We now consider several of the more exotic systems in which one or more positrons may be involved, some of which were introduced in subsection 1.2.3. The positronium negative ion (e–e+e–), Ps–, has been observed in the laboratory (Mills, 1981) and its lifetime against annihilation determined experimentally (Mills, 1983b). We discuss these experiments and the relevant theory in section 8.1. Observation of the positronium molecule, Ps2, and other systems containing more than one positron or positronium atom (as yet unrealized) depends upon the generation of large instantaneous densities of positrons. The situation here is more encouraging than might be expected, owing to progress in developing very intense brightness-enhanced and time-focussed beams, as summarized in subsection 1.4.4. Many-positron systems and how they may be observed are described in section 8.2.

Antihydrogen, as discussed in subsection 1.2.3, has recently been observed in the laboratory, although only at relativistic speeds. However, progress with the trapping of cold antiprotons and positrons, and the production of positronium in a cryogenic environment, leads us to anticipate the synthesis of antihydrogen atoms with very low kinetic energies (or temperatures); thus it may be possible to trap them, and perform precision spectroscopy upon them. The motivation for the production of low temperature antihydrogen is described in section 8.3, along with the mechanisms and methodologies involved in some of the proposed formation processes.

In this chapter we consider the physics of the positronium atom and what is known, both theoretically and experimentally, of its interactions with other atomic and molecular species. The basic properties of positronium have been briefly mentioned in subsection 1.2.2 and will not be repeated here. Similarly, positronium production in the collisions of positrons with gases, and within and at the surface of solids, has been reviewed in section 1.5 and in Chapter 4. Some of the experimental methods, e.g. lifetime spectroscopy and angular correlation studies of the annihilation radiation, which are used to derive information on positronium interactions, have also been described previously. These will be of most relevance to the discussion in sections 7.3–7.5 on annihilation, slowing down and bound states. Techniques for the production of beams of positronium atoms were introduced in section 1.5. We describe here in more detail the method which has allowed measurements of positronium scattering cross sections to be made over a range of kinetic energies, typically from a few eV up to 100–200 eV, and the first such studies are summarized in section 7.6.

Important advances continue to be made in measurements of the intrinsic properties of the positronium atom, e.g. its ground state lifetimes (Rich, 1981; Al-Ramadhan and Gidley, 1994; Asai, Orito and Shinohara, 1995) and various spectroscopic quantities (Berko and Pendleton, 1980, Mills, 1993; Hagena et al., 1993). These are reviewed in section 7.1.

Introduction

In this chapter we describe the elastic scattering of positrons by atoms and molecules over the kinetic energy range from zero to several keV, concentrating mainly on the angle-integrated cross section, σel. However, reference is also made to differential cross sections, dσel/dΩ, which have recently become amenable to experimental measurement using crossed gas and positron beams.

Particular attention is given to relatively simple targets, e.g. atomic hydrogen, helium, the alkali and heavier rare gas atoms and small molecules, and some comparisons are made with the corresponding data for electron impact. This again highlights the differences and similarities in the scattering properties of the two projectiles, which have already been mentioned in subsection 1.6.1 and in Chapter 2.

At energies below the lowest inelastic threshold, elastic scattering is the only open channel (except for electron–positron annihilation, which is always possible but which usually has a negligibly small cross section). For all atoms, the lowest inelastic threshold is that for positronium formation, at an energy EPs, but for the alkali atoms positronium formation is possible even at zero incident energy. Molecular targets usually have thresholds for rotational and vibrational excitation at energies below EPs, although the elastic scattering cross section is nevertheless expected to dominate over the cross sections for these inelastic channels.

We continue this chapter with a detailed description of the theoretical models applied to the elastic scattering of positrons by atoms and molecules.

Introduction

Many-body theory has been very successful in the ab initio calculation of electron–atom scattering cross sections. Its application has made it possible to take into account the target atom polarization in the collision process without the introduction of a semi-empirical potential. The many-body approach and the diagrammatic technique associated with it have also permitted the illumination of hidden difficulties in the description of the electron-atom scattering process.

