using only neutrinos or cosmic-ray particles, a great deal can be learned by making the detectors bigger and better. In the following sections, we shall discuss different types of detectors. Many beautiful and elegant tools are not treated here; however, once the ideas behind typical instruments are understood, it is easy to pick up more details concerning others. We also add a brief section about electronics because it is an integral part of any detection system.

The situation is familiar. At a meeting we are introduced to some stranger. A few minutes later we realize with embarrassment that we have already forgotten his name. Only after being reintroduced a few times do we begin to fit the stranger into our catalog of people. The same phenomenon takes place when we encounter new concepts and new facts. At first they slip away rapidly, and only after grappling with them a number of times do we become familiar with them. The situation is particularly true with particles and nuclei. There are so many that at first they seem not to have sharp identities. So what is the difference between a muon and a pion…

A conventional zoo is a collection of various animals, some familiar and some strange. The subatomic zoo also contains a great variety of inhabitants, and a number of questions concerning the catching, care, and feeding of these come to mind: (1) How can the particles be produced? (2) How can they be characterized and identified? (3) Can they be grouped in families? In the present chapter, we concentrate on the second question. In the first two sections, the properties that are essential for the characterization of the particles are introduced. Some members of the zoo already appear in these two sections as examples. In the later sections, the various families are described in more detail. Since there are so many animals in the subatomic zoo, some initial confusion in the mind of the reader is unavoidable. We hope, however, that the confusion will give way to order as the same particles appear again and again.

In Chapter 5 the members of the subatomic zoo have been classified according to interaction, symmetry, and mass. In the present chapter, we shall investigate some particles in more detail; in particular, we shall study the charged leptons, some hadrons and the ground-state structure of some nuclides. What do we mean by ground-state structure? For atoms, the answer is familiar: Structure denotes the spatial distribution of the electrons, and it is described by the ground-state wave function. For the hydrogen atom, neglecting spin, the probability density ρ(x) at point x is given by …

If the laws of the subatomic world were fully known, there would no longer be a need for investigating symmetries and conservation laws. The state of any part of the world could be calculated from a master equation that would contain all symmetries and conservation laws. In classical electrodynamics, for example, the Maxwell equations already contain the symmetries and the conservation laws. In subatomic physics, however, the fundamental equations are not yet established, as we shall see in Part IV. The exploration of the various symmetries and conservation laws, and of their consequences, therefore provides essential clues for the construction of the missing equations. One particular consequence of a symmetry is of the utmost importance: Whenever a law is invariant under a certain symmetry operation there usually exists a corresponding conservation principle. Invariance under translation in time, for instance, leads to conservation of energy; invariance under spatial rotation leads to conservation of angular momentum. This profound connection is used both ways: If a symmetry is found or suspected, the corresponding conserved quantity is searched for until it is discovered. If a conserved quantity turns up, the search is on for the corresponding symmetry principle. One word of warning is in place here: Intuitive feelings can be misleading. Often a certain symmetry principle looks attractive but turns out to be partially or completely wrong. Experiment is the only judge as to whether a symmetry principle holds…

In this chapter we shall first discuss the connection between conserved quantities and symmetries in a general way. Such a discussion is somewhat formal, but it paves the way for an understanding of the connection between symmetries and invariances. We shall then treat some additive conservation laws, beginning with the electric charge. The electric charge is the prototype of a quantity that satisfies an additive conservation law: The charge of an assembly of particles is the algebraic sum of the charges of the individual particles. Moreover it is quantized and has only been found in multiples of the elementary quantum e. Other additive conserved and quantized observables exist, and in the present chapter we shall discuss the ones that are established beyond doubt.

In this chapter we shall show that invariance under rotation in space leads to conservation of angular momentum. We shall then introduce isospin, a quantity that has many properties similar to ordinary spin, and discuss the “breaking” of isospin invariance.

In the previous chapter we have discussed two continuous symmetry operations: rotations in ordinary space and in isospin space. These rotations can be made as small as desired and consequently can be studied by employing infinitesimal transformations. Invariance under these rotations leads to conservation of spin and isospin, respectively. In this chapter we shall discuss examples of discontinuous transformations, which can lead to operators of the type already given in Eq. (7.11), namely…

In the previous nine chapters, we have used the concept of interaction without discussing it in detail. In the present part, we shall rectify this omission, and we shall outline the important aspects of the interactions that rule subatomic physics…

In this chapter we will examine the electroweak interaction of the standard model, and, in particular, the electromagnetic part of it. We relegate the weak part to the next chapter. The electromagnetic interaction is important in subatomic physics for two reasons. First, it enters whenever a charged particle is used as a probe. Second, it is the only interaction whose form can be studied in classical physics, and it provides a model after which other interactions can be patterned…

This chapter explores the weak interaction part of the electro-weak theory. The history of the weak interaction is a series of mystery stories. In each story, a puzzle appears, at first only in a vague form and then more and more clearly. Clues to the solution are present but are overlooked or discarded, usually for the wrong reason. Finally, the hero comes up with the right explanation and everything is clear until the next corpse is unearthed. In the treatment of the electromagnetic interaction, the well-understood classical theory provided an example which, properly translated and reformulated, guided the development of quantum electrodynamics. No such classical analog is present in the weak interaction, and the correct features had to be taken from experiment and from analogies to the electromagnetic interaction. We shall describe some of the puzzles and their solutions. In doing so we are hampered by the self-imposed constraint of not using the Dirac theory. We shall therefore not be able to write the interaction properly but shall use other means to explain the crucial concepts…

The following sections are included:

• Introduction
• Potentials in Quantum Mechanics—The Aharonov–Bohm Effect
• Gauge Invariance for Non-Abelian Fields
• The Higgs Mechanism; Spontaneous Symmetry Breaking
• General References

