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,ω;$E_0$) which allows a fast and reliable evaluation of cross sections. Unlike the dynamic structure factor (or scattering function) S(Q→,ω) in thermal neutron-scattering theory, T(Q,ω;$E_0$) 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→,ω) (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,ω;$E_0$) 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.