Table Of ContentGraduate Texts in Physics
Ingolf V. Hertel
Claus-Peter Schulz
Atoms,
Molecules and
Optical Physics 1
Atoms and Spectroscopy
Graduate Texts in Physics
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Ingolf V. Hertel (cid:2) Claus-Peter Schulz
Atoms, Molecules and
Optical Physics 1
Atoms and Spectroscopy
IngolfV.Hertel Claus-PeterSchulz
Max-Born-InstitutfürNichtlineareOptik Max-Born-InstitutfürNichtlineareOptik
undKurzzeitspektroskopie undKurzzeitspektroskopie
Berlin,Germany Berlin,Germany
ISSN1868-4513 ISSN1868-4521(electronic)
GraduateTextsinPhysics
ISBN978-3-642-54321-0 ISBN978-3-642-54322-7(eBook)
DOI10.1007/978-3-642-54322-7
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Preface
Atomic,MolecularandOpticalphysics–shortAMOphysics–isoneofthecanon-
icalfieldsofphysics,aprofoundknowledgeofwhichisessentialforunderstanding
almost any other area of modern physics. And while its roots reach back over a
century and are closely connected with the early days of modern physics, current
researchinAMOphysicsisstillhighlyproductiveinrespectofboth,cuttingedge
applications and fundamental insights – as several NOBEL prizes in recent years
havedocumentedconvincingly.
Lookingbackatthetechnicaldevelopmentofmodernindustrialsociety–which
is closely connected with modern physics – one may refer (COSE, 1998) to the
20thcenturyasthatoftheelectronwhilethe21stisthecenturyofthephoton.This
interesting particle, the essential ingredient of modern optics and quantum optics,
surpriseshumankindsinceNEWTONwithitswave-particledualism.Itdoesnotonly
play a key role in today’s information technology but is, from a general point of
view,also the primarycarrier of anyinformationwhichcan be obtainedaboutthe
constituentsofmatterandmaterials.Evencollisionsofparticleswithmassunderthe
influenceoftheCOULOMBforcemaybeviewedasexchangeofvirtualphotons.
Thetextbookspresentedheretrytogiveafairlycomprehensiveoverviewonthe
whole field. They cover state of the art experimental methods, and combine this
withpreparingthebasisforaserious,theorybasedunderstandingofkeyaspectsin
modern AMO research. The two volumes, originally written in German language
(HERTEL and SCHULZ, 2008), are a genuine authors translation – not just an En-
glish mirror image of the original. We have rewritten much of the text, extended
it wherever appropriate, and updated a number of aspects to catch up with recent
progressinthefield.
Ontheonehandweaddressadvancedstudentsofphysics,chemistryandother
neighbouring fields, typically at the end of their undergraduate studies, or during
their doctoral work. On the other hand we also wish to reach young postdocs or
even mature scientists, who feel it is time they connectfreshly with the topics ad-
dressedhere.Weconsiderthebasicsofclassicalgeometricalopticsandwaveoptics
aswellaselectrodynamicstobewellknownbyourreaders.Wealsoexpectacer-
vii
viii Preface
tainbasicknowledgeandunderstandingofatomisticconceptsinphysics,aswellas
ofelementaryquantummechanics.
Wedo,however,provideinChaps.1and2ofthisVol.1abriefrepetitionofthese
topics – essentially an extended list of keywords focussed on basic understanding
and knowledge. In the main part we cover the standard scope of atomic physics,
touchsomemodernaspectsofspectroscopy,andtrytoleadthereaderuptostate-
of-the-artresearchinsomemainareasofthefield–whereverpossibleandasfaras
spacepermits.Thesequenceofchaptersfollowsessentiallythelogicsofperturba-
tion theory. The strongest perturbation is treated first. Thus, after the introductory
chapterswherepureCOULOMBinteractionandtheHatomhavebeendiscussed,in
Chap.3weallowforcoarsedeviationsfromthe1/r potentialandfocusonquasi-
one-electronsystems.This,andsomecommonsense,allowsusalreadytointroduce
theperiodicsystemofelements.Next,inChap.4,wehavetotreatopticallyinduced
andspontaneoustransitions:theyareacentralthemeinAMOphysics.Thisrequires
a brief introduction to time dependent perturbation theory, a topic which is indis-
pensible in AMO physics, but which is often neglected in undergaduate quantum
mechanics.Toallowthereaderastepbystepapproachtowardsthemoredemand-
ingtopics,weimplementatthispoint‘only’thesemiclassicalapproach–bywhich
95%ofstandardatomicphysicsmaybetreated(resortingoccasionallytosomewhat
handwavingarguments)–andpostponefieldquantizationtoVol.2.
