Abstract
The incoherent approximation (IA) is often used for calculating the one-phonon inelastic neutron scattering cross section for arbitrary solids. It is valid for thermal neutrons but for slow neutrons it requires a correction, which is significant for isotopes that are strong coherent scatterers. In this article, we present the extension of the Placzek--Van Hove corrections for slow neutrons in the limit of low temperatures using the example of solid \emph{ortho}-deuterium (sD$_2$). Our approach yields realistic one-phonon up-scattering cross sections for sD$_2$ and shows the IA to be a factor of 2 to 5 too high for ultracold neutron (UCN) up-scattering in sD$_2$. Our calculations are compared with previously published Monte Carlo calculations of the one-phonon cross section based on the dynamic structure function $S(q,\omega)$ of polycrystalline \emph{ortho}-deuterium and are found to be consistent with them. Furthermore, we provide the means for easily replicable calculations of the one-phonon up-scattering cross sections of solid \emph{ortho}-deuterium for slow neutrons. These should from now on be used in calculations and simulations of UCN scattering in sD$_2$.
Highlights
The slowest neutrons—ultracold neutrons (UCNs)—can be produced by various methods
We present the extension of the Placzek–Van Hove corrections for slow neutrons in the limit of low temperatures using the example of solid ortho-deuterium
We provide the means for replicable calculations of the one-phonon up-scattering cross sections of solid ortho-deuterium for slow neutrons
Summary
The slowest neutrons—ultracold neutrons (UCNs)—can be produced by various methods. One of them is the superthermal production process, in which a cold neutron excites a phonon or rotational transition in a solid or liquid converter medium and becomes so slow that it falls in the velocity range of UCNs, from 0 to about 10 m/s. We present such corrections for solid ortho-deuterium in the UCN limit and show that the uncorrected IA, which has hitherto been used to explain the entire UCN scattering cross section [5], is a factor of 2–5 too high. This finding sheds new light on the existence of crystal defects in sD2 [6], which must be taken into account in the design and upgrade of UCN converters based on sD2
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