Types of interactions

In chapter 2 we have seen that the nuclear interaction is very much stronger than the electromagnetic interaction; their relative strengths are characterised by the difference in the ‘coupling constants’ which are discussed in more detail below. We may recognise at this stage two other forms of interaction, gravitational forces and the so-called ‘weak’ interaction. One of the most notable milestones of recent years has been the unification of the weak and electromagnetic interactions as different aspects of the same underlying force, in the theory of Glashow, Weinberg and Salam, and the discovery of the W and Z particles, the additional quanta of the unified interaction, with the properties predicted. This topic is treated in more detail in chapter 11.

We may summarise as follows:

Strong interactions are responsible for the interactions between nucleons, nucleons and mesons and a number of other particles. The mesons act as the quanta of the strong interaction on the nuclear scale. These interactions reflect the interaction between quarks due to the exchange of gluons on the sub-nucleon level.

Electromagnetic interactions are responsible for the force between electrically-charged particles and are mediated by the exchange of photons.

Weak interactions are responsible for many particle decays such as radioactive decay (the basic process n → p + e- + vg), pion and muon decay and a number of other decay processes.

Gravitational interactions exist between all particles having mass and are believed to be mediated by the so far undetected gravitons.

Introduction

There have always been close links between physics and astronomy and physics and cosmology. This is to be expected since astronomy and cosmology are fields of science which apply physics in an attempt to understand observations of the cosmos and to comprehend the structure, origin and evolution of the universe. Equally our understanding of physical laws and in particular their apparent universality in space and time, has in a number of instances depended crucially on astronomical data.

In the first half of the twentieth century a number of common areas of interest – relativity theory, nuclear reactions and stellar evolution, and cosmic rays, among others – provided fruitful points of contact between particle and nuclear physics on the one hand and cosmology on the other. After a period of less interaction common interests have increased dramatically over the last 10–15 years in a way which has been highly stimulating for both subjects.

Most fundamentally the development and general acceptance of the Big Bang model implies energy densities during the first instants after the Big Bang which can now be even distantly approached only in high energy particle collisions. On the other hand it is clear that no experiments we can ever do will attain the energies at which we might expect unification of all four forces including gravity (energies ∼ Planck mass ∼ 1019 GeV/c2) or even Grand Unification energies ∼ 1015 GeV, so that the only laboratory for direct study of these phenomena existed in the first instants after the Big Bang.

Introduction

The discovery of such a wealth of apparently ‘elementary’ particles stimulated new activity in the search for a pattern amongst them, as a first step towards the understanding of their nature. The discovery of such a pattern is analogous to, for instance, the discovery of the Rydberg formula in atomic spectroscopy. The Bohr atom finally provided an explanation of the formula, and we shall see that the quark model provides an explanation of the symmetry pattern of the elementary particles.

We have already become familiar with the limited symmetry of isotopic spin multiplets. In that case we grouped together particles which were the same except for properties associated with the electric charge. The degeneracy of the multiplet is removed by the symmetry-breaking Coulomb interaction. Alternatively, we can regard the members of the multiplet as states linked by rotations in isotopic spin space and we can define a group of rotation operators which enable us to step from one state to another.

The Coulomb interaction is not strong compared with the so called ‘strong’ interactions, and the symmetry breaking to which it gives rise is small. For instance, the masses of particles in the same isotopic spin multiplet differ only by at most a few per cent. In order to extend the symmetry, to group larger numbers of particles together, we must recognise the existence of much stronger symmetry breaking forces since the mass differences between, say, I-spin multiplets, are substantial, even compared with the particle masses themselves.

Introduction

An important part of the study of particle physics is an understanding of experimental tools – the accelerators, beams and detectors by means of which particles are accelerated, their trajectories controlled and their properties measured. There exist a limited number of types of accelerators and detectors in common use or which have in the past proved crucial to the progress of the subject. No more technical detail is included here than is essential to an understanding of the uses of these techniques in the study of particle physics. In the chapters which follow we shall assume that these techniques are familiar to the student, so that it will generally not be necessary to describe in detail the technique used in particular experiments.

Particle accelerators and beams

Introduction

Particle accelerators and their associated external beam lines are key elements in most particle physics experiments.