The first calculations of electron–hydrogen elastic scattering cross sections using the diagrammatic technique of many-body theory were performed by H. P. Kelly about thirty years ago. In that calculation, as well as in subsequent investigations involving helium, argon and xenon, the polarization of the target atom by slow and medium energy electrons was taken into account. The effects of the exchange between the projectile electrons and target electrons were also accounted for. Although, at first glance, the interaction between the incoming electrons and the atomic particles is of second order, the polarization of the target in these works included a number of higher order corrections. This inclusion has proven to be very important.

The subsequent application of many-body theory to the scattering of electrons from highly polarizable atoms led to the development of methods which permitted the incorporation of the corresponding corrections non-perturbatively. A connection between elastic scattering and negative ion formation has also allowed one to use many-body techniques for the calculation of electron affinities.

Introduction

The process of single photoionization occurs when an atom or molecule absorbs a photon and ejects a single electron. Photoionization studies of multi-electronic systems can provide excellent portraits of the many-body effects that lie within both the initial target state and the final state consisting of the ion plus the photoelectron. Important examples of many-body effects include autoionizing resonances, giant shape resonances, relaxation, and polarization. A common element of all of these effects is their prominence near ionization thresholds. In this chapter, we will examine the many-body effects that are present in atomic single photoionization problems within the framework of many-body perturbation theory (MBPT).

We will refer to the corrections to a one-electron approximation (such as a Hartree-Fock approximation) as correlation effects. Although a one-electron approximation is capable of describing many of the gross properties of photoionization in atoms, a scheme for including correlation effects will be necessary in order to describe many of the processes that are mentioned above.

There has been considerable development in experimental techniques to study photoionization over the past few decades. Synchrotron radiation has been used to measure total photoabsorption cross sections over a wide range of energies for many atomic species. Additionally, photoelectron spectroscopy has been used to partition total cross sections into channel cross sections. Methods for the measurement of the angular distribution asymmetry parameter, β(ω), and spin-polarization parameters have also been developed. (See chapter seven by S. Manson for a description of the β asymmetry parameter.)

Introduction

In recent years, experimental studies on low and intermediate energy (e, 2e) processes have accumulated large amounts of triply differential cross section data. These (e, 2e) results, in which the energies and angles of both of the outgoing electrons produced in the electron-impact ionization process are specified, display strong electron-correlation effects. Owing to the difficulty involved in describing precisely various electron correlations, in particular, the Coulomb interaction between the two final-state continuum electrons, only approximate theoretical treatments have been carried out. At present, theoretical understanding of these data and the underlying effects are far from complete.

The near-threshold energy dependence of two electrons escaping from a positive ion has been studied theoretically by many authors using a number of methods. These studies cover the threshold behavior of the total and the differential cross sections for electron-impact ionization of atoms and ions.

In the early 1950's, Wannier applied to this problem the idea that the near-threshold energy-dependence of a reaction could be derived by investigating only the long-range interactions among its final products, without having a detailed knowledge about a small “reaction zone,” the size of which is of the order of magnitude of the Bohr radius. He revealed the importance of the configuration r1 = −r2 for the double escape of slow electrons from a positive ion by using methods of classical mechanics.

Hugh Padraic Kelly died on June 29, 1992 after a brave and lengthy struggle against cancer.

Hugh was a graduate of Harvard University, receiving an AB degree in 1953. He continued on to UCLA where he was awarded an M.Sc. degree in 1954. He served in the Marine Corps for three years before returning to graduate school at Berkeley. He worked there with Kenneth Watson, receiving his Ph.D. degree in 1963 and proceeding on to a postdoctoral fellowship with Keith Brueckner at the University of California, San Diego, where he began his seminal work on many-body theory. He was appointed to the faculty of the University of Virginia in 1965. He was a distinguished administrator, serving the University as Chairman of the Department of Physics, as Dean of the Faculty and as Provost.

Hugh was a very special person. He was from his first research paper the leader in the application of many-body perturbation theory in atomic and molecular physics using diagrammatic techniques. He was renowned internationally not only for his brilliant researches but also for his extraordinary personal qualities. He was modest, unassuming, always supportive of others. He had an abundance of creative ideas, which he freely shared. Hugh was the least competitive of people. He saw science as a joint enterprise in which he participated with his friends and students.