Springer Handbooksof Atomic, Molecular, and Optical Physics

Springer Handbooks providea concise compilation of approvedkey information on methods ofresearch, general principles, andfunctional relationships in physicsand engineering. The world’s lead-ing experts in the fields of physicsand engineering will be assigned byone or several renowned editors towrite the chapters comprising eachvolume. The content is selected bythese experts from Springer sources(books, journals, online content)and other systematic and approvedrecent publications of physical andtechnical information.

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123

HandbookSpringerof Atomic, Molecular,

and Optical PhysicsGordon W. F. Drake (Ed.)

With CD-ROM, 288 Figures and 111 Tables

Editor:Dr. Gordon W. F. DrakeDepartment of PhysicsUniversity of WindsorWindsor, Ontario N9B 3P4Canada

Assistant Editor:Dr. Mark M. CassarDepartment of PhysicsUniversity of WindsorWindsor, Ontario N9B 3P4Canada

Library of Congress Control Number: 2005931256

ISBN-10: 0-387-20802-X e-ISBN: 0-387-26308-XISBN-13: 978-0-387-20802-2 Printed on acid free paper

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SPIN 10948934 100/3141/YL 5 4 3 2 1 0

V

Handbook of Atomic, Molecular, and Optical Physics

Editor

Gordon W. F. DrakeDepartment of Physics, University of Windsor, Windsor, Ontario, Canadagdrake@uwindsor.ca

Assistant Editor

Mark M. CassarDepartment of Physics, University of Windsor, Windsor, Ontario, Canadacassar@uwindsor.ca

Advisory Board

William E. Baylis – AtomsDepartment of Physics, University of Windsor, Windsor, Ontario, Canadabaylis@uwindsor.ca

Robert N. Compton – Scattering, ExperimentOak Ridge National Laboratory, Oak Ridge, Tennessee, USAahd@ornl.gov

M. Raymond Flannery – Scattering, TheorySchool of Physics, Georgia Institute of Technology, Atlanta, Georgia, USAflannery@eikonal.physics.gatech.edu

Brian R. Judd – Mathematical MethodsDepartment of Physics, The Johns Hopkins University, Baltimore, Maryland, USAjuddbr@pha.jhu.edu

Kate P. Kirby – Molecules, TheoryHarvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, USAkirby@cfa.harvard.edu

Pierre Meystre – Optical PhysicsOptical Sciences Center, The University of Arizona, Tucson, Arizona, USApierre@rhea.opt-sci.arizona.edu

VII

Foreword by Herbert Walther

The Handbook of Atomic, Molecular and Optical(AMO) Physics gives an in-depth survey of the presentstatus of this field of physics. It is an extended versionof the first issue to which new and emerging fields havebeen added. The selection of topics thus traces the re-cent historic development of AMO physics. The bookgives students, scientists, engineers, and other interestedpeople a comprehensive introduction and overview. Itcombines introductory explanations with descriptions ofphenomena, discussions of results achieved, and givesa useful selection of references to allow more detailedstudies, making the handbook very suitable as a desktopreference.

AMO physics is an important and basic field ofphysics. It provided the essential impulse leading to thedevelopment of modern physics at the beginning of thelast century. We have to remember that at that time notevery physicist believed in the existence of atoms andmolecules. It was due to Albert Einstein, whose work wecommemorate this year with the world year of physics,that this view changed. It was Einstein’s microscopicview of molecular motion that led to a way of calculatingAvogadro’s number and the size of molecules by study-ing their motion. This work was the basis of his PhDthesis submitted to the University of Zurich in July 1905and after publication became Einstein’s most quoted pa-per. Furthermore, combining kinetic theory and classicalthermodynamics led him to the conclusion that the dis-placement of a microparticle in Brownian motion variesas the square root of time. The experimental demonstra-tion of this law by Jean Perrin three years later finallyafforded striking proof that atoms and molecules area reality. The energy quantum postulated by Einstein inorder to explain the photoelectric effect was the basisfor the subsequently initiated development of quantumphysics, leading to a revolution in physics and many newapplications in science and technology.

