Surface charges and quantum reflection of hydrogen-isotope beams at grazing incidence
Abstract
Experiments with cryogenic beams of hydrogen isotopes (hydrogen (H), deuterium (D), and tritium (T)) can be used to study quantum reflection from solid dielectric mirrors. Most dielectric surfaces carry trapped electric charges whose field polarizes the incident atom. We study theoretically how such charges, distributed randomly, in clusters, with compensation over a finite length, or in order, change specular reflection and diffuse scattering of H, D, and T at grazing incidence on typical dielectric mirrors (SiO2/Si and MgF2), for longitudinal velocities of 100--300~m/s and normal velocities of 3--100~cm/s which might become available soon in grazing incidence experiments. Starting from the exact coupled-channel equations, we show that the specular wave feels only the laterally averaged polarization potential, which is fixed by the structure factor of the charges and, for uncorrelated charges, is an inverse-square tail −C2/z2. The exact solution replaces the linear threshold law 1−Rr∝vperp by the fractional power vperp2ν, ν=(1/4−ζ)1/2, with the coupling ζ∝ C2; for weak coupling, this appears as a logarithmic velocity dependence, and for ζ>1/4, the reflection coefficient oscillates log-periodically. At the surface charge density of 1012 cm−2, absorption increases by up to 26\% for SiO2/Si and by a factor of two to three for MgF2; the effect increases with atomic mass, saturates for compensated charges, and is accompanied by diffuse scattering below 10−3 of charge-induced loss. We also formulate the condition of complete absorption at the solid surface.
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BibTeX
@misc{voronin2026surface,
title = {{Surface charges and quantum reflection of hydrogen-isotope beams at grazing incidence}},
author = {A. Yu. Voronin and V. V. Nesvizhevsky},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03460},
eprint = {2611.03460},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03460},
}
RIS
TY - UNPB
TI - Surface charges and quantum reflection of hydrogen-isotope beams at grazing incidence
AU - A. Yu. Voronin
AU - V. V. Nesvizhevsky
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03460
UR - https://arxiv.org/abs/2611.03460
AB - Experiments with cryogenic beams of hydrogen isotopes (hydrogen (H), deuterium (D), and tritium (T)) can be used to study quantum reflection from solid dielectric mirrors. Most dielectric surfaces carry trapped electric charges whose field polarizes the incident atom. We study theoretically how such charges, distributed randomly, in clusters, with compensation over a finite length, or in order, change specular reflection and diffuse scattering of H, D, and T at grazing incidence on typical dielectric mirrors (SiO_2/Si and MgF_2), for longitudinal velocities of 100--300~m/s and normal velocities of 3--100~cm/s which might become available soon in grazing incidence experiments. Starting from the exact coupled-channel equations, we show that the specular wave feels only the laterally averaged polarization potential, which is fixed by the structure factor of the charges and, for uncorrelated charges, is an inverse-square tail −C_2/z^2. The exact solution replaces the linear threshold law 1−Rr∝vperp by the fractional power vperp^2ν, ν=(1/4−ζ)^1/2, with the coupling ζ∝ C_2; for weak coupling, this appears as a logarithmic velocity dependence, and for ζ>1/4, the reflection coefficient oscillates log-periodically. At the surface charge density of 10^12 cm^−2, absorption increases by up to 26\% for SiO_2/Si and by a factor of two to three for MgF_2; the effect increases with atomic mass, saturates for compensated charges, and is accompanied by diffuse scattering below 10^−3 of charge-induced loss. We also formulate the condition of complete absorption at the solid surface.
ER -