Chapter 10
Time-Resolved Measurements

I. Historic background of time-resolved methods

Early attempts at atomic lifetime measurement

PEB vs TOF
Becquerel
Phosphoroscope
Dunoyer

Time dependence of measured decay curves (Sect. 10.1)

Cascades and blends
Cataract
Halflife of dice
Multisided coins
Supported decay
Branched decay
Cascade simulation
Rutherford's measurements
Coat-of-Arms

Cosmological, geological, and archaeological dating

Uranium-lead dating
Successive decay equilibrium
Carbon dating
Bristle cone pine calibration
AMS - Shroud of Turin
J. Opt. A 6, 491 (2004) [3.4 MB]
Potassium-argon dating

II. Calculational formulations

Diagrammatic mnemonic (Sect. 10.1.1)

Population equation
Example
Iterate
Diagrams
Cascade order
Application
Single cascade
Indirect cascading
Maximum semilog slope
Two hump cascade
Cascade & primary with similar lifetime
Monte Carlo calculation
Anisotropic excitation
Cascade induced alignment

Driven excitation

Formulation
Iteration
Parts integration
Successive application
Iteration with operators
Examples of excitation
Impulsive, stepwise & rectangularly pulsed excitation
Gaussian excitation

Phase shift measurements (Sect. 10.1.2)

Compared with pulsed excitation
Modulated excitation
Reduction of mnemonic
Transfer function
Uncascaded and single cascade
Cascade joint analysis
Blend and two direct cascades
Indirect cascade
General expression

Strength of cascading

Criteria for heavy cascading
Replenishment ratio
R(0) from curve fits and intensity ratios
Integrated and differentiated

ANDC analysis (Sect. 10.2)

ANDC method
Multiexponential decay curve
Schematic decay curve Grotrian plot
ANDC Grotrian for 6p
Kr VIII Grotrian diagram
Parametric plot
Advantage of heavy cascading
Ne calibration
Unseen decay curve
Deblending
Window convolution
Advantages of cascade analysis

Other applications

Hanle effect (Sect. 10.4)

Preferential excitation
Larmor precession
Effective FWHM
Limiting cases

Differential lifetime measurements (Sect. 10.3)

Be-like Grotrian and Decay
Differential lifetimes
Differential decay curve
Branching of Singlet
Z²S Plot for 3-Bears

The exponential decay law

Experimental verification
Is it decay or only disintegration?
Webster
Aphorisms
Literary wisdom
Merzbacher

Implications of uncontrolled growth

The energy crisis Energy supply estimates Hubbert's candle Link to logistic curve Logistic equation
Population data
Interating the logistic equation
Chaotic behavior
Mandelbrot set

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Chapter 1;   Chapter 2;   Chapter 3;   Chapter 4;   Chapter 5;   Chapter 6

Chapter 7
Chapter 8
Chapter 9
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15

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Heavily cascaded decay curves

Isoelectronic trends
Simulations for Na sequence
Simulations for Kr VIII
Simulations for Cu XIX
Si IV and P V on isoelectronic plot
Relative lifetime trends
ANDC Grotrian for 3s3p
ANDC Grotrian for Y III
Si IV decay curves
ANDC Grotrian for 5p