Unusual nature of positronium-proton elastic scattering

The Lippmann-Schwinger equation for positronium-proton elastic scattering lacks a first-order term because the center of mass and center of charge are coincident. A consequence of this is that the high-energy behavior of the phase shift is governed by the second-Born approximation. Asymptotic analysis indicates that the high-energy form of the phase shift is δL∼O(1/k3), where k is the incident positronium momentum. The asymptotic analysis has been confirmed by an explicit close-coupling calculation including the Ps(1s), Ps(2s), Ps(2p), H(1s), H(2s), and H(2p) states.