Ideal-space treatment of the e++H to Ps+H+process

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Abstract
A new quantum mechanical formalism, is considered for the e+-H system; it explicitly introduces into the scattering picture the positronium (Ps) formation and breakup channels. In its lowest-order form the scattering T matrix of the theory (T(1)) contains two terms. The first of these (TB) is the conventional first Born approximation, while the second (TS), involving a non-local potential, can be interpreted as a screening of of the bare Coulomb interactions. Numerical applications seem to indicate that the new theory is characterised by much faster convergence properties than more conventional quantum mechanical treatments. In particular, the presence of the new Ts term, in the T(1) approximation, leads to differential and total cross sections comparable with distorted-wave results of the literature.

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