Alpha decay, fission and thermonuclear fusion all illustrate in different ways the importance of the phenomenon of quantum-mechanical tunnelling. In α-decay, an α-particle is contained by a barrier, called the Coulomb barrier, formed by the strong attractive potential and the electrostatic repulsive 1/r potential between the a-particle and the rest of the nucleus. The strong dependence of the probability of tunnelling through this barrier on the α-particle's energy is shown to account for the observed systematics of α-decay. In fission there is also a barrier arising from the nuclear and Coulomb forces and the observed spontaneous fission lifetimes are also explained by tunnelling.

The shape of the fission barrier is shown to depend significantly on shell corrections to the liquid drop model. These corrections explain the occurrence of fission isomers. The possibility of a chain reaction following neutron-induced fission and its application in nuclear reactors is then described. Finally the process of thermonuclear fusion of hydrogen within the sun and the possibility of making fusion reactors are discussed. It is shown how the luminosity of the sun can be understood as arising from the weak process: p + p → d + e+ + v, which is highly inhibited within the sun by the Coulomb barrier between the protons.

Alpha decay

From the semi-empirical mass formula most nuclei with A > 150 are unstable to decay by α-emission. This is not readily observed until nuclei with A > 200 because of the Coulomb barrier that the α-particles must penetrate by quantum-mechanical tunnelling.

The aim of this textbook is to give a student a thorough understanding of the principal features of nuclei, of nuclear decays and of nuclear reactions. The properties of nuclei at low excitation and low angular momentum have been thoroughly studied and are now generally understood, and current research is on nuclei at high interaction energies, high angular momentum and far from the valley of stability. Several models have been developed to explain the observed wide variety of phenomena and I have attempted to describe and justify them, and also to explain the connections between them in some detail. This involves trying to give a microscopic description of nuclei, which is an intriguing many-body problem and forms an important part of this book. Besides this interest, parts of nuclear physics are of importance in the study of elementary particle physics and several nuclear phenomena have particular significance in other fields: for example, fission in nuclear power, fusion in astrophysics and radioactivity in biological tracer techniques. Consequently, nuclear physics is an important part of any physics undergraduate course.

In the first part of the book, several models are described and used to explain nuclear properties with many illustrative examples given. Sections follow on α-, β- and γ-decay, fission, thermonuclear fusion, reactions, nuclear forces and nuclear collective motion. In all of these, many examples are discussed and the student should gain a thorough grounding in our current knowledge of the nucleus. A lot of interesting experimental techniques have been developed to study nuclei and examples of these are also given.

The discussion in chapter 2 of the change in energy, both kinetic and potential, when a spherical nucleus is deformed, showed that many nuclei would be expected to have quite significant quadrupole moments, in agreement with experiment. Moreover, a deformed shell model description was shown by Nilsson to provide a good quantitative description of the shape and spin of many nuclear ground states. However, what was not clear was what aspect of the Nilsson model accounted for nuclei being mainly prolate (cigar-shaped), as can be seen clearly in figure 2.15, and Lemmer and Weisskopf's argument that it is because of the shape of the nuclear potential is first presented.

After discussing the ground-state deformation of nuclei, a microscopic description of collective motion in terms of an independent-particle model is developed in the rest of this chapter. The ground state of the nucleus is generally described by a deformed intrinsic wavefunction. If the deformation is significant, then a variational approach to the motion of deformed nuclei, which avoids the problem of redundant variables inherent in the collective model, is shown to give rise to a rotational spectrum of excited states. The cranking-model expression for the moment of inertia is then derived and the influence of the pairing residual interaction is discussed.

In the shell model, if the residual interaction is diagonalised, then collective features are reproduced. In an approximate treatment of the residual interaction, the schematic model, collective vibrational states are found to correspond in the shell model to a coherent superposition of one-particle one-hole states.

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.