Unnuclear physics

TL;DR

This paper introduces the concept of unnucleus as a nonrelativistic conformal field theory entity, predicts a power-law behavior in nuclear reactions involving neutrons, and validates these predictions against existing experimental data.

Contribution

It defines the unnucleus in a nonrelativistic setting, predicts observable power-law cross sections in nuclear reactions, and connects these to universal fermion properties at unitarity.

Findings

Power-law singularity in recoil energy near maximal recoil.

Unnucleus behavior observed in neutron-emission nuclear reactions.

Excellent agreement with existing reaction data.

Abstract

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.