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Trends in Physical Chemistry   Volumes    Volume 22 
Scattering by atoms in zero-point states: from Debye and Waller to present days
Erik B. Karlsson
Pages: 1 - 15
Number of pages: 15
Trends in Physical Chemistry
Volume 22 

Copyright © 2022 Research Trends. All rights reserved

Ivar Waller published in 1923 a calculation of the effect of thermal vibrations of atoms on the interference in X-ray scattering. It was an extension and generalized treatment of the work by Peter Debye, first published in 1913. These two papers explained the reduction of peak intensities in X-ray diffraction. Both used the Planck distribution of oscillation frequencies based on the old quantum theory for calculating the mean square vibrational amplitudes of the scattering atoms. A zero-point residual term in the Planck formula was considered hypothetical and was neglected, but after evidence for zero-point effects had been found in the rotational energy of hydrogen molecules and Heisenberg had introduced his intrinsic uncertainties in positions and momenta, its contributions to the D-W factors were searched for in crystallographic data. With the increasing availability of low temperature scattering data in the middle of last century they were gradually observed and tabulated for atoms in different types of crystals. Scattering on hydrogen (H) represents an extreme case where zero-point motion is the dominating contribution to D-W factors. But observation of diffraction is limited both with X-rays (low coherent cross-section) and neutrons (largely incoherent due to spin-flip scattering). Therefore, its effect on H-scattering could first be studied in detail only in experiments with epithermal neutrons, starting in the 1990s. The most recent manifestation of zero-point effects is the so-called ‘hydrogen anomaly’ in Compton scattering, now understood as a reduction of neutron cross-section when it scatters on indistinguishable protons having inherent momentum uncertainties. The resulting broad distribution of scattering phases leads to a strong cross-section reduction when only a few particles are seen by each incoming neutron. The decay of the H-anomaly can be used to study chemical processes on the femtosecond scale.
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