Chapter 3
Semiempirical Parametrization of Energy Level Data

Historical Foundations

First observations of dispersed light
Solar spectrum
Melvill
Wollasten
Kirchoff and Bunsen
History of astronomical spectroscopy
Sample spectra
Sample spectra Spectra of various neutral atoms
Balmer and Ångström
Rydberg
Ritz

The Rydberg-Ritz quantum defect reduction

Data based mapping systematization
EBK formulation
EBK expansion
WKB phase shift
Quantum defect and Y phase shift
Reduced mass
Electron orbit distance
Relativistic two-body problem
Nonseparability of the reduced mass
Relativistic momentum
The Rydberg constant
Atomic constants
Quantum defect reduction
Example
Quantum defect as fctn of n
Penetration and polarization
Z dependences of portions of QD
Iteration example
Na I Grotrian diagram
Determination of the 5p-3/2 level

The Polarization Model

Expectation value expansion
Units
Non-penetrating orbits
Hydrogenic values
Na (Ne Core) polarizabilities
Mg (Na Core) polarizabilities
Penetrating orbits
Si III analysis
Other analyses
Rydberg orbital loci
Penetration formulation
Application to He I
Wave function overlap
Relationship to core electrons
Bohr calculation

Screening Parametrizations

Semiempirical methods
Li example
Dirac-H, Dirac-alkali, Schrödinger
Regular and irregular doublet laws
Reg. & irreg. doublets (continued)
X-Ray summary
X-Ray screening
(continued)

The Dirac-Sommerfeld Expansion

Expansion of Dirac Energy
Nested binomial expressions
Collecting terms and shifting sums
Formulation
Coefficients
Apply to Cu sequence 4p fs
Gravitational analogue

Quantum Electrodynamic Corrections

Semiclassical Lamb shift
Semiclass. Lamb shift (continued)
Energy splittings
Garcia-Mack expansion
Mohr residuals
2p(1/2) residuals
Screening of Lamb shift
Relativistic reduced mass
(continued)

Screening parametrization of fs

Phase shifts and radial scalings
Screening extrapolations up Rydberg series
Adding s-electrons to 4p
Differenced screening of 4sk4p
Combined plot
Adding s-electrons to 3p
Differenced screening of 3sk3p
Adding s-electrons to 5p
Differenced screening of 5sk5p
Screening extrapolations to other sequences

Screening expansions of line strength factors

Time dependent processes
Hartree charge-free units
Intrashell transitions
Intrashell transition element
Intrashell line strengths
H-like intrashell line strengths values
Alkali-Metallike sequences
Li-like Uranium dip
Dirac corrections to hydrogenlike case
Comparison with Li
Li-like Corrected
Na-like Corrected
Li-Na Johnson
PSD fs of Si XII
Cancellation Landscape

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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