  The possibility of using ultracold atoms to observe strong localization of
matter waves is now the subject of a great interest, as undesirable decoherence
and interactions can be made negligible in these systems. It was proposed that
a static disordered potential can be realized by trapping atoms of a given
species in randomly chosen sites of a deep 3D optical lattice with no multiple
occupation. We analyze in detail the prospects of this scheme for observing
localized states in 3D for a matter wave of a different atomic species that
interacts with the trapped particles and that is sufficiently far detuned from
the optical lattice to be insensitive to it. We demonstrate that at low energy
a large number of 3D strongly localized states can be produced for the matter
wave, if the effective scattering length describing the interaction of the
matter wave with a trapped atom is of the order of the mean distance between
the trapped particles. Such high values of the effective scattering length can
be obtained by using a Feshbach resonance to adjust the free space
inter-species scattering length and by taking advantage of confinement-induced
resonances induced by the trapping of the scatterers in the lattice.
