  We introduce a systematic approach to characterize the most general
non-relativistic WIMP-nucleus interaction allowed by Galilean invariance for a
WIMP of arbitrary spin $j_\chi$ in the approximation of one-nucleon currents.
Five nucleon currents arise from the nonrelativistic limit of the free nucleon
Dirac bilinears. Our procedure consists in (1) organizing the WIMP currents
according to the rank of the $2 j_\chi+1$ irreducible operator products of up
to $2 j_\chi$ WIMP spin vectors, and (2) coupling each of the WIMP currents to
each of the five nucleon currents. The transferred momentum $q$ appears to a
power fixed by rotational invariance. For a WIMP of spin $j_\chi$ we find a
basis of 4+20$j_\chi$ independent operators that exhaust all the possible
operators that drive elastic WIMP-nucleus scattering in the approximation of
one-nucleon currents. By comparing our operator basis, which is complete, to
the operators already introduced in the literature we show that some of the
latter for $j_\chi=1$ were not independent and some were missing. We provide
explicit formulas for the squared scattering amplitudes in terms of the nuclear
response functions, which are available in the literature for most of the
targets used in WIMP direct detection experiments.
