Momentum and Energy Dependent Resolution Function of the ARCS Neutron Chopper Spectrometer at High Momentum Transfer: Comparing Simulation and Experimen

Inelastic neutron scattering at high momentum transfers (i.e. $Q\ge20$ {\AA}) or DINS provides direct observation of the momentum distribution of light atoms, making it a powerful probe for studying single-particle motions in liquids and solids. The quantitative analysis of DINS data requires an accurate knowledge of the instrument resolution function $R_{i}({Q},E)$ at each $Q$ and energy transfer $E$, where the label $i$ indicates whether the resolution was experimentally observed $i={obs}$ or simulated $i=sim$. Here, we describe two independent methods for determining the total resolution function $R_{i}({Q},E)$ of the ARCS neutron instrument at the Spallation Neutron Source, Oak Ridge National Laboratory. The first method uses experimental data from an archetypical system (liquid $^4$He) studied with DINS, which are then numerically deconvoluted using its previously determined intrinsic scattering function to yield $R_{obs}({Q},E)$. The second approach uses accurate Monte Carlo simulations of the ARCS spectrometer, which account for all instrument contributions, coupled to a representative scattering kernel to reproduce the experimentally observed response $S({Q},E)$. Using a delta function as scattering kernel, the simulation yields a resolution function $R_{sim}({Q},E)$ with comparable lineshape and features as $R_{obs}({Q},E)$, but somewhat narrower due to the ideal nature of the model. Using each of these two $R_{i}({Q},E)$ separately, we extract characteristic parameters of liquid $^4$He such as the intrinsic linewidth $\alpha_2$ (which sets the atomic kinetic energy $\langle K\rangle\sim\alpha_2$) in the normal liquid and the Bose-Einstein condensate parameter $n_0$ in the superfluid phase. The extracted $\alpha_2$ values agree well with previous measurements, independently of which $R_i(Q,y)$ is used to analyze the data.