Positronium scattering

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. 

Positronium scattering by other atomic ions should also in principle be considered as part of a complete description of positron scattering by the relevant atom when the positronium formation channel is open, but few such calculations have been made. 

Detailed investigations of positronium scattering by atoms have been confined mainly to hydrogen, although some studies have also been made... 

Until recently there was no firm theoretical evidence that a positron could bind to any atom other than positronium it had been rigorously proved by Armour (1978, 1982) that it cannot bind to atomic hydrogen, and the evidence that it cannot bind to helium is overwhelming. The most likely candidates were the highly polarizable alkali atoms, and states of the positron-atom system below the positron-atom scattering threshold do indeed exist. However, they were all believed to lie above the threshold for positronium scattering by the corresponding positive ion, and were therefore not true bound states. 

Hara, S. and Fraser, P.A. (1975). Low-energy ortho-positronium scattering by hydrogen atoms. J. Phys. B At. Mol. Phys. 8 L472-L476. 

Positron and Positronium Scattering at Low Energies, J. W. Humberston How Perfect are Complete Atomic Collision Experiments H. Kleinpoppen and H. Handy Adiabatic Expansions and nonadiabatic Effects, R. McCarroll and D. S. F. Crothers Electron Capture to the Contiuum,... 

The total positron scattering cross section, erT, is the sum of the partial cross sections for all the scattering channels available to the projectile, which may include elastic scattering, positronium formation, excitation, ionization and positron-electron annihilation. Elastic scattering and annihilation are always possible, but the cross section for the latter process is typically 10-2O-10-22 cm2, so that its contribution to erT is negligible except in the limit of zero positron energy. All these processes are discussed in greater detail in Chapters 3-6. 

Fig. 2.1. Schematic illustration of the behaviour of the positron-helium and electron-helium total scattering cross sections. Notable are the large differences in magnitude of the cross sections at low energies, their merging at approximately 200 eV and the onset of inelastic processes at the positronium formation threshold EPS in the positron curve.

As the positron energy is raised above the positronium formation threshold, EPs, the total cross section undergoes a conspicuous increase. Subsequent experimentation (see Chapter 4) has confirmed that much of this increase can be attributed to positronium formation via the reaction (1.12). Significant contributions also arise from target excitation and, more importantly, ionization above the respective thresholds (see Chapter 5). In marked contrast to the structure in aT(e+) associated with the opening of inelastic channels, the electron total cross section has a much smoother energy dependence, which can be attributed to the dominance of the elastic scattering cross section for this projectile. 

Fig. 2.14. Compendium of total cross section data for positron-noble gas and electron-noble gas scattering. The arrows refer to thresholds for (in order of increasing energy) positronium formation (positrons only), excitation and ionization. (From Kauppila and Stein, 1982.)...

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