  We investigate a nonrelativistic version of Georgi's "unparticle physics." We
define the unnucleus as a field in a nonrelativistic conformal field theory.
Such a field is characterized by a mass and a conformal dimension. We then
consider the formal problem of scatterings to a final state consisting of a
particle and an unnucleus and show that the differential cross section, as a
function of the recoil energy received by the particle, has a power-law
singularity near the maximal recoil energy, where the power is determined by
the conformal dimension of the unnucleus. We argue that unlike the relativistic
unparticle, which remains a hypothetical object, the unnucleus is realized, to
a good approximation, in nuclear reactions involving emission of a few
neutrons, when the energy of the final-state neutrons in their center-of-mass
frame lies in the range between about 0.1 MeV and 5 MeV. Combining this
observation with the known universal properties of fermions at unitarity in a
harmonic trap, we predict a power-law behavior of an inclusive cross section in
this kinematic regime. We compare our predictions with previous effective field
theory and model calculations of the $^6$He$(p,p\alpha)2n$,
$^3$H$(\pi^-,\gamma)3n$, and $^3$H$(\mu^-,\nu_\mu)3n$ reactions and find
excellent agreement.
