  We study dark matter, assumed to be composed by weak interacting massive
particles (WIMPs), scattering off ${}^2$H and ${}^4$He nuclei. In order to
parameterize the WIMP-nucleon interaction the chiral effective field theory
approach is used. Considering only interactions invariant under parity, charge
conjugation and time reversal, we examine five interaction types: scalar,
pseudoscalar, vector, axial and tensor. Scattering amplitudes between two
nucleons and a WIMP are determined up to second order of chiral perturbation
theory. We apply this program to calculate the interaction rate as function of
the WIMP mass and of the magnitude of the WIMP-quark coupling constants. From
our study, we conclude that the scalar nuclear response functions result much
greater than the others due to theirs large combination of low energy
constants. We verify that the leading order contributions are dominant in this
low energy processes. We also provide an estimate for the background due to
atmospheric neutrinos.
