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

Area of Science:

• Materials Science
• Condensed Matter Physics
• Neutron Scattering Techniques

Background:

• Multiple scattering in small-angle neutron scattering (SANS) complicates structural analysis, especially for dense or highly scattering materials.
• Existing methods often rely on integral transforms or model-based assumptions, limiting their applicability.
• Accurate interpretation of SANS data requires effective correction of scattering artifacts.

Purpose of the Study:

• To develop a novel, model-agnostic framework for correcting multiple scattering in SANS data.
• To enable accurate reconstruction of the primary scattering intensity, improving structural interpretation.
• To provide a stable and versatile method applicable across different neutron scattering facilities and sample conditions.

Main Methods:

• Development of a finite-dimensional spectral desmearing framework.
• Expansion of primary intensity in an orthonormal basis, simplifying convolution to recursive tensor contraction.
• Direct evaluation of the multiple-scattering series within a finite-dimensional basis representation.

Main Results:

• The framework demonstrates stable forward-inverse mapping between apparent and primary spectra.
• Numerical tests confirm convergence and accurate recovery of single-scattering intensity.
• Successful application to SANS data from multiple facilities (SNS, HFIR, ILL) across various transmission levels, including challenging samples.

Conclusions:

• The developed method provides a robust and stable approach for multiple-scattering correction in SANS.
• It enables quantitative reconstruction of the underlying primary spectrum, enhancing data reliability.
• This model-agnostic framework facilitates consistent structural interpretation across diverse SANS instruments and experimental regimes.