  The evolution of pionium, the $\pi^+ \pi^-$ hydrogen-like atom, while passing
through matter is solved within the density matrix formalism in the first Born
approximation. We compare the influence on the pionium break-up probability
between the standard probabilistic calculations and the more precise picture of
the density matrix formalism accounting for interference effects. We focus our
general result in the particular conditions of the DIRAC experiment at CERN.
