Simulating quadrant detection of electron beam shifts using Particle and Heavy Ion Transport code System (PHITS)

Abstract

Beam shifts such as the Goos−Hänchen (GH) and Imbert−Fedorov (IF) effects describe nonspecular displacements of reflected beams that deviate from geometric optics predictions. While these effects have been widely studied with light, directly measuring electron beam shifts is still difficult because the shift is extremely small and hard to detect. We investigate whether a beam shift analog can emerge in a semi-classical framework using the Particle and Heavy Ion Transport code System (PHITS). We implement a θ−2θ scattering geometry with quadrant detection for a monoenergetic electron beam at 1.00 MeV and 10.0 MeV incident on silicon (Si) and gold (Au) slabs. We observe that the 〈y〉displacements remain negligible across all configurations, while the〈x〉displacements increases with tilt angle, ranging from 10⁻² cm at 15° to 10⁻¹ cm at 75°.  The largest displacement reaches −1.803 × 10⁻¹ cm for 1.00 MeV electrons in gold. Gold produces larger displacements than silicon at higher tilt angles, and agreement between electron-only and all-particle scoring modes suggest that the primary electrons drives the centroid shift. Fluence Φ across the quadrant detector remains on the order of 10⁻⁵ across all conditions and increases with tilt angle, with secondary particle contributions becoming more pronounced at 10.0 MeV. These results theoretically propose a measurable electronic analog of beam shift behavior within a quadrant detection framework and offer a semi-classical method to investigate centroid displacement in electron scattering.