Anomalous neutron scattering from hydrogen

• Published in: Journal of physics. Condensed matter 2006-06, Vol.18 (23), p.5291-5301
• Main Authors: Cowley, R A, Mayers, J
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Infrared, submillimeter wave, microwave and radiowave instruments, equipment and techniques; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Physics
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/0953-8984/18/23/003

The intensity of the high-energy neutron scattering from hydrogen suggests that the cross-section is smaller than expected from conventional scattering theory. There have been several suggestions for the origin of this discrepancy including quantum entanglement, the breakdown of the Born-Oppenheimer approximation and experimental error but the situation is still not resolved. In this paper we re-examine the analysis of the experimental data and show that it can only be performed if we assume the validity of the impulse approximation and conventional scattering theory. This is because the integral over energy of the scattering function along the constant scattering angle trajectory diverges, in principle, for all scattering angles. This result formally invalidates the procedure normally used for extracting the experimental intensity and calculating the zeroth and first moments of S(Q,D*w). We propose that a less assumption dependent way of obtaining the intensity is to combine the data from several individual detectors to produce a map of S(Q,D*w) and then to numerically integrate this along lines of constant wavevector to obtain the moments, which can then be compared directly with scattering theory without the use of the impulse approximation. We also consider two approximate analysis methods that use the impulse approximation. The one that assumes the validity of the y-scaling impulse approximation is the more satisfactory. We apply both methods to analyse some recent experimental data on polythene, and the results show that the hydrogen scattering is 20% less than expected. We then finally show that experiment and theory can be reconciled if the monitor detector efficiency is energy dependent and suggest that this or possibly a breakdown of the Born-Oppenheimer approximation coupled with a careful analysis, as described above, could account for the discrepancy between theory and experiment.