Atomic Structure and Lifetimes: A Conceptual Approach

282 Pages·2003·1.966 MB·English

by  Lorenzo J. Curtis

AtomicStructureandLifetimes
AConceptualApproach
This book presents a new approach to the teaching of introductory graduate courses on
atomicstructure.
Theauthor’sapproachutilizesconceptuallypowerfulsemiclassicalmodelingmethods,
and demonstrates the surprising degree to which the Maslov-indexed EBK quantization
elucidatesthequantummechanicalformulationoflevelenergiesandlifetimes.Itmerges
thiswithanupdateandextensionofthesemiempiricaldatasystematizationsdevelopedby
Bengt Edle´n to describe complex atoms, and adapts them to include the specification of
lifetimes.Thetextemphasizesthehistoricalbasisofthenomenclatureandmethodologies
ofspectroscopy;however,theinteractionmechanismsarepresenteddeductively,basedon
modernquantummechanicalandfieldtheoreticalmodelsratherthantracingtheirindirect
paths of discovery. Many worked examples provide applications to areas such as astro-
physics,hyperfinestructure,andcoherentanisotropicexcitation.Thebookpresentsafirm
foundationforspecialistsinatomicphysics,aswellasacapstoneapplicationforspecialists
inastrophysics,chemistry,condensedmatter,andotherrelatedfields.
lorenzo j. curtisreceivedhisPh.D.fromtheUniversityofMichiganin1963.Heholds
therankofDistinguishedUniversityProfessorandthedesignationMasterTeacheratthe
University of Toledo. His primary research interests involve time-resolved atomic spec-
troscopyandthestructureofhighlyionizedatoms.Hehasheldvisitingscientistpositions
in Sweden, Denmark, Norway, Germany, and France, as well as at Princeton University,
Argonne National Laboratory, and Brookhaven National Laboratory in the US. He has
publishedmorethan200refereedscientificarticlesandisaFellowofboththeAmerican
PhysicalSocietyandtheOpticalSocietyofAmerica.In1999hewasawardedthedegree
PhilosophiaeDoctoremHonorisCausabytheUniversityofLundinSweden.

Atomic Structure and Lifetimes
A Conceptual Approach
LorenzoJ.Curtis
UniversityofToledo
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Cambridge University Press
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© Lorenzo Curtis 2003
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without the written permission of Cambridge University Press.
First published in print format 2003
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Contents
Preface pagexi
Listofphysicalconstantsandusefulinterrelations xiii
1 Introduction 1
1.1 Atomicphysicsismorethanquantummechanics 1
1.2 Trajectoriesversusprobabilities 2
1.3 Semiempiricalparametrization 5
2 Semiclassicalconceptualmodels 6
2.1 Classicalpositionprobabilitydensitiesforperiodicsystems 6
2.2 Quantummechanicaloscillationofthelocalizability 7
2.3 Einstein–Brillouin–Kellerquantization 8
2.4 TheKeplerproblem 11
2.5 Semiclassicalformulationofthedecaymeanlife 37
3 Semiempiricalparametrizationofenergy-leveldata 42
3.1 Historicaldevelopment 42
3.2 Descriptionofcomplexatomsbytwo-bodycollectivemodes 44
3.3 TheRydbergformulaandtheRitzparametrization 47
3.4 Thecorepolarizationmodel 54
3.5 Screeningparametrizations 58
3.6 Screeningparametrizationofthefinestructure 61
3.7 Screeningparametrizationoftransitionrates 67
4 Thevectormodelofangularmomentum 72
4.1 TheSchro¨dingerapproximation 72
4.2 Theintrinsicangularmomentumandmagneticmomentoftheelectron 73
4.3 ThePaulispinmatrices 74
4.4 Internalmagneticfields 76
4.5 Couplingapproximations 77
4.6 Quantummechanicalvectorcouplingofangularmomenta 79
4.7 Theconnectionbetweenspinandstatistics 80
viii Contents
4.8 TheLande´ intervalrule 81
4.9 Externalmagneticfields 82
5 Theintermediatecouplingmodel 90
5.1 Spectroscopicnotation 90
5.2 Two-valence-electronsystems 92
5.3 ScreeningparametrizationsofSlaterparameters 107
5.4 Systemswiththreeormorevalenceelectrons 109
5.5 Antisymmetrizationofamultielectronsystem 112
6 Electricdipoleradiation 113
6.1 Hierarchiesintransitionarrays 114
6.2 Abinitiocalculations 120
6.3 CommutationrelationsinvolvingtheE1transitionmoment 123
6.4 QuadraticStarkeffectandatomicpolarizability 125
6.5 CorepolarizationcontributionstotheE1transitionmoment 129
6.6 Cancellation 131
7 Linestrengthsintwo-valence-electronsystems 138
7.1 RelativisticE1transitions 138
7.2 jj-basedreformulation 155
7.3 Gyromagneticratiosinintermediatecoupling 161
8 Magneticdipoletransitions 164
8.1 M1transitions 164
8.2 M1linestrengths 165
9 Absorptionofradiation 179
9.1 Drivendampedharmonicoscillator 180
9.2 Dopplerbroadening 182
9.3 ComparisonoftheLorentzianandGaussianfunctions 183
9.4 Convolutionsoflineshapefunctions 184
9.5 Equivalentwidth 187
9.6 AtomicderivationofthePlanckradiationlaw 191
10 Time-resolvedmeasurements 194
10.1 Timedependenceofmeasureddecaycurves 195
10.2 Adjustednormalizationofdecaycurve(ANDC)method 200
10.3 Differentiallifetimemeasurements 202
10.4 Hanleeffect 205
11 Hyperfinestructure 207
11.1 Theoriginsofhyperfinestructureobservations 207
11.2 Magneticdipolemomentofthenucleus 208
11.3 Electricquadrupolemomentofthenucleus 213
11.4 Example:hyperfinesplittingofthe4ptermin23Na 215
Contents ix
11.5 Isotopeshifts 215
11.6 Hyperfinequenching 218
12 Electrostaticpolarizabilitiesandlong-rangeinteractions 220
12.1 Rayleigh–Schro¨dingerperturbationtheory 220
12.2 TheDalgarno–Lewisoperator 222
12.3 Application:ground-statepolarizabilities 223
12.4 Nonadiabaticcorrelations 228
12.5 Casimir–Polderretardationcorrections 229
12.6 QuadraticStarkeffect 230
12.7 Indicesofrefractionforinertgases 231
13 Coherenceandanisotropicexcitation 234
13.1 Densitymatrixrepresentation 234
13.2 Stokesparameters 238
13.3 Applicationtoameasurementofellipticpolarization 243
13.4 Alignmentandorientation 246
13.5 Quantum-beatspectroscopy 248
13.6 Levelcrossingandopticaldoubleresonancespectroscopy 251
References 252
Index 261