  We study (anti)deuteron formation rates in heavy-ion collisions in the
framework of a wave-function based coalescence model. The main feature of our
model is that nucleons are emitted from the whole spherically symmetric
fireball volume, while antinucleons are emitted only from a spherical shell
close to the surface. In this way, the model accounts for nucleon-antinucleon
annihilations in the center of the reaction at lower beam energies. Comparison
with experimental data on the coalescence parameter in the range
$\sqrt{s_{NN}}= 4.7-200$ GeV allows us to extract radii of the respective
source geometries. Our results are qualitatively supported by data from the
UrQMD transport model which shows a comparable trend in the geometric radii as
a function of beam energy. In line with our expectations, we find that at lower
energies, the central region of the fireball experiences stronger annihilation
than at higher energies.
