Unnuclear physics: Conformal symmetry in nuclear reactions

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 verify our predictions with previous effective field theory and model calculations of the ⁶He[Formula: see text], ³H[Formula: see text], and ³H[Formula: see text] reactions and discuss opportunities to measure unnuclei at radioactive beam facilities.