Cross section for positronium formation

The differential cross section for positronium formation may be expressed in terms of the partial-wave K-matrix elements as... 

Fig. 4.7. The differential cross sections for positronium formation into the ground state and the nPS = 2 excited states in positron-hydrogen collisions at...

Fig. 4.8. Cross sections for positronium formation in positron collisions with...

Diana, L.M., Brooks, D.L., Coleman, P.G., Pendleton, P.K., Norman, D.M., Seay, B.E. and Sharma, S.C. (1986a). Total cross sections for positronium formation in molecular hydrogen, krypton and xenon. In Positron (Electron)-Gas Scattering, eds. W.E. Kauppila, T.S. Stein and J.M. Wadehra (World Scientific) pp. 293-295. 

The energetic positron slows down on its track to it s implantation depth, it ionizes the sample and leaves a spur of free electrons behind [27, 28]. The number of electrons at the terminal of the spur and their mobility determine the formation likelihood for positronium. The cross section for positronium formation becomes constant independent of incident energy. The second path to positronium formation is the 0re process [29]. When the potential energy needed to ionize an electron from a molecule is less than the binding... 

More experimental work on antiparticle/particle-atom collisions had to await the technical development of antiparticle beams of higher intensity and velocity definition at lower particle velocities. Since the late sixties, a large number of such experiments were performed for c /c impact on gaseous targets. Elastic- and total-scattering cross sections were measured as well as the cross section for positronium formation. A recent review of this work was given by Charlton and Laricchia [2.12]. Since 1980, it has become possible to measure cross sections for ionization and excitation in antiparticle-atom collisions. It is these results that are the primary subject of the present paper. However, we also include... 

Fig. 8.10. Cross sections for antihydrogen formation in collisions of stationary antiprotons with positronium atoms (from Igarashi, Toshima and Shirai, 1994). (a) is for IS positronium and (b) is for the 2P state (note the changes in scale). Key (same for both figures) dotted curve with crosses, formation into the nfl = 1 state short-broken line plus squares, formation into the ns = 2 state long-broken line plus triangles, formation into the nn = 3 state very-long-broken line plus inverted triangles, formation into the ns = 4 states. The solid curve with circles is the total cross section summed over all ns states and the double chain curve is this quantity as calculated by Mitroy and Stelbovics (1994).

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. 

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. 

Campeanu et al. (1987) also discussed the behaviour of the ionization cross sections for positrons and electrons near to the ionization threshold, but our treatment of this topic is deferred until subsection 5.4.5. Furthermore, in subtracting positronium formation threshold and the first excitation threshold of the helium atom. Their derived cross section appeared to contain a cusp or threshold anomaly around EPs, but more recent experimentation and theoretical analysis has cast some doubt on the existence of a feature of this size in helium. Further discussion of these interesting phenomena is given in Chapters 3 and 4. 

Fig. 3.12. Cross sections for positron-helium scattering in the vicinity of the positronium formation threshold (labelled Ps ex and ion denote the respective thresholds for excitation and ionization). , aT — aPS from Coleman el al. (1992) ...

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

The total positronium formation cross section in the Ore gap, constructed from the addition of accurate variational results for the first three partial waves and the values given by the Born approximation for all partial waves with l > 2, is plotted in Figure 4.4. On the scale of the ordinate, the s-wave contribution is too small to be visible. A very small s-wave contribution is found to be a feature of the positronium formation cross section for several other atoms. 

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