Probing Low-Energy Quantum Vacuum Fluctuations and Non-Additive Forces via Ultracold Neutron Scattering in Bounded Nano-Cavities

We present a comprehensive framework evaluating short-range quantum vacuum alterations onneutral baryonic systems. Eliminating the dominant Coulomb repulsion by transitioning from protonsto neutrons, we investigate the asymptotic 1/r7 Casimir-Polder potential and the non-additive 1/r9Axilrod-Teller-Muto three-body forces. Using Paul Dirac’s bra-ket formalism within a compositemulti-particle Hilbert space, we compute the s-wave phase shifts (δ0) and modifications to thebaseline nuclear scattering length (anuc). We outline an experimental protocol combining Dopplerlaser cooling of a sympathetic matrix inside a Diamond Anvil Cell (DAC) to achieve nanometre nodespacing, directly testable at high-precision facilities such as the TRIUMF Ultracold Neutron facility.