  Due to an accidentally large $s$-wave scattering length, in a relatively wide
range of energy, neutrons are approximately described by the nonrelativistic
conformal field theory of unitarity fermions, perturbed by one relevant and an
infinite number of irrelevant operators. We develop a formalism which provides
a nonperturbative definition of local operators in that nonrelativistic
conformal field theory. We compute the scattering-length and effective-range
corrections to the two-point functions of primary charge-three operators using
the technique of conformal perturbation theory. These calculations allow us to
find the first corrections to the scale-invariant behavior of the rate of
nuclear reactions with three neutrons in the final state in the regime when the
neutrons have small relative momenta.
