  We present a theoretical study of elastic photon scattering by atomic
targets. This process is of special interest since various channels from atomic
and nuclear physics as well as quantum elctrodynamics (QED) contribute to it.
In this work, we focus on Delbr\"uck scattering which proceeds via production
of virtual $e^+e^-$ pairs. In particular, we explore whether and how the
Delbr\"uck channel can be "seen" in present synchrotron experiments which
employ strongly linearly polarized light in the energy range of a few hundred
keV. In order to answer this question, detailed calculations have been
performed for the scattering of 300 keV and 889.2 keV photons off helium-like
tin ions. Based on these calculations, we argue that the Delbr\"uck scattering
for the energies below the threshold for $e^+e^-$ pair creation leads to a
shift in the angular distribution and the polarization of the scattered photons
which can be observed by state-of-the-art solid-state detectors.