The results of AMO physics initiated the devel-opment of quantum mechanics and quantum electro-

Prof. Dr. Herbert Walther

dynamics and as a consequence ledto a better understanding of the struc-ture of atoms and molecules and theirrespective interaction with radiationand to the attainment of unprece-dented accuracy. AMO physics alsoinfluenced the development in otherfields of physics, chemistry, astron-omy, and biology. It is an astonishingfact that AMO physics constantlywent through periods where new phenomena werefound, giving rise to an enormous revival of this area.Examples are the maser and laser and their many appli-cations, leading to a better understanding of the basicsand the detection of new phenomena, and new possi-bilities such as laser cooling of atoms, squeezing, andother nonlinear behaviour. Recently, coherent interfer-ence effects allowed slow or fast light to be produced.Finally, the achievement of Bose–Einstein condensationin dilute media has opened up a wide range of newphenomena for study. Special quantum phenomena areleading to new applications for transmission of infor-mation and for computing. Control of photon emissionthrough specially designed cavities allows controlledand deterministic generation of photons opening the wayfor a secure information transfer.

Further new possibilities are emerging, such as thetechniques for producing attosecond laser pulses andlaser pulses with known and controlled phase relationbetween the envelope and carrier wave, allowing syn-thesis of even shorter pulses in a controlled manner.Furthermore, laser pulses may soon be available that aresufficiently intense to allow polarization of the vacuumfield. Another interesting development is the genera-tion of artificial atoms, e.g., quantum dots, openinga field where nanotechnology meets atomic physics. Itis thus evident that AMO physics is still going strongand will also provide new and interesting opportunitiesand results in the future.

IX

Preface

The year 2005 has been officially declared by the UnitedNations to be the International Year of Physics to com-memorate the three famous papers of Einstein publishedin 1905. It is a fitting tribute to the impact of his workthat the Springer Handbook of Atomic, Molecular, andOptical Physics should be published in coincidence withthis event. Virtually all of AMO Physics rests on thefoundations established by Einstein in 1905 (includinga fourth paper on relativity and his thesis) and his sub-sequent work. In addition to the theory of relativity,for which he is best known, Einstein ushered in theera of quantum mechanics with his explanation of thephotoelectric effect, and he demonstrated the influenceof molecular collisions with his explanation of Brown-ian motion. He also laid the theoretical foundations forall of laser physics with his discovery (in 1917) of thenecessity of the process of stimulated emission, and hisdiscussions of the Einstein–Podolsky–Rosen Gedankenexperiment (in 1935) led, through Bell’s inequalities, tocurrent work on entangled states and quantum informa-tion. The past century has been a Golden Age for physicsin every sense of the term.

Despite this history of unparalleled progress, thefield of AMO Physics continues to advance more rapidlythan ever. At the time of publication of an earlier Hand-book published by AIP Press in 1996 I wrote “Theever increasing power and versatility of lasers con-tinues to open up new areas for study.” Since then,two Nobel Prizes have been awarded for the cool-ing and trapping of atoms with lasers (Steven Chu,Claude Cohen-Tannoudji, William D. Phillips in 1997),and for the subsequent achievement of Bose–Einsteincondensation in a dilute gas of trapped atoms (EricA. Cornell, Wolfgang Ketterle, Carl E. Wieman in 2001).Although the topic of cooling and trapping was coveredin the AIP Handbook, Bose–Einstein condensation wasbarely mentioned. Since then, the literature has explodedto nearly 2500 papers on Bose–Einstein condensationalone. Similarly, the topics of quantum informationand quantum computing barely existed in 1995, andhave since become rapidly growing segments of thephysics literature. Entirely new topics such as “fast light”and “slow light” have emerged. Techniques for both

Prof. Gordon W. F. Drake

high precision theory and measure-ment are opening the possibility todetect a cosmological variation of thefundamental constants with time. Allof these topics hold the promise ofimportant engineering and techno-logical applications that come withadvances in fundamental science.The more established areas of AMOPhysics continue to provide the basicdata and broad understanding of a great wealth of under-lying processes needed for studies of the environment,and for astrophysics and plasma physics.

