A Novel Pseudo-Spectral Time-Domain Theory of Magnetic Neutron Scattering Illustrated Using A Uniformly Magnetized Sphere

TL;DR

This paper introduces a new pseudospectral-time-domain numerical method for simulating magnetic neutron scattering, accounting for spin interactions, and demonstrates its application to a uniformly magnetized sphere, advancing neutron imaging analysis.

Contribution

The paper develops a comprehensive PSTD-based numerical approach for magnetic neutron scattering that includes spin dynamics, which was not previously available.

Findings

PSTD method accurately models neutron spin evolution in magnetic fields.

Comparison with Born-approximation validates the new method.

Provides a foundation for advanced neutron imaging techniques.

Abstract

A universal numerical method is developed for the investigation of magnetic neutron scattering. By applying the pseudospectral-time-domain (PSTD) algorithm to the spinor version of the Schr\"odinger equation, the evolution of the spin-state of the scattered wave can be solved in full space and time. This extra spin degree of freedom brings some unique new features absent in the numerical theory on the scalar wave scatterings [1]. Different numerical stability condition has to be re-derived due to the coupling between the different spin states. As the simplest application, the neutron scattering by the magnetic field of a uniformly magnetized sphere is studied. The PSTD predictions are compared with those from the Born-approximation. This work not only provides a systematic tool for analyzing spin-matter interactions, but also builds the forward model for testing novel neutron imaging methodologies, such as the newly developed thermal neutron Fourier-transform ghost imaging.