The neutron double differential cross-section of simple molecular fluids: refined computing models and nowadays applications

Abstract

A review of the available tools for the calculation of the neutron double-differential cross-section of fundamental molecules, such as hydrogen and methane, is reported here. The most common cases occurring in neutron data analysis are treated in detail with the aim of providing the reader with intelligible and efficient procedures. The utility nowadays of these kinds of computation are widely described, and applications discussed, with examples based on the comparison with experimental data. New advances and refinement/corrections of earlier work are given throughout the paper, as well as suggestions for practical implementation. Please note, a correction was made to this review (definition after equation (13)) on 10 November 2003

The static structure factor of hydrogen in the liquid state

“…A very good agreement was found with a path-integral Monte Carlo (PIMC) calculation performed with a realistic interaction potential, while the simpler Lennard-Jones model could be discriminated [5]. However, it nearly took another decade to obtain analogous results for the lighter isotope, H 2 , due to the much less favourable ratio of the coherent neutron scattering length to the incoherent one, and to the way they enter the expression for the inter-and intramolecular crosssection [6,7]. It is worth mentioning that the molecular H 2 and D 2 can be assumed to have the same electronic structure and, therefore, the same intermolecular potential, so that the differences in S(Q) are due to quantum effects related to the large mass ratio.…”

“…The static structure factor is then obtained from [12] IðQÞ ¼ A s;sc ðQÞuðQÞ½SðQÞ À 1; ð1Þ where I(Q) is the intermolecular intensity obtained from the fit, A s,sc is a Paalman and Pings attenuation coefficient [13], and u(Q) is the molecular form factor [6,7]. S(Q) is shown in Fig.…”

Neutron Brillouin scattering in simple liquids and the description of their collective dynamics

“…Then, the CM intermolecular dynamics can be extracted [7] to obtain the molecular analogue of S(Q,v) in monatomic fluids. From the experimental point of view, besides the rather large neutron scattering cross-sections of the C and D nuclei, one can also exploit the fact that no vibrational transitions are allowed at the above sample temperature with thermal neutrons and that the translational excitation energies are compatible with medium-resolution spectrometry.…”

Neutron study of non-Gaussian self dynamics in liquid parahydrogen

“…Taking into account that only the ground rotational and vibrational levels are thermally populated at the temperature of the liquid, and that no vibrational excitations are possible with the available neutron energy, the double-differential cross section for neutron scattering consists of replicas of S s (Q, ω) shifted by the rotational energies of the J → J transitions with odd J [28]. Due to the small moment of inertia of the molecule, these lines are well separated and only the most intense of them, the J = 0 → 1 transition corresponding to a shift ω 0→1 = 14.69 meV [29], is probed in the energy window of the experiment.…”

“…Here the factor a(Q) is a known, transition-specific, form factor [28]. Equation (10) allows for the extraction of S s (Q, ω) from an experimental set of constant-Q spectral intensity data, eliminating the rotational frequency shift, although the result remains broadened by the instrumental energy resolution function R(ω).…”