Anomalous neutron scattering from hydrogen

Abstract

The intensity of the high-energy neutron scattering from hydrogen suggests thatthe cross-section is smaller than expected from conventional scattering theory.There have been several suggestions for the origin of this discrepancy includingquantum entanglement, the breakdown of the Born–Oppenheimer approximation andexperimental error but the situation is still not resolved. In this paper we re-examine theanalysis of the experimental data and show that it can only be performed if weassume the validity of the impulse approximation and conventional scatteringtheory. This is because the integral over energy of the scattering function alongthe constant scattering angle trajectory diverges, in principle, for all scatteringangles. This result formally invalidates the procedure normally used for extractingthe experimental intensity and calculating the zeroth and first moments ofS(Q,ω). We propose that a less assumption dependent way of obtaining the intensityis to combine the data from several individual detectors to produce a map ofS(Q,ω) and then to numerically integrate this along lines of constant wavevector to obtain themoments, which can then be compared directly with scattering theory without the use ofthe impulse approximation. We also consider two approximate analysis methodsthat use the impulse approximation. The one that assumes the validity of they-scaling impulse approximation is the more satisfactory. We apply both methods to analysesome recent experimental data on polythene, and the results show that the hydrogenscattering is 20% less than expected. We then finally show that experiment and theory canbe reconciled if the monitor detector efficiency is energy dependent and suggest that this orpossibly a breakdown of the Born–Oppenheimer approximation coupled with a carefulanalysis, as described above, could account for the discrepancy between theory andexperiment.