In the preceding chapters the material necessary for studying photoionization processes in atoms using synchrotron radiation and electron spectrometry was presented. The discussion will now be completed with some examples of current research activities. These include:

1. photon-induced electron emission around the 4d ionization threshold in xenon from which a complete mapping of these spectra can be obtained and many features characteristic of inner- and outer-shell photoprocesses are well visualized;

2. a complete experiment for 2p photoionization in magnesium which also provides a detailed illustration of the role that many-electron effects have on main photolines;

3. an investigation of discrete satellite lines in the outer-shell photoelectron spectrum of argon which demonstrates for a simple case the origin of satellite processes in electron correlations, and also the importance that instrumental resolution has on the determination of satellite structures;

4. a complete experiment for 5p3/2 photoionization in xenon which includes a measurement of the photoelectron's spin polarization;

5. a quantitative study of postcollision interaction (PCI) between 4d5/2 photoelectrons and N5–O2, 3O2, 31S0 Auger electrons in xenon which also serves as an example of energy calibration in accurate experiments;

6. the determination of coincidences between 4d5/2 photoelectrons and N5–O2, 3O2, 31S0 Auger electrons in xenon which allows a spatial view of the angular correlation pattern for this two-electron emission process;

7. a near-threshold study of state-dependent double photoionization in the 3p shell of argon in which the cross section approaches zero and two electrons of extremely low kinetic energy have to be measured in coincidence.

Description of the K–LL Auger spectrum

Inner-shell ionization is accompanied by subsequent radiative and non-radiative decay. In the context of electron spectrometry, the non-radiative or Auger decay is of special interest, because the emitted Auger electron can be detected. After some remarks on the general description and classification of Auger transitions following 1s ionization in neon, the calculation of K–LL Auger transition rates and the formulation of intermediate coupling in the final ionic state of the K–LL Auger transition will be addressed. This information then provides the basis for a detailed analysis of the experimental K–LL Auger spectrum of neon which is organized similarly to the previous discussion of photoelectrons: namely, with respect to line positions, linewidths, line intensities, and angular distributions.

General aspects

In addition to the photoelectron lines, other discrete structures appear in the electron spectrum of neon if the photon energy is higher than the threshold for 1s ionization. These lines are due to radiationless transitions called Auger transitions [Aug25]; the 1s-hole created by photoionization is filled by a subsequent two-electron transition induced by the Coulomb interaction between the electrons. This interaction causes one outer-shell electron to jump down, filling the 1s-hole, simultaneously ejecting another outer-shell electron, the Auger electron, into the continuum. This process has been sketched schematically in Figs. 1.3 and 2.5.

Theoretical background and general aims

In the non-relativistic limit, the electronic structure of an atom is determined by the Coulomb interaction between the electrons and the nucleus and the Coulomb interaction between the electrons themselves. In the relativistic case, other interactions have to be added, of which the spin–orbit interaction represents the largest contribution. The complete and exact description of these forces in the atom follows from quantum electrodynamics which is nowadays a well-established theory. Therefore, structure studies in atoms as compared to other systems (nuclei or elementary particles) have the advantage of involving forces which are known exactly. However, even for an ideal case it is extremely difficult accurately to calculate the atomic parameters for a many-electron system. As an example the structure of the helium atom in its ground state wavefunction will be discussed, first within the model of independent particles and then for two types of wavefunction which take into account electron correlations, i.e., the correlated motions of the electrons. The fundamental features demonstrated for this relatively simple case can then also be applied to the more complicated dynamical process of photoionization. Here the observed effects of electron–electron interactions and their theoretical treatment brought a renaissance of atomic physics with exciting new insight into the structure and dynamics of atoms interacting with photons, and this aspect will appear in many places throughout the book.

Atomic structure

In order to understand atomic structure, some results from quantum mechanics have to be recalled.

Introduction to the density operator

Motivation and definition

It is often inconvenient, for one reason or another, to keep track of all the variables of a complex system. For example, in a many-body system it would be impracticable to consider the co-ordinates of each particle. Furthermore, such information is actually not of much interest. Thus in a spin system the behaviour of the individual magnetic moments is unimportant; the components of the total magnetisation are the variables of primary interest. Very generally, for a system with ∼ 1023 co-ordinates, one is unlikely to need more than, say, ten variables to describe its observable properties. However, it is quite clear that this reduced amount of information is no longer sufficient to write down a wavefunction and, therefore, it is no longer possible to calculate the evolution of such a system using the usual methods of quantum mechanics.

In Chapter 5 we saw that it was possible, by the introduction of probabilistic arguments, to calculate the evolution of the total magnetisation of a spin system. The calculations were performed using the machinery of quantum mechanics and meaningful and useful results were thereby obtained. In this chapter we will look at things from a rather different point of view. We will not, initially, be concerned with the expectation values of certain specified observables, rather we direct our attention to the general description of the ‘state’ of the system and the way it evolves with time – possibly towards thermal equilibrium.

This book started as a joint project between Michael Richards and myself. We discussed and planned the work in great detail but somewhere along the way Michael moved away from physics, drawing on his experience at Sussex University, to become a psychotherapist. Notwithstanding the plans we made, his withdrawal from the project has resulted in a book hardly recognisable from that originally envisaged. Since the publication of Anatole Abragam's encyclopaedic treatise on nuclear magnetism in 1961 the field has grown at such a pace that no single book could hope to cover its many aspects. However the coverage of this book is without doubt narrower and its content impoverished as a consequence of Michael's career change.

Mea culpa. I am guilty of the very sin of which I have accused others. The motivation for writing a book on NMR was that the various books available, since Abragam's, did not cover the material which I, my colleagues and research students required. It seemed that the new books comprised assorted collections of topics in NMR. Michael and I wanted to redress this, but in surveying the finished product I see no more than yet another assortment of topics. This time, however, it is my collection of topics. While the broader aim might not have been achieved my hope is that this assortment will have its appeal.

In the preface to Abragam's book in 1960 he wrote that he hoped his book would still be the book on the subject thirty years after its publication. That was prophetic; his wish has been amply fulfilled.