Positronium excitation

The formation potential is usually negative for nPs = 1, and therefore positronium emission is allowed. However, with the possible exception of a diamond surface (Brandes, Mills and Zuckerman, 1992), it is positive for nPs > 2, which therefore precludes the emission of excited state positronium following positron thermalization in the material. 

Positrons exhibit resonance phenomena in collisions with some atomic and molecular targets and, as with electrons, an infinite series of resonances is expected to be associated with each degenerate excitation threshold (Mittleman, 1966). For electrons, such thresholds can only arise with hydrogenic targets, but for positrons there are also degenerate thresholds in the excitation of positronium. Several of these resonances have been identified theoretically for a few simple target systems, but they are too narrow to be observed experimentally with the presently available energy resolution of positron beams. 

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. 

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.)...

S-5P excitation — —, 5S-4D excitation uneven solid curve, at bottom of figure, sum of 5S-6S and 5S-6P excitation cross sections positronium formation. 

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

Most other calculations of positronium formation in positron-helium scattering have employed much simpler methods of approximation, but results have usually been obtained over energy ranges extending well beyond the Ore gap. It must therefore be borne in mind that the experimental results include contributions from positronium formation into excited states as well as into the ground state. The Born approximation, used first by Massey and Moussa (1961) and subsequently by Mandal, Ghosh... 

Positronium formation into nPs = 2 excited states in positron H2 scattering was investigated in the first Born approximation by Ray, Ray and Saha (1980) and also by Biswas et al. (1991b). 

---