Neutron Compton scattering by proton and deuteron systems with entangled spatial and spin degrees of freedom

Several recent experiments on liquid and solid samples containing protons or deuterons have shown an interesting anomaly, which is apparently absent when the hydrogen isotopes are replaced by heavier particles. The anomaly is a shortfall in the intensity of energetic neutrons scattered by the samples; specifically, the intensity per hydrogen isotope in bulk samples is smaller than the intensity for total scattering by an isolated hydrogen isotope. Short-lived correlations in the spatial and spin degrees of freedom of the hydrogen isotopes have been proposed as an explanation of the anomaly. The correlations involve entanglements of the degrees of freedom created by the requirements of quantum mechanics applied to identical particles. By using energetic neutrons to perform Compton scattering experiments on the hydrogen isotopes the time-scale of the experimental probe covers the region of 10-16 - 10-15 s where entangled states might still be expected to survive. The proposed explanation is pursued here by reporting the cross-section for Compton scattering, also known as deep inelastic-scattering, by two identical nuclei occupying non-equivalent states. The model reproduces the observed dependence of the cross-section on energy transfer, in which intensity accumulates at the recoil energy of a single nucleus. Several features of the model demand that the intensity at the recoil energy is indeed less than the intensity for total scattering by an isolated nucleus. Although the pair approximation used here is unquestionably a first approximation to real many-body entanglements it is a compelling explanation of all the observations, including the restoration of the normal cross-section at longer observation-times achieved by moving to longer scattering-times. (author)