# Chapter 3 - Atomic Structure and Lifetimes

*Semiempirical Parametrization of Energy-Level Data*

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## Part I: Historical Foundations (Sect. 3.1)

### Dispersion

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First observation?
Refraction and dispersion by spheres
Parhelia
Sun dogs
### Newton and the "Phænomena of Colours"

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Newton's studies
Take apart and
put together again
The misfortune of the circular hole
### Two types of light sources

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The various Rydberg series
Emission and absorption spectra
Solar spectrum
First observations of dispersed light
Melvill
Wollasten
Kirchhoff and Bunsen
Stellar absorption spectra
History of
astronomical spectroscopy
Spectra
of various neutral atoms
### Balmer and the hydrogen spectrum

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Balmer, Rydberg and Ritz
Balmer's plot of Ångström's data
Balmer's plot revisited
Rydberg's seminar
"Janne Rydberg, his life and work,"
Nucl. Instr. Meth. (in press)

## Part II: Quantum Defect Methods

### The Rydberg-Ritz quantum defect reduction (Sect. 3.3)

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Data-based mapping systematization
Quantum defect, phase shift, and *n*
n dependence of average powers of *r*
Grotrian diagrams
### The two-body problem (Sect. 3.2)

Reduced mass
The Rydberg constant
Atomic constants
### Application of Rydberg-Ritz (Sect. 3.3.2)

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Na I Grotrian diagram

Determination of the 5p-3/2 level

Na data
Quantum defect reduction
Quantum defect plot
Search IP
Smooth and extrapolate
### Interpretation of Ritz parameters (Sect. 3.3.2)

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Quantum defect on both sides?
Solution by iteration
Quantum defect as fctn of *n*
continued
Penetration and polarization
Isoelectronic landscape
Charge dependence
### Semiclassical derivation of Rydberg-Ritz formula (Sect. 3.3.1)

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EBK formulation
Coulombic at large *r*
Taylor expand
### The Polarization Model (Sect. 3.4)

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Expectation value expansion
Non-penetrating orbits
Hydrogenic values
Quantum defect
Tight and loose cores
Compare polarizabilities
Si III analysis
Other analyses
Penetration formulation

## Part III: Screening Parametrizations (Sect. 3.5)

### Characterizing regions of large and small *r* (Sect. 3.5.1)

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Phase shifts and radial scalings
### Regular and irregular doublet laws (Sect. 3.5.2)

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Irregular doublet law
Applied to Na sequence
Regular doublet law
X-ray notation
X-ray screening parameter plots
(continued)
Characteristic X-rays
Summary of X-ray screening parameters
Apply to optical spectra
### The Dirac-Sommerfeld expansion (Sect. 3.6.1)

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Expansion of Dirac Energy
Nested binomial expressions
Collecting terms and shifting sums
Formulation
Coefficients
### Applications to complex systems (Sect. 3.6.2)

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Apply to Cu sequence 4p fs
Screening extrapolations up Rydberg series
Adding s-electrons to 4p

Differenced screening of 4s^{k}4p

Combined plot

### Relative importance of higher order terms (Sect 3.6.3)

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Gravitational analogue
### Quantum electrodynamic corrections

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Semiclassical Lamb shift
Energy splittings
Schematic plot
Screening of Lamb shift

### Screening expansions of transition rates (Sect. 3.7)

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Time dependent processes
Line strength factors
H-like intrashell line strengths values
Alkali-Metallike sequences
### Relativistic corrections (Sect. 3.7.2)

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Li-like uranium anomaly
Relativistic corrections for hydrogen
Comparison with Li
Na-like Corrected
### Current state of knowledge

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Li and Na vs theory
Cancellation Landscape
PSD multiplexed detection
Block diagram of SE approach

Chapter 1

Chapter 2

Bridge A

Chapter 4

Bridge B

Chapter 5

Chapter 6

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