These changes and advances provide more than suf-ficient justification to prepare a thoroughly revised andupdated Atomic, Molecular and Optical Physics Hand-book for the Springer Handbook Program. The aimis to present the basic ideas, methods, techniques andresults of the field at a level that is accessible to grad-uate students and other researchers new to the field.References are meant to be a guide to the literature,rather than a comprehensive bibliography. Entirely newchapters have been added on Bose–Einstein condensa-tion, quantum information, variations of the fundamentalconstants, and cavity ring-down spectroscopy. Otherchapters have been substantially expanded to includenew topics such as fast light and slow light. The intentis to provide a book that will continue to be a valuableresource and source of inspiration for both students andestablished researchers.

I would like to acknowledge the important roleplayed by the members of the Advisory Board in theircontinuing support of this project, and I would espe-cially like to acknowledge the talents of Mark Cassar asAssistant Editor. In addition to keeping track of the sub-missions and corresponding with authors, he read andedited the new material for every chapter to ensure uni-formity in style and scientific content, and he composednew material to be added to some of the chapters, asnoted in the text.

February 2005 Gordon W. F. Drake

XI

List of Authors

Nigel G. AdamsUniversity of GeorgiaDepartment of ChemistryAthens, GA 30602-2556, USAe-mail: adams@chem.uga.edu

Miron Ya. AmusiaThe Hebrew UniversityRacah Institute of PhysicsJerusalem, 91904, Israele-mail: amusia@vms.huji.ac.il

Nils AndersenUniversity of CopenhagenNiels Bohr InstituteUniversitetsparken 5Copenhagen, DK-2100, Denmarke-mail: noa@fys.ku.dk

Nigel R. BadnellUniversity of StrathclydeDepartment of PhysicsGlasgow, G40NG, United Kingdome-mail: n.r.badnell@strath.ac.uk

Thomas BartschGeorgia Institute of TechnologySchool of Physics837 State StreetAtlanta, GA 30332-0430, USAe-mail: bartsch@cns.physics.gatech.edu

Klaus BartschatDrake UniversityDepartment of Physics and AstronomyDes Moines, IA 50311, USAe-mail: klaus.bartschat@drake.edu

William E. BaylisUniversity of WindsorDepartment of PhysicsWindsor, ON N9B 3P4, Canadae-mail: baylis@uwindsor.ca

Anand K. BhatiaNASA Goddard Space Flight CenterLaboratory for Astronomy & Solar PhysicsCode 681, UV/Optical Astronomy BranchGreenbelt, MD 20771, USAe-mail: anand.k.bhatia@nasa.gov

Hans BichselUniversity of WashingtonCenter for Experimental Nuclear Physics andAstrophysics (CENPA)1211 22nd Avenue EastSeattle, WA 98112-3534, USAe-mail: bichsel@npl.washington.edu

Robert W. BoydUniversity of RochesterDepartment of Physics and AstronomyRochester, NY 14627, USAe-mail: boyd@optics.rochester.edu

John M. BrownUniversity of OxfordPhysical and Theoretical Chemistry LaboratorySouth Parks RoadOxford, OX1 3QZ, Englande-mail: john.m.brown@chem.ox.ac.uk

Henry BuijsABB Bomem Inc.585, Charest Boulevard EastSuite 300Québec, PQ G1K 9H4, Canadae-mail: henry.l.buijs@ca.abb.com

Philip BurkeThe Queen’s University of BelfastDepartment of Applied Mathematicsand Theoretical PhysicsBelfast, Northern Ireland BT7 1NN, UKe-mail: p.burke@qub.ac.uk

XII List of Authors

Denise CaldwellNational Science FoundationPhysics Division4201 Wilson BoulevardArlington, VA 22230, USAe-mail: dcaldwel@nsf.gov