Chapter5furtherextendsthisknowledge,treatingshapesandwidthsofspectral
lines and introducing multiphoton processes as well as transitions into the contin-
uum.WearenowreadytounderstandinChap.6anextstepofcomplication,fine
structure(FS)interaction.Inordertoallowthereadertoappreciatetheexperimen-
tal efforts, we also give a brief introduction to high resolution and precision laser
spectroscopy. This leads us automatically to the LAMB shift and calls for a short
sidestepintothebasicsofquantumelectrodynamics(QED).InChap.7twoelec-
tronsystemsaretreated,mainlytheHeatomandHelikeions.Exchangeinteraction
maybesmallerorlargerthanFS,dependingonthesystem,butthesteptomultielec-
tronsystemsaddsanewdegreeofcomplexityandsetsthestageforaquantitative
treatmentofthePAULIexclusionprinciple.
ThenextfinerstepinthehierarchyofperturbationsistreatedinChap.8,includ-
inginteractionsbetweenatomicelectronsandexternalmagneticandelectricfields,
leading to ZEEMAN and STARK effect, respectively. At this point, a small detour
into the world of interaction between atoms and very intense laser fields is appro-
priate,asthetheoreticalformalismusedisessentiallyanextensionofthesocalled
dynamical STARK effect. As a last refinement we include in Chap. 9 hyperfine in-
teractions between the atomic nucleus and electrons. These lead to very small but
highlysignificantsplittingsofatomicenergylevels(HFS)andofferawealthofprac-
ticalapplications.InthelastChap.10ofVol.1wearefinallyreadytotreatgenuine
multi-electronsystemswithalargenumberofelectrons.Wediscusstheappropriate
theoretical tools (such as HF equations, CI methods, and DFT), and present some
relevantmethodsofX-rayspectroscopyandsourcesforgeneratingX-rayradiation.
Asarule,wetrytoavoidextensivemathematicalderivations.Rather,inthe‘spirit
ofthesebooks’weprefertogivethereadersomegeneralguidanceonhowtoreach
Preface ix
the final, physically important results – which we discuss and illustrate usually in
some detail. In addition, we provide several appendices for the reader interested
inmoredetail.Wehavee.g.collectedatoolboxforangularmomentumalgebrain
atomicandmolecularphysics–withoutanyclaimforfullmathematicalconsistency,
butquitecompactandpossiblyusefulinpractice.
Somewordsaboutformats,notation,units,typographyappearinorder:
• Eachchapterbeginswithabrief“motto”settingthetuneofthechapter,followed
byshortabstractguidingthereaderthroughthetext.Attheendofeachsectiona
shortsummaryrecallswhatthereadersshouldhavelearnedfromthepreceding
text. All chapters build upon each other, but may be read by advanced readers
alsoindividually:thisisfacilitatedbyintensivecrossreferencingofformulasand
figures,extendedindicescoveringbothvolumes,alistofacronymsandimportant
terminologyaswellasreferencesattheendofeachchapter.
• For clarity and homogeneity we do not reproduce original drawings or other
materialfromtheliterature.Rather,allpublisheddatahavebeenredrawn(after
digitalization if necessary), are presented in a standard format, and all sources
usedinthefiguresandtextareproperlyquoted.
• WeconsequentlyusetheSI-Systemforallmeasurablequantities,andweempha-
sizethepedagogicalandpracticalvalueofa“dimensionalanalysis”forcomplex
physical formulas.1 On the other hand, atomic units (a.u.) facilitate the writing
ofmanyrelationsinatomicandmolecularphysicsdramatically.Hence,weuse
themintensively–considering,however,E ,a andt etc.simplyasabbrevia-
h 0 0
tionsforquantitieswithdimensions.Phrasingssuchas“weset(cid:2),e,m ,c equal
e
tounity”areavoided,sincetheyarehighlymisleading.
