  Starting from fundamental multiple scattering theory it is shown that
negative refraction indices are feasible for matter waves passing a
well-defined ensemble of scatterers. A simple approach to this topic is
presented and explicit examples for systems of scatterers in 1D and 3D are
stated that imply negative refraction for a generic incoming quantum wave
packet. Essential features of the effective scattering field, densities and
frequency spectrum of scatterers are considered. Additionally it is shown that
negative refraction indices allow perfect transmission of the wave passing the
ensemble of scatterers. Finally the concept of the superlens is discussed,
since it is based on negative refraction and can be extended to matter waves
utilizing the observations presented in this paper. This paves the way for
'untouchable' quantum systems in analogy to cloaking devices for
electromagnetic waves.
