One thing to consider. The 0.56 MeV is the maximum energy of your e+.
Most of them have much lower energies. The range of 0.56 MeV positrons
(or electrons) is 0.16 grams/cm^2 of a materiol. For most of your
positrons, using 0.2 MeV as a representative typical energy, the range
is about 0.04 g/cm^2. Are you sure you are not screening positrons
somewhere?
Ludwik Kowalski