Chapter 3
Semiempirical Parametrization of Energy Level Data

First observations of dispersed light
Newton's studies
White light
Take apart and put together again
Solar spectrum
The misfortune of the circular hole
Melvill's paper of 1752: see p.243

Laboratory Astrophysics

Melvill
Wollasten
Kirchhoff and Bunsen
History of astronomical spectroscopy
Sample spectra
Spectra of various neutral atoms

Balmer and the hydrogen spectrum

Balmer and Ångström
Balmer's plot revisited
Rydberg's seminar
"Janne Rydberg, his life and work," N.I.M. 235, 17 (2005)
Ritz

The 2 body problem (Sect. 3.2)

Reduced mass
Electron orbit distance

Relativistic two-body problem

Nonseparability of the reduced mass

Relativistic momentum
The Rydberg constant
Atomic constants

Part II: Quantum defect methods (Sect. 3.3)

The Rydberg-Ritz quantum defect reduction (Sect. 3.3.1)

Data based mapping systematization
Quantum defect, phase shift, and n
Unshifted H wave functions
EBK formulation
Coulombic at large r
Expansion

Application of Rydberg-Ritz (Sect. 3.3.2)

Quantum defect reduction
Grotrian diagram relative to hydrogen
Determination of the 5p-3/2 level
Propagation of uncertainties
Quantum defect as fctn of n
continued
Rydberg orbital loci
Penetration and polarization
Isoelectronic landscape
Z dependences of portions of QD
Charge dependence
Quantum defect on both sides?
Iteration example
Iteration example 2

Quantum defect problem
Solution

The Polarization Model (Sect. 3.4)

Expectation value expansion
Wave function overlap
Hydrogenic values
P IV example

Polarization model problem

Hydrogenic values

Solution

Plot

Penetration corrections

Relationship to core electrons
Compare polarizabilities
Si III analysis
Non-penetrating orbits
Application to He I

Part III: Screening Parametrizations (Sect. 3.5)

Semiempirical methods
Near and far parametrizations

Regular and irregular doublet laws Sect. 3.5.2

Li example
Irregular doublet law
Applied to Na sequence
Regular doublet law
Apply to fine structure in optical spectra
X-ray notation
X-ray levels
X-ray screening parameter plots
(continued)
Summary of X-ray screening parameters

The Dirac-Sommerfeld Expansion (Sect. 3.6)

Expansion of Dirac Energy
Nested binomial expressions
Collecting terms and shifting sums
Formulation
Coefficients

Quantum electrodynamic and reduced-mass corrections

Apply to Cu sequence 4p fs
Gravitational analogue
Semiclassical Lamb shift
Schematic plot
Screening of Lamb shift

Buildup of alkalilike Screening

Adding s and p electrons to 4p
Difference from Cu-like
Adding s-electrons to 3p
Difference from Na-like
Clocks: stopped and running slow

Parametrizing line strengths (Sect. 3.7.1)

Time dependent processes
Hydrogenic units
Line strength factors

Problem: screening parametrization
Plot
X-ray screening parameter plots
Grotrian diagram
losning
Alkali-Metallike sequences
H-like intrashell line strengths values
Alkaline-Earthlike sequences
Intrashell transitions
Li-like Uranium dip

Relativistic form of the line strength (Sect. 3.7.2)

Dirac corrections to hydrogenlike case
Comparison with Li
Li-like Corrected
Na-like Corrected

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Chapt. 1
Chapt. 2
Chapt. 4
Chapt. 5
Chapt. 6
Chapt. 7
Chapt. 8
Chapt. 9
Chapt. 10
Chapt. 11
Chapt. 12
Chapt. 13

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