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.

One of the central questions of science is: how are complex things made from simple things? In many cases larger systems are more complicated than their smaller subsystems. In biology and chemistry the issue is how to understand large molecules in terms of atoms. In atomic physics one may strive to understand properties of many electron systems in terms of single electron properties. The general theme is interdependency of subsystems, or ‘correlation’.

Correlation may be regarded as a conceptual bridge from properties of individuals to properties of groups or families. In atoms and molecules correlation occurs because electrons interact with one another – the electrons are interdependent. This electron correlation determines much of the structure and dynamics of many electron systems, i.e., how complex electronic systems are made from single electrons. Complexity is the more significant idea, but complexity may be seldom, if ever, understood. Correlation is the key to complexity.

Understandably, much has been done on the correlation of static systems. There are many excellent methods and computer codes to evaluate energies and wavefunctions for complex atomic and molecular systems. However, the dynamics of these many electron systems is less well understood. Hence, the dynamics of electron correlation is a central theme in this book.

The dynamics of electron correlation may affect single electron transitions. However, this effect is sometimes difficult to separate from other effects.

This introductory chapter begins with a review of uncorrelated classical probabilities and then extends these concepts to correlated quantum systems. This is done both to establish notation and to provide a basis for those who are not experts to understand material in later chapters.

Probability of a transition

Seldom does one know with certainty what is going to happen on the atomic scale. What can be determined is the probability P that a particular outcome (i.e. atomic transition) will result when many atoms interact with photons, electrons or protons. A transition occurs in an atom when one or more electrons jump from their initial state to a different final state in the atom. The outcome of such an atomic transition is specified by the final state of the atom after the interaction occurs. Since there are usually many atoms in most systems of practical interest, we can usually determine with statistical reliability the rate at which various outcomes (or final states) occur. Thus, although one is unable to predict what will happen to any one atom, one may determine what happens to a large number of atoms.

1 Single particle probability

A simple basic analogy is tossing a coin or dice. Tossing of a coin is analogous to interacting with an atom. In the case of a simple coin there are two outcomes: after the toss one side of the coin (‘heads’) will either occur or it will not occur.

There are, in general, many possible transitions of electrons in atoms. In some processes of practical interest more than one electron may undergo a transition. Such multiple electron transitions are the topic of the next and subsequent chapters. In this chapter the simpler topic of single electron transitions is considered, where the activity of a single electron in an atom is the focus of attention. Even this relatively simple case may be impossible to fully understand if the electron of interest is influenced by other electrons in the atom. So in this chapter the interdependency of electrons in the system is ignored. That is, the electrons are treated independently. Typically, such an independent electron is regarded as beginning in an initial state characterized by some effective nuclear charge ZT and a set of quantum numbers n, l, m, s, ms from which all possible properties (e.g., energy, shape, magnetic properties, etc.) may be determined. Interaction with something else, (usually a particle of charge Z and velocity, v), may cause a transition to a different final state of the atom.

The simplest transition occurs in interaction of atomic hydrogen with a structureless projectile. There are various ways to evaluate the transition probability for such a system. Exact calculations usually require use of a computer. Approximate calculations may be done more easily. Calculations for many electron systems are often done approximately using single electron transition probabilities.

Correlation

There is a significant difference between complex and merely large. This difference is related to the the notion of correlation which defines the rules of interdependency in large systems. The relevant question is: how may one make complicated things from simple ones? Biological systems are complex because the atomic and molecular subsystems are correlated. From the point of view of atomic physics correlation in condensed matter, chemistry and biology is determined at least in part by electron correlation in chemical bonds and the complex interdependent structures of electronic densities. Understanding correlation in this broad sense is a major challenge common to most of science and much of technology. This is sometimes referred to as the many body problem. In a general sense correlation is a conceptual bridge from properties of individuals to properties of groups or families.

The concept of correlation arises in many different contexts. ‘Individual’ may mean an individual electron, an individual molecule or in principle an individual person, musical note or ingredient in a recipe. In this book individual refers to electron for the most part. In this case the interaction between individuals is well known, namely l/r12. However, that does not mean that electron correlation is well understood in general. Although much has been done to investigate correlation in various areas of physics, chemistry, statistics, biology and materials science, in many cases little is well understood except in the limit of weak correlation.