Wave vector matching in charge exchange collisions involving positrons

We present a simple model based upon wave vector matching which gives a plausible explanation for the empirical observation that, for positron collisions with a wide variety of targets, cross sections for positronium formation are largest when the projectile kinetic energy is in the vicinity of twice the relevant threshold energy. The model is used to make predictions of cross-section trends for charge exchange processes for collisions involving a number of other positronic species.