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

The experimental determination of the lifetime of pionium provides a very i mportant test of chiral perturbation theory. This quantity is determined in the DIRAC experiment at CERN. In the analysis of this experiment, the brea kup probabilities of pionium in matter are needed to high accuracy as a the oretical input. We study in detail the influence of the target electrons. T hey contribute through screening and incoherent effects. We use Dirac-Hartr ee-Fock-Slater wavefunctions in order to determine the corresponding form f actors. We find that the inner-shell electrons contribute less than the wea kly bound outer electrons. Furthermore, we establish a more rigorous estima te for the magnitude of the contribution from the transverse current (magne tic terms thus far neglected in the calculations).