Pressure Broadening of Spectral Lines: The Theory of Line Shape in Atmospheric Physics

639 Pages·2020·4.255 MB·English

by  Peter Joseph Rayer

PRESSURE BROADENING OF SPECTRAL LINES
Presenting the quantum mechanical theory of pressure broadening and its application in
atmospheric science, this is a unique treatment of the topic and a useful resource for
researchers and professionals alike. Rayer proceeds from molecular processes to broad
scale atmospheric physics to bring together both sides of the problem of remote sensing.
Explanationsoftherelationshipbetweenaseriesofincreasinglygeneraltheoreticalpapers
areprovided,andallkeyexpressionsarefullyderivedtoprovideafirmunderstandingof
assumptionsmadeasthesubjectevolved.Thisbookwillhelptheatmosphericphysicistto
crossintothequantumworldandappreciatethemoretheoreticalaspectsoflineshapeand
itsimportancetotheirownwork.
peter rayer has 30 years’ experience as a scientist with the Met Office in the United
Kingdom. He has undertaken extensive research in modelling atmospheric radiative
transferandhasdevelopedaparticularinterestinfundamentalprocessesatthemolecular
level.

PRESSURE BROADENING OF
SPECTRAL LINES
The Theory of Line Shape in Atmospheric Physics
PETER RAYER
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DOI:10.1017/9781108768825
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Firstpublished2020
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LibraryofCongressCataloging-in-PublicationData
Names:Rayer,Peter(PeterJoseph),1950–author.
Title:Pressurebroadeningofspectrallines:thetheoryoflineshapeinatmosphericphysics/PeterRayer.
Description:Cambridge;NewYork,NY:CambridgeUniversityPress,2020.|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2019043635(print)|LCCN2019043636(ebook)|
ISBN9781108488044(hardback)|ISBN9781108768825(epub)
Subjects:LCSH:Pressurebroadening.|Spectrallinebroadening.|Atmosphericphysics.
Classification:LCCQC467.R6952020(print)|LCCQC467(ebook)|
DDC539.7/57–dc23
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Contents
Preface pagexi
PartOne PreparingtheWay 1
1 Introduction 3
1.1 MatterandRadiation 3
1.2 LineBroadening 6
1.3 SomeApproximations 9
1.4 OpticalCollisions 12
1.5 PlanoftheBook 14
2 FundamentalIdeas 19
2.1 QuantumSystems 19
2.2 RadiativeInteraction 31
2.3 DipoleAbsorption 40
3 MoleculesatWork 49
3.1 TheRadiatorSpectrum 49
3.2 Collisions 64
PartTwo BroadeningTheory 93
4 IsolatedLines 95
4.1 Preliminaries 95
4.2 Anderson’sApproach 107
4.3 OpticalCross-Section 115
5 OverlappingLines 129
5.1 Preliminaries 129
5.2 Baranger’sApproach 141
5.3 LineShape 171
6 LiouvilleFormalism 188
6.1 Preliminaries 188
vii
viii Contents
6.2 SomeGeneralizations 197
6.3 Fano’sApproach 219
6.4 ReductionandBalance 240
PartThree AtmosphericSpectra 257
7 LineShapeTheory 259
7.1 LineFar-Wing 259
7.2 LineCore 307
8 AbsorptionbyGases 323
8.1 AbsorptionCoefficient 323
8.2 SpectralComputation 350
PartFour TheBackground 383
SelectionofMaterial 385
Appendix1 StateSpace 388
A1.1 ReciprocalSets 388
A1.2 NormalOperators 392
A1.3 AntilinearOperators 396
A1.4 TheDensityOperator 400
Appendix2 ProductSpace 405
A2.1 TensorProducts 405
A2.2 SeparableBasis 408
A2.3 RadiatorandBath 411
A2.4 LineSpace 414
A2.5 Superoperators 418
A2.6 LiouvilleConjugation 422
Appendix3 Projectors 424
A3.1 Decomposition 424
A3.2 Fano’sProjector 426
Appendix4 VectorOperators 433
A4.1 Dyadics 433
A4.2 T-ClassVectors 438
A4.3 VectorComponents 441
A4.4 SelectionRules 443
Appendix5 QuantumDynamics 446
A5.1 BasedontheHamiltonian 446
A5.2 BasedontheLiouvillian 451
Contents ix
Appendix6 ScatteringTheory 457
A6.1 TheLippmann–SchwingerEquation 457
A6.2 TheScatteringMatrix 466
A6.3 ScatteringStates 471
Appendix7 ResolventMethods 477
A7.1 ResolventExpansions 477
A7.2 TheTransitionOperator 479
A7.3 TheConnectedOperator 484
A7.4 TheRelaxationOperator 490
A7.5 TotheMarkovLimit 493
Appendix8 LinearResponse 498
A8.1 ResponseFunction 498
A8.2 SusceptibilityTensor 500
Appendix9 CorrelationFunction 505
A9.1 ProcessStatistics 505
A9.2 TheWiener–KhinchinTheorem 506
A9.3 FollowingAnderson 510
A9.4 UncoupledLines 515
Appendix10 ComplexTime 518
A10.1 TheFluctuation–DissipationTheorem 518
A10.2 InitialCorrelations 521
Appendix11 Absorption 528
A11.1 PolarizingField 528
A11.2 AbsorbingMedium 531
Appendix12 MultipoleMoments 537
A12.1 TheMultipoleExpansion 537
A12.2 CartesianMultipoles 541
A12.3 SphericalTensors 543
A12.4 DipoleTransitions 547
Appendix13 AngularMomentum 550
A13.1 StatesandOperators 550
A13.2 VectorAddition 554
Appendix14 TheWigner–EckartTheorem 558
A14.1 GeneralOutline 558
A14.2 TheVectorCase 561
A14.3 TransitionStrength 565