  We study the strong localization of atomic matter waves in a disordered
potential created by atoms pinned at the nodes of a lattice, for both
three-dimensional (3D) and two-dimensional (2D) systems. The localization
length of the matter wave, the density of localized states, and the occurrence
of energy mobility edges (for the 3D system), are numerically investigated as a
function of the effective scattering length between the atomic matter wave and
the pinned atoms. Both positive and negative matter wave energies are explored.
Interesting features of the density of states are discovered at negative
energies, where maxima in the density of bound states for the system can be
interpreted in terms of bound states of a matter wave atom with a few pinned
atomic scatterers. In 3D we found evidence of up to three mobility edges, one
at positive energies, and two at negative energies, the latter corresponding to
transitions between extended and localized bound states. In 2D, no mobility
edge is found, and a rapid exponential-like increase of the localization length
is observed at high energy.