Mark M. CassarUniversity of WindsorDepartment of PhysicsWindsor, ON N9B 3P4, Canadae-mail: cassar@uwindsor.ca

Kelly ChanceHarvard-Smithsonian Center for Astrophysics60 Garden StreetCambridge, MA 02138-1516, USAe-mail: kchance@cfa.harvard.edu

Raymond Y. Chiao366 Leconte HallU.C. BerkeleyBerkeley, CA 94720-7300, USAe-mail: chiao@physics.berkeley.edu

Lew CockeKansas State UniversityDepartment of PhysicsManhattan, KS 66506, USAe-mail: cocke@phys.ksu.edu

James S. CohenLos Alamos National LaboratoryAtomic and Optical TheoryLos Alamos, NM 87545, USAe-mail: cohen@lanl.gov

Bernd CrasemannUniversity of OregonDepartment of PhysicsEugene, OR 97403-1274, USAe-mail: berndc@uoregon.edu

David R. CrosleySRI InternationalMolecular Physics Laboratory333 Ravenswood Ave., PS085Menlo Park, CA 94025-3493, USAe-mail: david.crosley@sri.com

Derrick CrothersQueen’s University BelfastDepartment of Applied Mathematics andTheoretical PhysicsUniversity RoadBelfast, Northern Ireland BT7 1NN, UKe-mail: d.crothers@qub.ac.uk

Lorenzo J. CurtisUniversity of ToledoDepartment of Physics and Astronomy2801 West Bancroft StreetToledo, OH 43606-3390, USAe-mail: ljc@physics.utoledo.edu

Alexander DalgarnoHarvard-Smithsonian Center for Astrophysics60 Garden StreetCambridge, MA 02138, USAe-mail: adalgarno@cfa.harvard.edu

Abigail J. DobbynMax-Planck-Institut für StrömungsforschungGöttingen, 37073, Germany

Gordon W. F. DrakeUniversity of WindsorDepartment of Physics401 Sunset St.Windsor, ON N9B 3P4, Canadae-mail: gdrake@uwindsor.ca

Joseph H. EberlyUniversity of RochesterDepartment of Physics and Astronomyand Institute of OpticsRochester, NY 14627-0171, USAe-mail: eberly@pas.rochester.edu

Guy T. EmeryBowdoin CollegeDepartment of Physics15 Chestnut Rd.Brunswick, ME 04011, USAe-mail: gemery@bowdoin.edu

List of Authors XIII

Volker EngelUniversität WürzburgInstitut für Physikalische ChemieAm HublandWürzburg, 97074, Germanye-mail: voen@phys-chemie.uni-wuerzburg.de

Paul EngelkingUniversity of OregonDepartment of Chemistryand Chemical Physics InstituteEugene, OR 97403-1253, USAe-mail: engelki@uoregon.edu

Kenneth M. Evenson†

James M. FarrarUniversity of RochesterDepartment of Chemistry120 Trustee RoadRochester, NY 14627-0216, USAe-mail: farrar@chem.rochester.edu

Gordon FeldmanThe Johns Hopkins UniversityDepartment of Physics and AstronomyBaltimore, MD 21218-2686, USAe-mail: gordon.feldman@jhu.edu

Paul D. FeldmanThe Johns Hopkins UniversityDepartment of Physics and Astronomy3400 N. Charles StreetBaltimore, MD 21218-2686, USAe-mail: pdf@pha.jhu.edu

Charlotte F. FischerVanderbilt UniversityDepartment of Electrical EngineeringComputer SciencePO BOX 1679, Station BNashville, TN 37235, USAe-mail: charlotte.f.fischer@vanderbilt.edu

Victor FlambaumUniversity of New South WalesDepartment of PhysicsSydney, 2052, Australiae-mail: v.flambaum@unsw.edu.au

M. Raymond FlanneryGeorgia Institute of TechnologySchool of PhysicsAtlanta, GA 30332-0430, USAe-mail: ray.flannery@physics.gatech.edu

