Differential cross sections 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...

McAlinden, M.T. and Walters, H.R.J. (1994). Differential cross sections for elastic scattering and positronium formation for positron collisions with Ne, Ar, Kr and Xe. Hyperfine Interactions 89 407-418. 

After discussing the theory of positronium formation, with applications to several relatively simple systems, we shall describe various techniques used to measure positronium formation cross sections and present the results so obtained, comparing them with theoretical predictions wherever applicable. The chapter also includes a discussion of the angular dependence of the positronium formation cross section. As well as being of intrinsic interest as a test of theory, the differential formation cross section, da-ps/dQ, is also relevant for the production of energy-tunable beams of positronium atoms. This topic is treated more fully in section 7.6. 

The measurement of daPs/dQ is not an easy task and, as we shall see, there is little experimental information presently available. We note here that many experimental arrangements which could be used to measure differential positronium formation cross sections sum over all the possible quantum states (nPs, lPs) of the positronium, whereas calculations usually refer to one particular state. Some differentiation between positronium states with different values of nPs can be achieved if the time of flight of the positronium, and hence its kinetic energy, is measured, and such a technique has been used to investigate beams of positronium atoms produced in positron-gas collisions (see section 7.6). 

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.

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