An algebraic convolution formulation for multiple-scattering correction in small-angle neutron scattering

Journal Article · Fri May 01 00:00:00 UTC 2026 · The Journal of Chemical Physics

DOI: https://doi.org/10.1063/5.0331405 · OSTI ID:3364700

Tung, Chi-Huan  ^[1]; Huang, Guan-Rong ^[2]; Wang, Yangyang  ^[1]; Carrillo, Jan Michael  ^[1]; Kim, Tae-Hwan ^[3]; Astner, Anton F  ^[1]; Porcar, Lionel ^[4]; Shinohara, Yuya  ^[1]; Shang, Yingrui  ^[1]; Rother, Gernot  ^[1]; Do, Changwoo  ^[1]; Chen, Wei-Ren  ^[1]

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1. ORNL
2. National Tsing Hua University, Taiwan
3. Korea Atomic Energy Research Institute (KAERI)
4. Institut Laue-Langevin (ILL)

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. The method provides a stable, model-agnostic framework for multiple-scattering correction in SANS and enables consistent structural interpretation across instruments and scattering regimes.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 3364700
• Journal Information: The Journal of Chemical Physics, Journal Name: The Journal of Chemical Physics Vol. 164
• Country of Publication: United States
• Language: English