  This article presents a study of the passage of dimuonium through the foil of
ordinary matter. First, we provide an overview of how dimuonium is planned to
be produced for such a type of experiment and how it is expected to interact
with the ordinary atoms -- predominantly electromagnetically via the screened
coulomb potential of the atomic nuclei. Then, we describe the transport
equations that represent the evolution of dimuonium states during the passage
and their solution methods. Finally, for three different foils (Beryllium,
Aluminium and Lead), we present the results of this study. To estimate impact
of uncertainties in the potential of a target atom, we study 15 different
approximations of the atomic potential and show that the corresponding
atomic-potential-model-dependent error in the yields of the low lying states of
dimuonium is quite small within the framework of the applied Born
approximation. The convergence of the results after truncation of the infinite
system of transport equations to the finite number of quantum states of
dimuonium is also studied, and good convergence for the yields of low-lying
states is demonstrated.