• ThefinitenumberoflettersintheLatinandGreekalphabetsmakessomeincon-
sistencies or unusual designationsunavoidable:we mentionspecifically,that in
ordertoallowtheuseofE fortheelectricfieldstrength(animportantquantity
inAMO)weuseW (withappropriateindices)forenergiesofvarioustypes(with
theexceptionoftheatomicunitofenergywhichisinternationallydefinedasE ).
h
Occasionally we use the letter T for kinetic energy and try to avoid the neigh-
bourhoodoftimeandtemperaturewhichareoftenalsodesignatedbyT.Vectors
arewrittenasr ork,unitvectorsinthesedirectionsaree ande ,respectively.
r k
WewriteoperatorsasH(cid:2),vector-operatorsas(cid:2)p andtensorsofrankk asCk.For
(cid:2)
the unit operator and unit matrix we use 1. For integer numbers we mostly use
calligraphic letters such as N, while number densities are simply N to distin-
guish them from the index of refraction n which is also an often used quantity
throughout this text. Oscillations and other periodic processes are mostly char-
acterizedbytheirangularfrequenciesω(sometimesalsobytheirfrequenciesν)
andthecorrespondingenergiesare(cid:2)ω(orhν).
1Wemake,however,useofallowedprefixes(NIST,2000a),suchascm−1asunitofwavenumbers
(whichappearsineradicableintheliterature).Wealsouse“accepted”unitsoutsidetheSI(NIST,
2000b),suchastheenormouslypracticalenergyuniteV(electronvolt),orb(barn)asunitforcross
sections.
x Preface
Finally,wehopethatthesebookswillbecomeacontinuingsourceofreference
forthefastidiousreader,workinginorjustneedingtouseAMOphysicsinheror
hisspecialfield.Weaskallofyoutokindlyprovideuswiththenecessaryfeedback.
Weshalltrytoreacttousefulsuggestionpromptly.Atthehomepageofthebooks,
http://www.mbi-berlin.de/AMO/book-homepage, we shall continuously report on
the status, list errata and possibly present additions. For additional reading and
crossreferencingwehavecollectedafewrelatedtextbooksandmonographsinthe
reference list below, just as typical examples without any claim for completeness.
BerlinAdlershof,Germany IngolfV.Hertel
January2014 Claus-PeterSchulz
AcronymsandTerminology
AMO: ‘Atomic,molecularandoptical’,physics.
a.u.: ‘atomicunits’,seeSect.2.6.2.
CI: ‘Configurationinteraction’,mixingofstateswithdifferentelectronicconfigu-
rationsinatomicandmolecularstructurecalculations,usinglinearsuperposition
ofSLATERdeterminants(seeSect.10.2.3).
DFT: ‘Densityfunctionaltheory’,todayoneofthestandardmethodsforcomputing
atomicandmolecularelectrondensitiesandenergies(seeSect.10.3).
FS: ‘Fine structure’, splitting of atomic and molecular energy levels due to spin
orbitinteractionandotherrelativisticeffects(Chap.6).
HF: ‘HARTREE-FOCK’, method (approximation) for solving a multi-electron
SCHRÖDINGERequation,includingexchangeinteraction.
HFS: ‘Hyperfinestructure’,splittingofatomicandmolecularenergylevelsdueto
interactionsoftheactiveelectronwiththeatomicnucleus(Chap.9).
NIST: ‘National institute of standards and technology’, located at Gaithersburg
(MD)andBoulder(CO),USA.http://www.nist.gov/index.html.
QED: ‘Quantum electrodynamics’, combines quantum theory with classical elec-
trodynamicsandspecialrelativity.Itgivesacompletedescriptionoflight-matter
interaction.
References
ATKINS,P.W.andR.S.FRIEDMAN:2010.MolecularQuantumMechanics.Oxford:OxfordUni-
versityPress,2ndedn.
BERGMANN,L.andC.SCHAEFER:1997.ConstituentsofMatter–Atoms,Molecules,Nucleiand
Particles.Berlin,NewYork:WalterderGruyter,902pages.
BLUM,K.:2012.DensityMatrixTheoryandApplications.Atomic,Optical,andPlasmaPhysics
64.Berlin,Heidelberg:SpringerVerlag,3rdedn.,343pages.
BORN,M.andE.WOLF:2006.PrinciplesofOptics.CambridgeUniversityPress,7th(expanded)
edn.
