Chapter 5 - Atomic Structure and Lifetimes
The Intermediate Coupling Model (Multielectron Atoms)

LS Coupling Notation (Sect. 5.1)

  • Spectroscopic nomenclature

    • Two-valence-electron systems (Sect. 5.2)

    Solution of the unperturbed problem (Sect. 5.2.1)

  • Separation of uncoupled Schrödinger Equations
  • Symmetric and antisymmetric products
  • Spin/space antisymmetrization
  • The exclusion principle

    • Consequences of exchange symmetry for equivalent electrons (Sect. 5.2.2)

  • Terms ruled out by exclusion
  • Carbon example

    • Antisymmetrization of a multielectron system (Sect. 5.5)

  • The Slater determinant
  • Paper size needed to specify wave functions

    • Electrostatic corrections: the Slater parameters (Sect. 5.2.3)

  • Perturbed spin/space wavefunctions
  • Direct and exchange electron-electron
  • Two-center expansion
  • Fk and Gk expansions
  • Invoke angular orthogonality

    • Calculation of G1(sp) (Sect. 5.2.5)

  • Hydrogenic wave functions
  • Gamma functions
  • Values for G1(ns, np)
  • Maple program

    • Spin-orbit interaction (Sect. 5.2.4)

  • Electron-electron and spin-orbit perturbations
  • Spin-orbit coupling

    • Example: nsn'p and nsn'p5 configurations (Sect. 5.2.5)

  • Off-diagonal matrix
  • Diagonalization of 2x2 matrices
  • Application to sp
  • Term splitting
  • Relate to measured splittings
  • sp and p5s IC diagrams
  • Mixing angles as a function of Z
  • Log-log plot

    • Screening parametrization of the Slater parameters (Sect. 5.3)

  • Nuclear charge scaling
  • Edlén's linearization
  • Isoelectronic plot
  • Homologous representation

    • Example: p2 configuration (Sect. 5.2.6)

  • Off-diagonal matrix
  • Mixing angles
  • Diagonalized solution
  • Term splitting
  • p2 and p4 IC diagrams
  • Transitions


    Chapter 1
    Chapter 2
    Chapter 3
    Bridge A
    Chapter 4
    Bridge B

    Homepage







    Deferred Topics

    Branching fractions and g-factors

  • Eigenvectors
  • Energy level diagram
  • SE vs measurement
  • IC g-factors

    Multiple Electron Systems

    Example: p3 configuration

  • Matrix diagonalization
  • Inversion of coefficients from known roots
  • Application
  • Matrices
  • p3 IC diagram

    Intermediate coupling

  • Gyromagnetic ratios
  • sp case
  • Application
  • Limiting cases
  • nsnp limits
  • Radial and angular integrals
  • Relate to measured splittings
  • Semiempirical parametrization
  • One-to-one reduction
  • Mixing angles as a function of Z
  • Log-log plot
  • Sm sequence

    • Example 2: p2 configuration

  • The Pb sequence

    • Semiempirical mapping of Slater quantities

    Forbidden transitions
    Sm construction

    Mixing Angle Formulations of M1 Line Strengths and E1 Branching Fractions

    M1 line strengths
    Shortley-Pasternack formula
    Applications
    Mixed transitions
    p2 case
    sp case
    Pb sequence mixing angles
    Eigenvectors
    Application

    Complex atoms

  • Periodic table
  • Penetration of s orbitals
  • Electron configurations
  • More electron configurations