Chapter 5
The Intermediate Coupling Model
Notation (Sect. 5.1)
Spectroscopic nomenclature
Two electron systems (Sect. 5.2)
Wave Functions (Sect. 5.2.1)
Separation of uncoupled Schrödinger Equations
Symmetric and antisymmetric products
Perturbed spin/space wavefunctions
Direct and exchange electron-electron
Invoke angular orthogonality
Slater energies (Sect. 5.2.3)
F
k
and
G
k
expansions
Magnetic energies (Sect. 5.2.4)
Spin-orbit coupling
Matrix formulation
Off-diagonal matrix
Diagonalization of 2x2 matrices
Application to sp
Transformation formulation
Term splitting
Reduction of Slater parameters from data
Problem
Intermediate coupling
Example 1: sp configurations (Sect. 5.2.5)
sp
case
Representation
sp
and
p
5
s
IC diagrams
nsnp
limits
s
l
configuration
Generalized Landé rule
Hydrogenic calculation of
G
1
(2
s
,2
p
)
G
1
(2
s
,2
p
) (continued)
(continued)
Semiempirical formulation (Sect 5.3)
Edlén's parametrization
Relate to measured splittings
Isoelectronic plot
Problem: sp
Solution
Screening parametrization
Coefficients
Homologous representation
Exchange symmetries (Sect. 5.2.2)
The exclusion principle
Terms ruled out by exclusion
Carbon example
Example 2: p
2
configurations (Sect 5.2.6)
p
2
formulation
Diagonalized
Deduction of parameters
Problem
Solution
Splitting
Representation
p
2
and
p
4
IC diagrams
The Si sequence
Three electron systems (Sect 5.4)
Three open-shell p electrons
p
3
matrix diagonalization
Inversion of coefficients from known roots
Application
Matrices
LS
to
jj
p
3
matrix diagonalization
Slater determinant (Sect. 5.5)
Antisymmetrization: the Slater determinant
Paper size needed to specify wave functions
Chapt. 1
Chapt. 2
Chapt. 3
Chapt. 4
Chapt. 6
Chapt. 7
Chapt. 8
Chapt. 9
Homepage
Deferred Topics
Intermediate coupling amplitudes
LS and j coupling
Example 1: nsnl
Construction
(continued)
(continued)
Characterizing IC
Mixing angles
Generalized Landé by mixing angles
Semiempirical mapping of Slater quantities
Forbidden transitions
Sm construction
Gyromagnetic ratios
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
Self-consistent field methods
Self-consistent potential
(cont.)
(cont.)
PE of symmetric distribution
SCSCF
Koopman's theorem
(cont.)
Measurement of wavelengths and establishment of levels
Wavelength measurement
Establishing energy levels and uncertainties
Lithium-like quartets
F VII data
Ne VIII data
Measured wavelengths and uncertainties
Least squares constraints
Coefficients
Isoelectronic plot
Parametrized output
QM Many-Body Problems
Two Body Problem
Three Body Problem
Different from Sequential Two-Body Problems
Two Particle QM Problem
Product Solutions
Slater Parameters
Self-Consistent Field
SCF Applied
Potential energy with screening
SCF Applied (continued)