  In the present work we examine the implications on dark matter searches of
the possibility of a partial decay of a neutron into a dark matter particle,
slightly lighter than itself. Such a scenario recently proposed is required to
bridge the discrepancy between the results of two different experiments
measuring the life time of the neutron. It was subsequently suggested that this
light dark matter candidate could make up the whole of dark matter in the
universe. We thus first compute the nucleon cross section based on such models.
Then we proceed explore the various signatures appearing in dark matter
searches involving nuclear targets, in the case of such a light dark matter
candidate.