David R. FlowerUniversity of DurhamDepartment of PhysicsSouth RoadDurham, DH1 3LE, United Kingdome-mail: david.flower@durham.ac.uk

A. Lewis FordTexas A&M UniversityDepartment of PhysicsCollege Station, TX 77843-4242, USAe-mail: ford@physics.tamu.edu

Jane L. FoxWright State UniversityDepartment of Physics3640 Colonel Glenn HwyDayton, OH 45419, USAe-mail: jane.fox@wright.edu

Matthias FreybergerUniversität UlmAbteilung für QuantenphysikAlbert Einstein Allee 11Ulm, 89069, Germanye-mail: matthias.freyberger@uni-ulm.de

Thomas FultonThe Johns Hopkins UniversityThe Henry A. Rowland Departmentof Physics and AstronomyBaltimore, MD 21218-2686, USAe-mail: Thomas.Fulton@jhu.edu

Alexander L. GaetaCornell UniversityDepartment of Applied and Engineering PhysicsIthaca, NY 14853-3501, USAe-mail: a.gaeta@cornell.edu

XIV List of Authors

Alan GallagherJILA, University of Colorado and National Instituteof Standards and TechnologyQuantum Physics DivisionBoulder, CO 80309-0440, USAe-mail: alang@jila.colorado.edu

Thomas F. GallagherUniversity of VirginiaDepartment of Physics382 McCormick RoadCharlottesville, VA 22904-4714, USAe-mail: tfg@virginia.edu

Muriel GargaudObservatoire Aquitain des Sciences de l’Univers2 Rue de l’Observatoire33270 Floirac, Francee-mail: gargaud@obs.u-bordeaux1.fr

Alan GarscaddenAirforce Research LaboratoryArea B1950 Fifth StreetWright Patterson Air Force Base,OH 45433-7251, USAe-mail: alan.garscadden@wpafb.af.mil

John GlassBritish TelecommunicationsSolution DesignRiverside Tower (pp RT03-44)Belfast, Northern Ireland BT1 3BT, UKe-mail: john.glass@bt.com

S. Pedro GoldmanThe University of Western OntarioDepartment of Physics & AstronomyLondon, ON N6A 3K7, Canadae-mail: goldman@uwo.ca

Ian P. GrantUniversity of OxfordMathematical Institute24/29 St. Giles’Oxford, OX1 3LB, UKe-mail: ipg@maths.ox.ac.uk

Donald C. GriffinRollins CollegeDepartment of Physics1000 Holt Ave.Winter Park, FL 32789, USAe-mail: griffin@vanadium.rollins.edu

William G. HarterUniversity of ArkansasDepartment of PhysicsFayetteville, AR 72701, USAe-mail: wharter@uark.edu

Carsten HenkelUniversität PotsdamInstitut für PhysikAm Neuen Palais 10Potsdam, 14469, Germanye-mail: carsten.henkel

@quantum.physik.uni-potsdam.de

Eric HerbstThe Ohio State UniversityDepartments of Physics191 W. Woodruff Ave.Columbus, OH 43210-1106, USAe-mail: herbst@mps.ohio-state.edu

Robert N. Hill355 Laurel AvenueSaint Paul, MN 55102-2107, USAe-mail: rnhill@fishnet.com

David L. HuestisSRI InternationalMolecular Physics LaboratoryMenlo Park, CA 94025, USAe-mail: david.huestis@sri.com

Mitio InokutiArgonne National LaboratoryPhysics Division9700 South Cass AvenueBuilding 203Argonne, IL 60439, USAe-mail: inokuti@anl.gov

List of Authors XV

Takeshi IshiharaUniversity of TsukubaInstitute of Applied PhysicsIbaraki 305Tsukuba, 305-8577, Japan

Juha JavanainenUniversity of ConnecticutDepartment of PhysicsUnit 30462152 Hillside RoadStorrs, CT 06269-3046, USAe-mail: jj@phys.uconn.edu

Erik T. JensenUniversity of Northern British ColumbiaDepartment of Physics3333 University WayPrince George, BC V2N 4Z9, Canadae-mail: ejensen@unbc.ca

