DOE OSTI · 3364700
An algebraic convolution formulation for multiple-scattering correction in small-angle neutron scattering
Abstract
Multiple scattering in small-angle neutron scattering (SANS) redistributes spectral weight and distorts structural interpretation, particularly for thick or strongly scattering samples. We develop a finite-dimensional spectral desmearing framework that corrects multiple scattering without resorting to integral transforms or model-dependent extrapolation. The primary intensity is expanded in an orthonormal basis adapted to the isotropic transverse-momentum measure, under which convolution reduces to a recursive tensor contraction, allowing the Poisson-weighted multiple-scattering series to be evaluated directly in a finite-dimensional basis representation. This formulation yields a stable forward–inverse mapping between apparent and primary spectra. Numerical tests demonstrate convergence under repeated convolution and accurate recovery of the single-scattering intensity. Application to SANS measurements collected at multiple neutron facilities, including the Spallation Neutron Source, the High Flux Isotope Reactor, and the Institut Laue-Langevin, shows the quantitative reconstruction of the underlying primary spectrum across a wide range of transmission conditions, including strongly attenuating samples. Here, the method provides a stable, model-agnostic framework for multiple-scattering correction in SANS and enables consistent structural interpretation across instruments and scattering regimes.
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Tung, Chi-Huan [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)] (ORCID:0000000221972074), Huang, Guan-Rong [National Tsing Hua University, Hsinchu (Taiwan); National Center for Theoretical Sciences, Taipei (Taiwan)] (ORCID:0000000163939574), Wang, Yangyang [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)] (ORCID:0000000170429804), Carrillo, Jan-Michael [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)] (ORCID:000000018774697X), Kim, Tae-Hwan [Jeonbuk National University, Jeonju-si (Korea, Republic of)], Astner, Anton F. [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)], Porcar, Lionel [Institut Laue-Langevin (France)], Shinohara, Yuya [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)] (ORCID:000000018284751X), Shang, Yingrui [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)] (ORCID:0000000301743992), Rother, Gernot [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)] (ORCID:0000000349216294), Do, Changwoo [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)] (ORCID:0000000183588417), Chen, Wei-Ren [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)] (ORCID:0000000251920777). 2026-05-04. An algebraic convolution formulation for multiple-scattering correction in small-angle neutron scattering. https://doi.org/10.1063/5.0331405
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