Elastic positron scattering

The value of Zeff is a measure of the probability that the positron is at essentially the same position as any of the electrons in the target, and it can be calculated from the wave function representing elastic positron scattering by the target. If the wave function is H(ri, r2,..., rz+1), where r is the positron coordinate and r2,. . . , rz+1 are the coordinates of the Z electrons in the target system, then... 

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. 

A discussion of elastic positron-atom scattering is most conveniently introduced in the context of positron-hydrogen scattering, and we therefore describe this system in considerable detail and use it to illustrate some of the more important methods of approximation used in positron collision... 

Let us now consider further the use of the method of models in elastic positron-helium scattering, which is the sole open channel for positron energies below 17.8 eV, the threshold for ground state positronium formation. The total Hamiltonian of the system is... 

Fig. 3.13. Total (tot, upper solid line) and elastic (el, lower solid line) cross sections for positron-noble gas scattering near the positronium formation threshold from the R-matrix analysis of Moxom et al. (1994). Graphs (a)-(e) correspond to helium through to xenon. The data points shown are total cross section measurements from the literature (see Chapter 2 and Moxom et al., 1994, for details) except for the solid diamonds for helium, which are the

Fig. 3.15. Schematic illustration of the crossed-beam apparatus developed by Hyder et al. (1986) for the measurement of positron elastic differential scattering cross sections. Reprinted from Physical Review Letters 57, Hyder et al, Positron differential elastic scattering cross section measurements for argon, 2252-2255, copyright 1986 by the American Physical Society.

Fig. 3.17. Positron-argon elastic differential scattering cross sections. Experiment , o, Smith et al. (1990) A, Coleman and McNutt (1979) , Floeder et al.

Fig. 3.18. Experimental elastic positron-argon differential scattering cross sections in the range 5-50 eV from Smith et al. (1990). The theoretical data...

Coleman, P.G., Johnston, K.A., Cox, A.M.G., Goodyear, A. and Charlton, M. (1992). Elastic positron-helium scattering near the positronium formation threshold. J. Phys. B At. Mol. Opt. Phys. 25 L585-L588. 

Doolen, G., McCartor, G., McDonald, F.A. and Nuttall, J. (1971). s-wave elastic positron-hydrogen scattering in the ionization region. Phys. Rev. A 4 108-111. 

Gianturco, F.A. and Paioletti, P. (1997). Elastic collisions and rotational excitation in positron scattering from CO2 molecules. Phys. Rev. A 55 3491-3503. 

We do not discuss elastic scattering here because it is not particularly interesting to most chemists, and it has been reviewed recently [l]. Comparisons of electron and positron scattering is treated only briefly here because it is the subject of a recent comprehensive review [2]. We limit the present discussion to topics of most interest to chemists. These inevitably involve molecular (not atomic) targets, and are concerned in particular with electronic (i.e., orbital) structure, vibrational effects, bond breaking, and the formation of compounds that contain positrons. 

The APH method is applicable to any three particle rearrangement collision for which the potential is known. A good example of this is a problem from atomic physics, a positron scattering with a hydrogen atom. Positrons are antipartides, positively charged electrons. Besides the usual elastic and inelastic scattering processes a rearrangement process also... 

Below To, the phonon-positron scattering is no longer elastic and the effectiveness of phonons in shortening the positron mean free path is strongly reduced. In pure... 

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. 

If elastic scattering is the only open channel (except for electron-positron annihilation with its very small cross section), the total and elastic scattering cross sections are identical, and the cross section may be calcu-... 

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