Incoherent approximation for neutron up-scattering cross sections and its corrections for slow neutrons and low crystal temperatures

TL;DR

This paper extends the incoherent approximation for neutron up-scattering cross sections to slow neutrons at low temperatures, providing more accurate calculations for solid ortho-deuterium relevant to ultracold neutron experiments.

Contribution

It introduces corrected formulas for the incoherent approximation applicable to slow neutrons and low temperatures, specifically for solid ortho-deuterium, improving accuracy over previous models.

Findings

Incoherent approximation overestimates cross sections by a factor of 2 to 5 for UCN in sD₂.

The extended corrections align well with Monte Carlo simulations based on the dynamic structure function.

Provides accessible methods for calculating up-scattering cross sections in ultracold neutron research.

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$_2$.