Brian R. JuddThe Johns Hopkins UniversityDepartment of Physics and Astronomy3400 North Charles StreetBaltimore, MD 21218, USAe-mail: juddbr@pha.jhu.edu

Alexander A. KachanovResearch and DevelopmentPicarro, Inc.480 Oakmead ParkwaySunnyvale, CA 94085, USAe-mail: akachanov@picarro.com

Isik KanikCalifornia Institute of TechnologyJet Propulsion LaboratoryPasadena, CA 91109, USAe-mail: isik.kanik@jpl.nasa.gov

Savely G. KarshenboimD.I.Mendeleev Institute for Metrology (VNIIM)Quantum Metrology DepartmentMoskovsky pr. 19St. Petersburg, 190005, Russiae-mail: sek@mpq.mpg.de

Kate P. KirbyHarvard-Smithsonian Center for Astrophysics60 Garden Street MS-14Cambridge, MA 02138, USAe-mail: kkirby@cfa.havard.edu

Sir Peter L. KnightImperial College LondonDepartment of PhysicsBlackett LaboratoryPrince Consort RoadLondon, SW7 2BW, UKe-mail: p.knight@imperial.ac.uk

Manfred O. KrauseOak Ridge National Laboratory125 Baltimore DriveOak Ridge, TN 37830, USAe-mail: mok@ornl.gov

Kenneth C. KulanderLawrence Livermore National Laboratory7000 East Ave.Livermore, CA 94551, USAe-mail: kulander@llnl.gov

Paul G. KwiatUniversity of Illinois at Urbana-ChampaignDepartment of Physics1110 West Green StreetUrbana, IL 61801-3080, USAe-mail: kwiat@uiuc.edu

Yuan T. LeeAcademia SinicaInstitute of Atomic and Molecular SciencePO BOX 23-166Taipei, 106, Taiwan

Stephen LeppUniversity of NevadaDepartment of Physics4505 Maryland PkwyLas Vegas, NV 89154-4002, USAe-mail: lepp@unlv.edu

XVI List of Authors

Maciej LewensteinICFO–Institut de Ciéncies FotóniquesC. Jordi Ginora 29 Nexus IIBarcelona, 08034, Spaine-mail: maciej.lewenstein@icfo.es

James D. LouckLos Alamos National LaboratoryRetired Laboratory FellowPO BOX 1663Los Alamos, NM 87545, USAe-mail: jimlouck@aol.com

Joseph H. MacekUniversity of Tennessee and Oak Ridge NationalLaboratoryDepartment of Physics and Astronomy401 Nielsen Physics Bldg.Knoxville, TN 37996-1200, USAe-mail: jmacek@utk.edu

Mary L. MandichLucent Technologies Inc.Bell Laboratories600 Mountain AvenueMurray Hill, NJ 07974, USAe-mail: mandich@lucent.com

Edmund J. ManskyOak Ridge National LaboratoryControlled Fusion Atomic Data CenterOak Ridge, TN 37831, USAe-mail: edmundmansky@intdata.com

Steven T. MansonGeorgia State UniversityDepartment of Physics and AstronomyAtlanta, GA 30303, USAe-mail: smanson@gsu.edu

William C. MartinNational Institute of Standards and TechnologyAtomic Physics DivisionGaithersburg, MD 20899-8422, USAe-mail: wmartin@nist.gov

Jim F. McCannQueen’s University BelfastDept. of Applied Mathematicsand Theoretical PhysicsBelfast, Northern Ireland BT7 1NN, UKe-mail: j.f.mccann@qub.ac.uk

Ronald McCarrollUniversité Pierre et Marie CurieLaboratoire de Chimie Physique11 rue Pierre et Marie Curie75231 Paris Cedex 05, Francee-mail: mccarrol@ccr.jussieu.fr

Fiona McCauslandNorthern Ireland Civil ServiceDepartment of Enterprise Trade and InvestmentMassey AvenueBelfast, Northern Ireland BT4 2JP, UKe-mail: fiona.mccausland@detini.gov.uk

