Coherent and incoherent atomic scattering: formalism and application to pionium interacting with matter

Abstract

The experimental determination of the lifetime of pionium provides avery important test of chiral perturbation theory. This quantity isdetermined in the DIRAC experiment at CERN. In the analysis of thisexperiment, the breakup probabilities of pionium in matter are neededto high accuracy as a theoretical input. We study in detail theinfluence of the target electrons.They contribute through screening and incoherent effects. We useDirac-Hartree-Fock-Slaterwavefunctions in order to determine the corresponding form factors.We find that the inner-shell electrons contribute less thanthe weakly bound outer electrons. Furthermore, we establish a morerigorous estimate for the magnitude of the contribution from thetransverse current (magnetic terms thus far neglected in thecalculations).