Several recent experiments on liquid and solid samples containing protons or deuterons show an interesting anomaly, which is a shortfall in the intensity of energetic neutrons scattered by the samples. Previously we demonstrated that quantum correlations in the spatial and spin degrees of freedom of the hydrogen isotopes lead to entanglement in scattering and a reduction in the scattered intensity. The viability of short-lived quantum correlations as the cause of the observed anomalies is further explored and found to be entirely feasible. General features of the basic premiss, that quantum entanglement reduces the scattered signal, are discussed and the interpretation of the neutron scattering experiments is set in context to related work on other systems. For the experiments in question, the duration of a scattering event, τ s , is a fraction of a femtosecond which is extremely short compared to solid-state relaxation times. Increasing τ s , by suitably changing experimental conditions, restores the intensity to the standard value calculated from the single atom cross-section and concentration of particles. Our physical picture of the restoration is evolution with increasing τ s from a pure state of the particles (described by a wavefunction) to a mixed state (described by a density matrix) that is created, through decoherence, by steadily engaging the solid-state environment of the particles.
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 ${10}^{\ensuremath{-}16}--{10}^{\ensuremath{-}15}\mathrm{s}$ 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 nonequivalent 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.
Abstract Quantum entanglement in scattering processes has most often been treated in general terms only. A few examples of detailed calculations exist for atomic systems but for nuclear processes it is an almost unexplored area, although it may be important for interpretation of some measured quantities. The present treatment is a study of the time-development of the deuteron-like compound state created in the n – p scattering process. The increase and decay of neutron–proton entanglement in this state is calculated for low transferred momenta over the atto-second range. It is well known that the very high value for the bound proton cross sections ( σ = 81.9 barns) is caused by a specific feature in the deuteron, a virtual 0+ state close to its binding level. In scattering this state causes a negative phase shift δ s in the outgoing neutron wave function, increasing linearly with the transferred momentum. This phase shift is produced during a short-lived virtual energy transfer Δ E in exciting the 0+ state and Δ E is estimated here from the ratio of the phase shift δ observed and the time Δ t it takes to create the entanglement. It is further argued that the nuclear excitation decreases after the n – p encounter in proportion to the degree of n – p entanglement calculated, i.e. as long as the scattering state has deuteron characteristics. This phase shift is neglected in low energy neutron scattering text-books (which are based on the Fermi pseudo potential) and may be negligible for thermal neutron scattering, but will be important already at epithermal energies (0.1–1 eV). The phase shift has measurable consequences in interpretation of INS (inelastic neutron scattering) since its associated energy shift increases quadratically with the transferred momentum. It explains quantitatively certain anomalies found in scattering on water, where water vibration modes are excited far below the expected transferred momentum limit. This paper ends with a short discussion about quantum entanglement in scattering processes in general, with the present example as a starting point.
We present neutron-scattering measurements of the momentum distribution of liquid $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ mixtures. The experiments were performed at wave vectors
Q, $26\ensuremath{\leqslant}Q\ensuremath{\leqslant}29\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$, on the MARI time-of-flight spectrometer at the ISIS Facility, Rutherford Appleton Laboratory, a spallation neutron source. Mixtures with
3He concentrations
x between 0 and 20% were investigated both in the superfluid and normal phases. From the data, we extract the Bose-Einstein condensate fraction
n0 and the momentum distributions of
3He and
4He atoms. We find that
n0 increases somewhat above the pure
4He value when
3He is added; e.g., from ${n}_{0}=(7.25\ifmmode\pm\else\textpm\fi{}0.75)%$ at
x=0 to $(11\ifmmode\pm\else\textpm\fi{}3)%$ at
x=15−−20. This agrees with predictions but is less than the only previous measurement. We find a
4He kinetic energy
K4 for pure
4He that agrees with previous determinations.
K4 decreases somewhat with increasing
3He concentration, less than observed previously and found in early calculations but in agreement with a more recent Monte Carlo calculation. The
3He response is not well reproduced by a Fermi-gas momentum distribution,
n(k). Rather an
n(k) having a small step height at the Fermi surface and a substantial high-momentum tail characteristic of a strongly interacting Fermi liquid provides a good fit. This
n(k) is consistent with calculated
n(k). Thus agreement between theory and experiment is obtained comparing
n(k) in contrast to earlier findings based on comparing calculated and observed
3He kinetic energies.
We present neutron scattering measurements of the momentum distribution of liquid
3He-
4He mixtures. The experiments were performed at wavevectors
Q, 26
≤ Q ≤ 29 {Å
−1}, on the MARI time-of-flight spectrometer at the ISIS Facility, Rutherford Appleton Laboratory, a spallation neutron source. Mixtures with
3He concentrations
x between 0 and 20% were investigated both in the superfluid and normal phases. From the data, we extract the Bose-Einstein condensate fraction
n0 and the momentum distributions of
3He and
4He atoms. We find that
n0 increases somewhat above the pure
4He value when
3He is added; e.g from
n0=(7.25±0.75) at
x= 0 to
(11±3) at
x= 15-20%. This agrees with predictions but is less than the only previous measurement. We find a
4He kinetic energy
K4 for pure
4He that agrees with previous determinations.
K4 decreases somewhat with increasing
3He concentration, less than observed previously and found in early calculations but in agreement with a more recent Monte Carlo calculation. The
3He response is not well reproduced by a Fermi gas momentum distribution,
n(k). Rather an
n(k) having a small step height at the Fermi surface and a substantial high momentum tail characteristic of a strongly interacting Fermi liquid provides a good fit. This
n(k) is consistent with calculated
n(k). Thus agreement between theory and experiment is obtained comparing
n(k) in contrast to earlier findings based on comparing calculated and observed
3He kinetic energies.