William J. McConkeyUniversity of WindsorDepartment of PhysicsWindsor, ON N9B 3P4, Canadae-mail: mcconk@uwindsor.ca

Robert P. McEachranAustralian National UniversityAtomic and Molecular Physics LaboratoriesResearch School of Physical Sciencesand EngineeringCanberra, ACT 0200, Australiae-mail: robert.mceachran@anu.edu.au

James H. McGuireTulane UniversityDepartment of Physics6823 St. Charles Ave.New Orleans, LA 70118-5698, USAe-mail: mcguire@tulane.edu

Dieter MeschedeRheinische Friedrich-Wilhelms-Universität BonnInstitut für Angewandte PhysikWegelerstraße 8Bonn, 53115, Germanye-mail: meschede@iap.uni-bonn.de

List of Authors XVII

Pierre MeystreUniversity of ArizonaDepartment of Physics1118 E, 4th StreetTucson, AZ 85721-0081, USAe-mail: meystre@physics.arizona

Peter W. Milonni104 Sierra Vista Dr.Los Alamos, NM 87544, USAe-mail: pwm@lanl.gov

Peter J. MohrNational Institute of Standards and TechnologyAtomic Physics Division100 Bureau Drive, Stop 8420Gaithersburg, MD 20899-8420, USAe-mail: mohr@nist.gov

David H. MordauntMax-Planck-Institut für StrömungsforschungGöttingen, 37073, Germany

John D. Morgan IIIUniversity of DelawareDepartment of Physics and AstronomyNewark, DE 19716, USAe-mail: jdmorgan@udel.edu

Michael S. MurilloLos Alamos National LaboratoryTheoretical DivisionPO BOX 1663Los Alamos, NM 87545, USAe-mail: murillo@lanl.gov

Evgueni E. NikitinTechnion-Israel Institute of TechnologyDepartment of ChemistryHaifa, 32000, Israele-mail: nikitin@techunix.technion.ac.il

Robert F. O’ConnellLouisiana State UniversityDepartment of Physics and AstronomyBaton Rouge, LA 70803-4001, USAe-mail: oconnell@phys.lsu.edu

Francesca O’RourkeQueen’s University BelfastDepartment of Applied Mathematics andTheoretical PhysicsUniversity RoadBelfast, BT7 1NN, UKe-mail: s.orourke@qub.ac.uk

Ronald E. OlsonUniversity of Missouri-RollaPhysics DepartmentRolla, MO 65409, USAe-mail: olson@umr.edu

Barbara A. PaldusSkymoon Ventures3045 Park BoulevardPalo Alto, CA 94306, USAe-mail: bpaldus@skymoonventures.com

Josef PaldusUniversity of WaterlooDepartment of Applied Mathematics200 University Avenue WestWaterloo, ON N2L 3G1, Canadae-mail: paldus@scienide.uwaterloo.ca

Gillian PeachUniversity College LondonDepartment of Physics and AstronomyLondon, WC1 E6BT, UKe-mail: g.peach@ucl.ac.uk

Ruth T. PedlowQueen’s University BelfastDepartment of Applied Mathematicsand Theoretical PhysicsUniversity RoadBelfast, Northern Irland BT7 1NN, UKe-mail: r.pedlow@qub.ac.uk

David J. PeggUniversity of TennesseeDepartment of PhysicsNielsen BuildingKnoxville, TN 37996, USAe-mail: djpegg@utk.edu

XVIII List of Authors

Ekkehard PeikPhysikalisch-Technische BundesanstaltBundesallee 100Braunschweig, 38116, Germanye-mail: ekkehard.peik@ptb.de

Ronald PhaneufUniversity of NevadaDepartment of PhysicsMS-220Reno, NV 89557-0058, USAe-mail: phaneuf@unr.edu

Michael S. PindzolaAuburn UniversityDepartment of PhysicsAuburn, AL 36849, USAe-mail: pindzola@physics.auburn.edu

