Quantum Effects of Neutron Scattering on Indistinguishable Particles

A recent paper by Matsumoto et. al [1] revitalizes the discussion of neutron scattering on indistinguishable particles, started in 2000 by Karlsson and Lovesey [2]. In a QENS measurement, Matsumoto et al. showed that the proton entanglement created in scattering on SiH2 (deposited on Si-surfaces) changes the conditions for vibrational excitations of the SiH2 “molecules”; the second scissor mode at 226 meV was strongly reduced compared to the first one at 113 meV. The present note will discuss the selection rules for vibrational excitations when the proton pairs are quantum entangled during scattering, and relate them to the reduced Compton cross-sections for such proton pairs, first discussed theoretically in [2]. It is well known that in the collision of two particles of the same kind, like in electron-electron scattering, their space and spin states become entangled, which leads to interference terms in the cross-section (see Schiff [3], Ch. 6). But the same is valid also for two or more identical particles of any kind which are interacting coherently with a neutron or an X-ray photon in scattering experiments (measurement-induced entanglement). In QNES as well as in Compton scattering, the coherence volume Vcoh = lx × ly × lz contains more than one particle if the energy resolution (determining lz) is high and the detector solid angles (determining lx and ly) are small enough. For the simplest case of only two particles a and b within Vcoh, the initial state of the scattering system can be taken as [[2],