Positron scattering

J. P. Vigier and V. Wataghin, High energy electron-positron scattering, Nuovo Cimento, Ser X 36, 672 (1965). 

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. 2.5. Schematic illustration of the apparatus used by the Bielefeld group to measure total scattering cross sections. Reprinted from Journal of Physics B 13, Sinapius, Raith and Wilson, Low-energy positrons scattering from noble gas atoms, 4079-4090, copyright 1980, with permission from IOP Publishing.

The final apparatus we describe briefly here is that used by the Detroit group (Zhou et al., 1994a) for the first measurements of the total cross section for positron scattering by atomic hydrogen, and again it... 

Fig. 2.19. Positron-H2 and electron- total scattering cross sections at low energies, (a) Positron scattering. Experiment , Hoffman et al. (1982) ,...

We have chosen H2O for detailed comment rather than other molecules because it was, until recently, one of the few with a large permanent dipole moment to have been studied. The positron scattering data of Sueoka, Mori and Katayama (1987) are shown in Figure 2.23, and they were obtained using a similar TOF system to that described in section... 

It is a reasonably good approximation to consider an alkali atom as a single electron moving in the modified Coulomb field of the ionic core, and this approximation has been made in almost all theoretical investigations of positron scattering by the alkali atoms. The interaction of the electron with the core is expressed as a local central potential of the general form... 

The scattering process can now be considered as a three-body problem, rather similar to positron scattering by atomic hydrogen but with the important difference that, because the ionization energy of an alkali atom is less than the binding energy of positronium, 6.8 eV, the positronium formation channel is open even at zero positron energy. 

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. 4.6. The two double-binary collision processes resulting in positronium formation following positron impact at high energies. The positron collides with an atomic electron on the left the electron then scatters off the residual ion into the same direction as the positron, whilst on the right the process is shown in which the positron scatters off the residual ion.

The first Born approximation is known to provide a rather inaccurate description of positronium formation, even at high energies, because the process then becomes essentially two-stage this can be understood as follows. In order to form positronium, the positron and an electron must emerge from the target with very similar velocities, and the simplest way in which this can be achieved is via one or other of the processes represented in Figure 4.6. In both cases, first the positron scatters from the electron and then either the electron or the positron is scattered into the required final direction by the nucleus. It is therefore to be expected that the second Born approximation, with its quadratic... 

Fig. 4.18. Positronium formation cross sections plotted as functions of the positronium kinetic energy for the following gases (a) helium, (b) neon, (c) argon, (d) krypton, (e) xenon. The ionization threshold in each case is indicated by ion . Reprinted from Physical Review A50, Moxom et al, Threshold effects in positron scattering on noble gases, 3129-3133, copyright 1994 by the American Physical Society.

Fig. 4.28. Schematic illustrating the principle of angle-resolved measurements of positronium formation in positron-gas collisions (following Falke et at, 1997). Reprinted from Journal of Physics B30, Falke et al, Differential Ps-formation and impact-ionization cross sections for positron scattering on Ar and Kr atoms, 3247-3256, copyright 1997, with permission from IOP Publishing.

---