Conformal symmetry plays an important role in quantum field theory and statistical physics. A nonrelativistic version of the conformal symmetry, also called Schrödinger symmetry, is approximately realized in various physical systems, including neutrons in nuclear physics and ultracold atoms. Nonrelativistic conformal field theories realize Schrödinger symmetry and possess many interesting properties. After reviewing some facts about nonrelativistic conformal field theory, we describe how it can be applied to the physics of nuclear reactions with several neutrons in the final state.