Slow-neutron scattering by molecular gases: A synthetic scattering function

Abstract

Motivated by the practical requirements of reactor-physics calculations as well as the necessity of applying inelasticity corrections to the observed spectrum in neutron-diffraction work on molecular gases and liquids, I have developed a synthetic scattering function T(Q,\ensuremath{\omega};${E}_{0}$) which allows a fast and reliable evaluation of cross sections. Unlike the dynamic structure factor (or scattering function) S(Q\ensuremath{\rightarrow},\ensuremath{\omega}) in thermal neutron-scattering theory, T(Q,\ensuremath{\omega};${E}_{0}$) does not contain a detailed description of the atomic motions in the molecular units nor correlation between pairs, but rather it is intended to reproduce satisfactorily some integral properties of S(Q\ensuremath{\rightarrow},\ensuremath{\omega}) (the self-component). However, the main characteristics of the molecular dynamics are retained through the introduction of an effective mass, and temperature and vibrational factors which depend on the incident neutron energy ${E}_{0}$. This is achieved by the use of the Krieger-Nelkin procedure for orientational averages and by the introduction of ``switching functions'' P(${E}_{0}$) which define the variation with ${E}_{0}$ of the above effective quantities. A very simple form is thus obtained for T(Q,\ensuremath{\omega};${E}_{0}$) which yields analytic expressions for the scattering kernel and the total cross section. To gauge the merits and limitations of this prescription I compared its predictions with experiments and other theories in the following cases involving hydrogen-containing molecules: (i) the total cross section of ${\mathrm{H}}_{2}$O and ${\mathrm{C}}_{6}$${\mathrm{H}}_{6}$; (ii) the scattering cross sections (angular distributions) of ${\mathrm{H}}_{2}$O and ${\mathrm{D}}_{2}$O at several energies; and (iii) the average of the cosine of the scattering angle in ${\mathrm{H}}_{2}$O. It is concluded from the comparisons that the model works in a very satisfactory way. It is anticipated that the present prescription could be a useful tool for the evaluation of departures from elasticity in time-of-flight experiments, where a wide range of neutron wavelengths may contribute at each channel in the observed diffraction spectrum.