Soon after the discovery of the neutron by Chadwick in 1932, Heisenberg proposed that nuclei consisted of neutrons and protons bound together by a strong nuclear force. This model avoided the difficulties of the proton plus electron model of the nucleus and was gradually accepted. By the early thirties a considerable number of nuclear masses had been measured by Aston and others using mass spectrometers and it was found that the binding energy per nucleon was approximately constant for all nuclei. The volumes of nuclei had also been determined from scattering experiments to be roughly proportional to the number of nucleons in the nucleus, which implied an approximately constant nuclear density and that the nuclear radius was proportional to A⅓. Numerically the radius of a nucleus is given by R = r0A⅓ fm where r0 ≈ 1.2.

In this chapter a number of models of nuclei are described which account for different aspects of nuclear behaviour. It is shown that for the bulk properties of nuclei a liquid drop model of a nucleus is very useful. However, to understand the spins of nuclei and the occurrence of magic numbers a description of the motion of individual nucleons is required and this is provided by the simple shell model. The existence of large nuclear electric quadrupole moments indicates that nuclei are generally deformed in shape and the generalisation of the simple shell model to account for this is described.

Introduction

The study of nuclear reactions provides considerable information on the structure of nuclei as well as on the nature of their interaction. In this chapter there is first a brief discussion of some experimental details, before the general features of nuclear reactions are described. Then methods for describing reactions are developed. First some general predictions are given followed by a discussion of the simplest reactions, elastic and inelastic scattering, for both light and heavy ions. After this the theory of compound nucleus reactions is presented and the occurrence of slow neutron resonances described. Isobaric analogue resonance and isospin forbidden reactions are then discussed.

At higher incident energies direct reactions become important and the use of first-order perturbation theory, the Born approximation, for the description of pick-up and stripping reactions by both light and heavy ions is described. For heavy-ion direct reactions new features are seen reflecting the more classical behaviour of the ions: selectivity arising through kinematic matching and characteristic bell-shaped angular distributions. At energies above the Coulomb barrier, as well as compound nucleus (fusion) reactions, deep-inelastic reactions are also observed, with substantial cross-sections for very heavy ions. In these reactions there is a considerable transfer of the incident energy to internal excitation of the product nuclei. For even higher energies, a new phase of nuclear matter, a quark-gluon plasma, is predicted to be found in reactions with relativistic heavy ions, and it is in this area that nuclear and particle physics overlap.

Nuclear physics is an intriguing subject because of the great variety of phenomena that occur. Nuclei exhibit many different types of behaviour, from the classical, where the nucleus behaves like a liquid drop, to the quantum-mechanical, where nuclei show a shell structure similar to that found in atoms. It is a considerable intellectual challenge to try and understand this behaviour and many models have been devised. These models are described in chapter 2 and used to understand the principal properties of nuclei and their excited states.

The study of beta and gamma decay in nuclei has given considerable information on the structure of nuclei; and from experiments on beta decay on the nature of the weak interaction, for example parity violation and the helicity of the neutrino. These topics are discussed in chapters 3 and 4.

The importance of quantum-mechanical tunnelling in nuclear physics is illustrated by a discussion in chaper 5 of α-decay, fission and thermonuclear fusion. The last two have considerable significance in other fields, for example nuclear power and nuclear astrophysics.

The interactions between nuclei offer a rich variety of phenomena and these are described in chapter 6. The basic types of nuclear reactions: compound nucleus, direct and deep-inelastic, and typical features such as the occurrence of resonances and characteristic angular distributions, are first described before reaction theories are developed.

The forces between nucleons are discussed in chapter 7. The information from neutron-proton and proton-proton scattering is analysed and the characteristics of the nuclear force explained.

The description of scattering processes using quantum mechanics, as discussed in Chapter 2, has two obvious deficiencies. Firstly, it is not formulated in a relativistically invariant manner. The particle spin, which was incorporated by having a multicomponent wave function, must also be treated in a Lorentz invariant way. Secondly, it deals with scattering processes where the incident particle is scattered by a force represented by a fixed potential (or effective potential). However, in high energy scattering processes particles can be created or annihilated. Fermions must be created or destroyed as particle–antiparticle pairs, whereas any number of bosons may be involved. Thus the formalism needed to discuss the interaction of particles must include these points. Indeed, great care must be taken as to the actual definition of a particle and its properties. For example, a ‘free’ electron can dissociate (see Fig. 3.1) into an electron and a photon, or more complex states involving loops of e+ e- (or any other charged particles). A ‘dressed’ particle, with which we deal experimentally, has different properties to the ‘bare’ particle, the wave equations of which are discussed in this chapter.

The fundamental particles in the standard electroweak model are the spin ½ leptons and quarks, the spin 1 gauge bosons W±, γ and Z0 (which propagate the forces), and the spin 0 Higgs bosons (which are necessary to give the W±, Z0 and the fermions their masses).

The development of our present understanding of the weak and electromagnetic interactions, and of their unification, has proven to be a fascinating dialogue between profound theoretical insights and remarkable experimental discoveries. The electromagnetic and weak interactions appear to be describable by local gauge theories. Phenomena involving charged leptons and photons can be described, to impressive precision, by the relativistic field theory of Quantum Electrodynamics. The incorporation of weak phenomena led, eventually, to the Glashow–Salam–Weinberg model, the so-called standard model. This theory describes the electroweak properties of leptons and quarks, and successfully predicted the existence of the massive W± and Z0 vector bosons. At present, the standard model is compatible with all well established experimental data, amassed by some tens of thousands of man-years of effort. This is an impressive state of affairs.

This book has its origins in a course of lectures given to first-year postgraduate students (mainly experimentalists) in high energy physics in Oxford. An elementary knowledge of high energy particle physics, together with the basic ideas of quantum mechanics and relativity, is assumed. However, these topics, in as far as they are required for later use, are reviewed in Chapters 1 and 2. An introduction to group theories and symmetries, concepts of great importance in particle physics, is also given in Chapter 2. In Chapter 3, the single particle wave equations for spin 0, spin ½ and spin 1 particles are developed, and an introduction to some of the concepts of field theory is given.

In this chapter the production and properties of the massive gauge bosons W± and Z0 are discussed. The properties of the other gauge boson, the massless photon, were described in Chapters 4, 5 and 7. The properties of time-like virtual W± particles were discussed in Chapters 6 and 8, in the context of the decays of leptons and hadrons. Both the photon and the W± can be used as probes of the elementary constituents of hadrons. Here, for space-like four momenta such that Q2 ≳ 5 GeV2, the gauge bosons behave essentially as point-like probes. For much lower values of Q2, the W±, Z0 and the photon (in particular, the real photon) have hadronic components, arising from their fluctuations to qq pairs. Because of the difficulty in measuring the variables xBJ and Q2 in deep inelastic scattering in the case of neutral current interactions, these reactions have mainly been used to study the couplings of the Z0 to quarks (Section 8.8), rather than to study QCD effects. Interference phenomena between γ and Z0 exchange have been observed for space-like momenta in charged lepton deep inelastic scattering (Section 8.9.1), and for time-like momenta in e+ e- annihilation (Section 6.3 and 8.9.2).

Experimentally, the most important missing ingredient of the standard model is the Higgs scalar, which is needed to give masses to the particles. The complete list of quarks and leptons must also be established.