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

The experimental determination of the lifetime of pionium provides a very important test of chiral perturbation theory. This quantity is determined in the DIRAC experiment at CERN. In the analysis of this experiment, the breakup probabilities of pionium in matter are needed to high accuracy as a theoretical input. We study in detail the influence of the target electrons. They contribute through screening and incoherent effects. We use Dirac-Hartree-Fock-Slater wavefunctions in order to determine the corresponding form factors. We find that the inner-shell electrons contribute less than the weakly bound outer electrons. Furthermore, we establish a more rigorous estimate for the magnitude of the contribution from the transverse current (magnetic terms thus far neglected in the calculations).