Chapter 3
Semiempirical Parametrization of Energy Level Data

Part I: Historical foundations (Sect. 3.1)

Two types of light sources

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

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)

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

    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
    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

    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
    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

    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
    X-ray screening parameter plots
    Grotrian diagram
    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

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