Elastic electron-atom scattering in amplitude-phase representation with application to electron diffraction and spectroscopy

The amplitude-phase representation (APR) [W. E. Milne, Phys. Rev. 35, 863 (1930)] is applied to the relativistic radial Schroedinger equation corresponding to the Dirac equations with central potential. The initial conditions, hitherto unspecified, for the nonlinear second-order amplitude equation a...

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Bibliographic Details
Published in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2007-11, Vol.76 (19), p.195441, Article 195441
Main Author: Rundgren, J.
Format: Article
Language:English
Subjects:
AMPLITUDES
CENTRAL POTENTIAL
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CRYSTALS
DIRAC EQUATION
ELECTRON DIFFRACTION
ELECTRON SPECTROSCOPY
ELECTRON-ATOM COLLISIONS
ELECTRONS
ENERGY DEPENDENCE
EXCHANGE INTERACTIONS
Fysik
MUFFIN-TIN POTENTIAL
NATURAL SCIENCES
NATURVETENSKAP
NONLINEAR PROBLEMS
OXIDES
PHASE SHIFT
Physics
RELATIVISTIC RANGE
SCHROEDINGER EQUATION
SPHERES
WAVE FUNCTIONS
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Summary:The amplitude-phase representation (APR) [W. E. Milne, Phys. Rev. 35, 863 (1930)] is applied to the relativistic radial Schroedinger equation corresponding to the Dirac equations with central potential. The initial conditions, hitherto unspecified, for the nonlinear second-order amplitude equation at the finite radius of a muffin-tin (MT) sphere are established by a semiconvergent method. This opens the possibility of using APR for the calculation of electron scattering phase shifts with a finite MT radius as well as with a large atomic radius, whereby the first wave node is phase of reference equal to a multiple of {pi}, adding nothing to the phase shifts. Furthermore, APR is used for benchmarking wave functions obtained by ordinary differential equation integration of the Dirac equations up to high energy and high orbital quantum number. The present APR procedure is discussed with reference to earlier numerical methods. To complete the physical picture, the paper ends with a discussion on exchange-correlation dependent scattering potential in MT spheres of optimized radii, a crystal potential model whose dependence on radii and energy dependent inner potential has recently been corroborated by low energy electron diffraction in oxides with many atoms per unit cell.
ISSN:1098-0121
1550-235X
1550-235X
DOI:10.1103/PhysRevB.76.195441