[Paper Review] Coherent Neutron Scattering in Polycrystalline Deuterium and its Implications for Ultracold Neutron Production

C. M. Lavelle, D. J. Salvat+2 more|arXiv (Cornell University)|May 6, 2010

Atomic and Subatomic Physics Research4 references3 citations

TL;DR

This paper presents a first-principles calculation of neutron scattering cross-sections in polycrystalline ortho-D₂, incorporating coherent scattering, molecular rotations, and phonon dynamics via a Monte Carlo simulation with a realistic force tensor. It shows that ultracold neutron (UCN) upscattering cross-sections are 2–4 times smaller than previous incoherent approximation predictions, significantly revising estimates for UCN source design.

ABSTRACT

This paper presents a calculation of the neutron cross-sections in solid materials (used in practical neutron sources) with a large coherent scattering contribution. In particular, the dynamic structure function S(Q, $ω$) of polycrystalline ortho-D$_2$ is evaluated using a Monte-Carlo calculation that performs an average over scattering angles relative to crystal axes in random orientations. This method uses an analytical dispersion function with force constants derived from neutron scattering data of single crystal D$_2$ in the framework of an axially symmetric force tensor. The resulting two dimensional map of S(Q, $ω$) captures details of the phonon branches as well as the molecular rotations, that can be compared directly to data from inelastic neutron scattering on polycrystalline D$_2$. This high resolution information is used to calculate the absolute cross-sections of production and upscattering loss of ultracold neutron (UCN). The resulting scattering cross-sections are significantly different, especially for UCN upscattering, from the previous predictions using the approach centered on the incoherent approximation.

Motivation & Objective

• To address the limitations of the incoherent approximation (IA) in modeling neutron scattering in solid deuterium, especially for ultracold neutrons (UCN).
• To incorporate coherent scattering, molecular rotations, and collective excitations (phonons) into a unified scattering model for polycrystalline ortho-D₂.
• To calculate accurate absolute cross-sections for UCN production and upscattering, critical for optimizing neutron source design.
• To resolve discrepancies between experimental UCN yield data and prior theoretical predictions, particularly at temperatures above 10 K.

Proposed method

• A Monte Carlo simulation computes the dynamic structure factor S(Q, ω) by averaging over random crystal orientations and scattering angles relative to crystal axes.
• An axially symmetric force tensor is derived from neutron scattering data on single-crystal D₂, enabling realistic phonon dispersion modeling.
• The model includes coherent inelastic scattering, incoherent scattering, and rotational excitations governed by spin statistics and Fermi-Dirac statistics.
• The full scattering kernel is used in a Monte Carlo transport code to simulate neutron energy downscattering and upscattering in solid D₂.
• The model is validated by comparing simulated S(Q, ω) maps to experimental inelastic neutron scattering data on polycrystalline D₂.
• UCN upscattering cross-sections are extracted by fitting simulated UCN yields to experimental data, with results compared to the incoherent approximation.

Experimental results

Research questions

• RQ1 How does coherent scattering in polycrystalline ortho-D₂ affect the dynamic structure factor S(Q, ω) and the resulting neutron scattering cross-sections?
• RQ2 What is the impact of molecular rotations and phonon modes on ultracold neutron upscattering in solid deuterium?
• RQ3 How do the full model predictions for UCN upscattering cross-sections compare to those from the widely used incoherent approximation?
• RQ4 Why do experimental UCN yield data show a steeper temperature dependence above 10 K than predicted by the incoherent model?
• RQ5 To what extent do coherent scattering effects alter neutron moderation and phase space compression in solid D₂ moderators?

Key findings

• The full model accurately reproduces the detailed structure of S(Q, ω) in polycrystalline D₂, including phonon branches and molecular rotational modes.
• UCN upscattering cross-sections in solid D₂ are reduced by a factor of 2 to 4 compared to predictions from the incoherent approximation across the temperature range of interest.
• The incoherent approximation is excluded at the 2σ level or higher for temperatures above 10 K, where upscattering cross-sections exceed 1 barn.
• Experimental data from the FP12, PSI, and UCNA experiments agree best with simulations using the full model's upscattering cross-sections, not the incoherent approximation.
• The discrepancy in temperature dependence observed in LANL and Mainz experiments is attributed to vapor-phase upscattering in windowless UCN guides, not bulk material properties.
• The developed Monte Carlo algorithm is generalizable to other materials with significant coherent scattering, such as 4He, O₂, and N₂, provided their quasi-particle dispersion is known.