  The capture rates of non-relativistic neutrinos on beta decaying nuclei
depends on whether their mass is Dirac or Majorana. It is known that for relic
neutrinos from the big-bang, and within minimal assumptions, the rate is a
factor two larger in the Majorana case. We show that this difference also
depends on the value of the lightest neutrino mass and on the type of mass
hierarchy. If the lightest neutrino has a mass below the meV, so that it is
still relativistic today, its capture rate for the case of Dirac masses becomes
equal to that for Majorana masses. As a consequence, for the case of normal
neutrino mass hierarchy, for which the total capture rate is dominated by the
contribution from the lightest neutrino, if this one is below the meV the
distinction between the Dirac and Majorana scenarios can only rely on the
detection of the two heavier neutrinos, which is something very challenging.
