Using the dynamical proton (pseudospin)-heavy ion (lattice) model and the Green function formalism, the effective total differential cross sections for both coherent and incoherent neutron scattering are derived. The characteristic interference effects due to both tunnelling of light ions (protons) and mixed proton-heavy ion scattering processes are expressed by corresponding pseudospin and pseudospin-phonon form-factors. The scattering intensity pattern in antiferroelectric phase is accomplished by polar modulation effects and additional interference in the cross sections. The theoretical predictions are related to experimental studies of ADP, Rochelle salt and NaNO 2 . Their possible application to test the coexistence of (anti)ferroelectric and superconducting phases in high-T c copper-oxide superconductors is briefly discussed too.