# Chapter 5

*The Intermediate Coupling Model*

####

### Notation (Sect. 5.1)

### Two electron systems (Sect. 5.2)

### 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)

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)

### 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

#### 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)