  The Galaxy hosts a widespread population of low-energy positrons revealed by
successive generations of gamma-ray telescopes through a bright annihilation
emission from the bulge region, with a fainter contribution from the inner
disk. The exact origin of these particles remains currently unknown. We
estimate the contribution to the annihilation signal of positrons generated in
the decay of radioactive 26Al, 56Ni and 44Ti. We adapted the GALPROP
propagation code to simulate the transport and annihilation of radioactivity
positrons in a model of our Galaxy. Using plausible source spatial
distributions, we explored several possible propagation scenarios to account
for the large uncertainties on the transport of ~1MeV positrons in the
interstellar medium. We then compared the predicted intensity distributions to
the INTEGRAL/SPI observations. We obtain similar intensity distributions with
small bulge-to-disk ratios, even for extreme large-scale transport
prescriptions. At least half of the positrons annihilate close to their
sources, even when they are allowed to travel far away. In the high-diffusion,
ballistic case, up to 40% of them escape the Galaxy. In proportion, this
affects bulge positrons more than disk positrons because they are injected
further off the plane in a tenuous medium, while disk positrons are mostly
injected in the dense molecular ring. The predicted intensity distributions are
fully consistent with the observed longitudinally-extended disk-like emission,
but the transport scenario cannot be strongly constrained by the current data.
Nucleosynthesis positrons alone cannot account for the observed annihilation
emission in the frame of our model. An additional component is needed to
explain the strong bulge contribution, and the latter is very likely
concentrated in the central regions if positrons have initial energies in the
100keV-1MeV range.