Charged particles are accelerated by passing across a region of potential difference which in practice is normally a cavity fed with radiofrequency power and phased such that the particle is accelerated as it passes through. Since practicable fields and dimensions are such that a single passage through the cavity can produce only a rather small acceleration, the particle must either pass through many such cavities or pass many times through the same group of cavities by guidance around a cyclic path.

Introduction

Dynamic symmetries and supersymmetries provide a convenient framework within which spectra of nuclei, either individually (symmetries) or in a set (supersymmetries) can be analyzed. However, they usually provide only a first approximation to the observed properties and furthermore there are nuclei for which they cannot be used. In these cases, one needs to do numerical studies. The starting point for these studies is the diagonalization of the Hamiltonian for the combined system of bosons and fermions written in one of its forms. Computer programs are available for the numerical solution of this problem (Scholten, 1979). The structure of the Hamiltonian is as in (1.16). Numerical studies are done by first analyzing the spectra of even-even nuclei as in Volume 1. This analysis determines the parameters appearing in HB. In a second step, the spectra of odd-even nuclei are studied. For odd-even nuclei with one unpaired particle, HF contains only the single-particle energies, ηJ. If states originating from only one single-particle level are studied, there is only one single-particle energy, η, which can be chosen as zero on the energy scale. If states originating from m single-particle orbits are included, the number of input parameters for the calculation is m – 1, since the lowest level can be chosen as zero on the energy scale. The crucial property that determines the structure of spectra of odd-even nuclei is the coupling between the collective degrees of freedom (bosons) and the single-particle degrees of freedom (fermions).

Introduction

The interacting boson-fermion model-1 describes properties of odd-even nuclei by coupling collective and single-particle degrees of freedom much in the same way this is done in the collective model (Bohr and Mottelson, 1975). The collective degrees of freedom are described either by shape variables αμ (μ = 0, ±1, ±2) or by boson operators s, dμ (μ = 0, ±1, ±2), with no direct link to the underlying microscopic structure. A microscopic description of nuclei is provided by the spherical shell model. Collective features in this model can be obtained by introducing the concept of correlated pairs with angular momentum and parity Jp = 0+ and Jp = 2+. A treatment of these pairs as bosons leads to the interacting boson model. However, since there are protons and neutrons, one has the possibility of forming proton and neutron pairs. In heavy nuclei, the neutron excess prevents the formation of correlated proton-neutron pairs and one thus is led to consider only proton-proton and neutron-neutron pairs. The corresponding model is the interacting boson model-2 (Arima et al., 1977; Otsuka et al., 1978). The introduction of fermions in this models leads to the interacting boson-fermion model-2. In addition to a more direct connection with the spherical shell model, the interacting boson-fermion model-2 has features that cannot be obtained in the interacting boson-fermion model-1.

The structure of model-2 is very similar to that of model-1.

Introduction

In addition to low-lying collective modes extensively discussed in Volume 1 and in this book in terms of bosonic degrees of freedom, nuclei also display high-lying collective modes. The microscopic description of these modes is different from that of the low-lying modes, as shown schematically in Fig. 12.1. The latter are built from correlated pairs of nucleons in the valence shell, while the former are built from correlated particle-hole pairs, with one or more particles outside the valence shell. A description of high-lying modes in terms of bosons is also possible, although not particularly useful in itself since only one vibrational state of each mode is observed. It becomes useful only when coupling low-lying and high-lying modes. This coupling leads to the splitting and mixing of the high-lying modes which is often observed.

High-lying collective modes have been introduced in the interacting boson model by Morrison and Weise (1982) and, independently, by Scholtz and Hahne (1983). They proposed a description of the giant dipole resonance via a p boson coupled to a system of interacting s and d bosons and solved the resulting Hamiltonian numerically. Subsequently, Rowe and Iachello (1983) showed that, for deformed nuclei, a class of Hamiltonians exists that correspond to dynamic symmetries and that for such Hamiltonians analytic results can be obtained for energies and transition matrix elements. Since then the model has been applied to several (series of) isotopes (Maino et al., 1984; 1985; Scholtz, 1985; Maino et al., 1986a; Scholtz and Hahne, 1987; Nathan, 1988) and has been extended to include monopole and quadrupole giant reso-nances (Maino et al., 1986b) and dipole resonances in light (Maino et al., 1988) and odd-even nuclei (Maino, 1989).