The following sections are included:

• Introduction
• The Gauge Bosons and Weak Isospin
• The Electroweak Interaction
• Tests of the Standard Model
• References

All good things must come to an end. In chapters 10 and 11 we have seen that the electromagnetic and the weak interactions of leptons at low energies were characterized each by a single coupling constant. Furthermore, nature uses only one type of current for the electromagnetic interaction, a vector; and two for the weak interaction, a vector and an axial vector. The situation with the strong interaction at low energies is much more complicated. In the nucleon-nucleon interaction, for instance, almost every term allowed by general symmetry principles appears to be required to fit the experimental data. In addition, at energies ≲1 GeV the phenomenological strong interactions do not provide any evidence that they are goverened by one universal coupling constant. Consider, for instance, Figs. IV.1 and IV.3. The strength of the interaction of the pion with the baryon is described by the constant f_πNN^* in the first case, and by f_πNN in the second one. The two constants are not identical. The interaction of the pion with pions is characterized by yet another constant. Since many hadrons exist, a large number of coupling constants occur. The corresponding interactions are all called strong because they all are about two orders of magnitude stronger than the electromagnetic one. However, they are not exactly alike. While some connections among the coupling constants can be derived by using symmetry arguments, these relations are only approximate, and many constants appear at present to be unrelated. The situation resembles a jigsaw puzzle in which it is not known if all pieces are present and in which the shape of some pieces cannot be seen clearly…

Atomic physics is very well understood. A simple model, the Rutherford model, describes the essential structure: A heavy nucleus gives rise to a central field, and the electrons move primarily in this central field. The force is well known. The equation describing the dynamics is the Schrödinger equation or, if relativity is taken into account, the Dirac equation. Historically, this satisfactory picture is not the end result of one single line of research, but it is the confluence of many different streams of discoveries, streams that at one time appeared to have nothing in common. The Mendeleev table of elements, the Balmer series, the Coulomb law, electrolysis, black-body radiation, cathode rays, the scattering of alpha particles, and Bohr's model all were essential steps and milestones. What is the situation with regard to particles and nuclei? We have described the elementary particle zoo and the nature of the forces. Are the known facts sufficient to build a coherent picture of the subatomic world? The theoretical description of nuclei is in good shape: There exist successful models, and most aspects of the structure and the interaction of nucleons and nuclei can be described reasonably well. Although many nuclear properties can be obtained from first principles (e.g., through a time-dependent Hartree–Fock treatment), the complexity of the many-body problem usually leads to the replacement of such a description by specific models. They involve the known properties of the nuclear forces but focus on simple modes of motion. Much remains to be done until nuclear theory is as complete and as free from assumptions as atomic physics. The particle situation is in about the same shape. Many properties of the particle zoo can be explained rather well in terms of quarks and gluons. The so-called standard model, which includes QCD for the strong interactions and the electroweak theory of Chapter 13, can be used to fit much data…

The following sections are included:

• Introduction
• Quarks as Building Blocks of Hadrons
• Hunting the Quark
• Mesons as Bound Quark States
• Baryons as Bound Quark States
• The Hadron Masses
• QCD and Quark Models of the Hadrons
• Heavy Mesons: Charmonium, Upsilon, …
• Outlook and Problems
• References
• Problems

Computations of nuclear properties ab initio are very difficult and have only been carried out for light nuclei. The force is very complicated, and nuclei are many-body problems. It is therefore necessary with most nuclear problems to simplify the approach and use specific nuclear models combined with simplified nuclear forces…

The liquid drop and the Fermi gas models represent the nucleus in very crude terms. While they account for gross nuclear features, they cannot explain specific properties of excited nuclear states. In Section 5.11 we have given some aspects of the nuclear energy spectrum, and we have also pointed out that progress in atomic physics was tied to an unraveling of the atomic spectra. In atomic physics, solid-state physics, and quantum electrodynamics, unraveling began with the independentparticle model. It is therefore not surprising that this approach was tried early in nuclear theory also. Bartlett, and also Elsasser, pointed out that nuclei display particularly stable configurations if Z or N (or both) is one of the magic numbers…

Although the shell model describes the magic numbers and the properties of many levels very well, it has a number of failures. The most outstanding one is the fact that many quadrupole moments are much larger than those predicted by the shell model. It was shown by Rainwater that such large quadrupole moments can be explained within the concept of a shell model if the closed-shell core is assumed to be deformed. Indeed, if the core is ellipsoidal it acquires a quadrupole moment proportional to the deformation. A deformation of the core is evidence for manybody effects, and collective modes of excitation are possible. The appearance of such modes is not surprising. Lord Rayleigh investigated the stability and oscillations of electrically charged liquid drops in 1877, and Niels Bohr and F. Kalckar showed in 1936 that a system of particles held together by their mutual attraction can perform collective oscillations. A classical example of such collective effects is provided by plasma oscillations. The existence of large nuclear quadrupole moments provides evidence for the possibility of collective effects in nuclei. From about 1950, Aage Bohr and BenMottelson started a systematic study of collective motions in nuclei; over the years, they and their collaborators have improved the treatment so that today the model combines the desirable features of shell and collective models and is called the unified nuclear model…

For millenia, the stars, Sun, and Moon have fascinated humans; their properties have been subject to much speculation. Up to a short time ago, however, observation of the heavens was restricted to the very small optical window between about 400 and 800 nm, and mechanics was the branch of physics most intimately involved in astronomy. In the last century, the situation has changed dramatically and physics and astronomy have become much more closely intertwined. In this chapter, we shall sketch some of the areas in which subatomic physics and astrophysics are linked…

The following section is included:

• Index