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2 results

  • 13 - Many-Electron Systems

  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book:
    Quantum Mechanics in Nanoscience and Engineering
    Published online:
    11 May 2023
    Print publication:
    01 June 2023, pp 200-236

  • Summary

    The foundations for understanding the electronic structure of many-electron atoms are introduced. We start from the discovery of the spin and introduce spin operators. The spin existence is shown to “upgrade” the state of single particles into a product space with the spin subspace, and to impose constraints on states of identical particles, which must be symmetric (bosons) or antisymmetric (fermions) under particle transpositions. The many-electron state in the atom is therefore approximated as an antisymmetrized products (Slater determinant) of single-electron states (spin-orbitals). The variationally optimal orbitals are shown to be solutions to the Hartree–Fock equations, and the assignment of electrons to these orbitals in the atomic ground state reflects the Pauli exclusion and Aufbau principles, thus explaining the trends in the periodic table of the elements in terms of their electronic configurations. Special attention is given to two-electron systems, demonstrating the exchange stabilization of triplet versus singlet states (Hund’s rule).

  • Spin-Dependent Nonlinear Contrast Transfer in Transmission Electron Microscopy

  • Markus Lentzen
  • Journal:
    Microscopy and Microanalysis , FirstView
    Published online by Cambridge University Press:
    14 September 2022, pp. 1-9

  • In this study, the spin-dependent nonlinear contrast transfer in transmission electron microscopy is derived from the eikonal expansion of the Dirac equation. The transmission cross-coefficient of the standard imaging theory is amended by a spin-dependent factor, whose effect is investigated for single scattering in the object by an electrical field under polarized and unpolarized illumination, and it is illustrated with numerical results and plots for a kinetic energy of 80 keV. The resulting image displacement and image convolution increase with decreasing kinetic energy but are always smaller than a wavelength. General features of the cross-coefficient are discussed to identify favorable conditions for the measurement of the small spin effects, possibly in an unmodified instrument.