Eric H. PinningtonUniversity of AlbertaDepartment of PhysicsEdmonton, AB T6H 0B3, Canadae-mail: pinning@phys.ualberta.ca

Richard C. PowellUniversity of ArizonaOptical Sciences CenterTuscon, AZ 85721, USAe-mail: rcpowell@email.arizona.edu

John F. ReadingTexas A&M UniversityDepartment of PhysicsCollege Station, TX 77843, USAe-mail: reading@physics.tamu.edu

Jonathan R. SapirsteinUniversity of Notre DameDepartment of Physics319 Nieuwland ScienceNotre Dame, IN 46556, USAe-mail: jsapirst@nd.edu

Stefan ScheelImperial College LondonBlackett LaboratoryPrince Consort RoadLondon, SW7 2BW, UKe-mail: s.scheel@imperial.ac.uk

Axel SchenzleLudwig-Maximilians-UniversitätDepartment für PhysikTheresienstraße 37München, 80333, Germanye-mail: axel.schenzle@physik.uni-muenchen.de

Reinhard SchinkeMax-Planck-Institut für Dynamik &SelbstorganisationBunsenstr. 10Göttingen, 37073, Germanye-mail: rschink@gwdg.de

Wolfgang P. SchleichUniversität UlmAbteilung für QuantenphysikAlbert Einstein Allee 11Ulm, 89069, Germanye-mail: wolfgang.schleich@uni-ulm.de

David R. SchultzOak Ridge National LaboratoryPhysics DivisionOak Ridge, TN 37831-6373, USAe-mail: schultz@mail.phy.ornl.gov

Michael SchulzUniversity of Missouri-RollaPhysics Department1870 Miner CircleRolla, MO 65409, USAe-mail: schulz@umr.edu

Peter L. SmithHarvard UniversityHarvard-Smithsonian Center for Astrophysics60 Garden StreetCambridge, MA 02138, USAe-mail: plsmith@cfa.havard.edu

List of Authors XIX

Anthony F. StaraceThe University of NebraskaDepartment of Physics and Astronomy116 Brace LaboratoryLincoln, NE 68588-0111, USAe-mail: astarace1@unl.edu

Glenn StarkWellesley CollegeDepartment of Physics106 Central StreetWellesley, MA 02481, USAe-mail: gstark@wellesley.edu

Allan StaufferDepartment of Physics and AstronomyYork University4700 Keele StreetToronto, ON M3J 1P3, Canadae-mail: stauffer@yorku.ca

Aephraim M. SteinbergUniversity of TorontoDepartment of PhysicsToronto, ON M5S 1A7, Canadae-mail: steinberg@physics.utoronto.ca

Stig StenholmRoyal Institute of TechnologyPhysics DepartmentRoslagstullsbacken 21Stockholm, SE-10691, Swedene-mail: stenholm@atom.kth.se

Jack C. StratonPortland State UniversityUniversity Studies117P Cramer HallPortland, OR 97207, USA

Michael R. StrayerOak Ridge National LaboratoryPhysics DivisionOak Ridge, TN 37831-6373, USAe-mail: strayer@csep2.phy.ornl.gov

Carlos R. Stroud Jr.University of RochesterInstitute of OpticsRochester, NY 14627-0186, USAe-mail: stroud@optics.rochester.edu

Arthur G. SuitsState University of New YorkDepartment of ChemistryStony Brook, NY 11794, USAe-mail: arthur.suits@sunysb.edu

Barry N. TaylorNational Institute of Standards and TechnologyAtom Physics Division100 Bureau DriveGaithersburg, MD 20899-8401, USAe-mail: barry.taylor@nist.gov

Aaron TemkinNASA Goddard Space Flight CenterLaboratory for Solar and Space PhysicsSolar Physics BranchGreenbelt, MD 20771, USAe-mail: aaron.temkin-1@nasa.gov

Sandor TrajmarCalifornia Institute of TechnologyJet Propulsion Laboratory3847 Vineyard DriveRedwood City, 94063, USAe-mail: strajmar@comcast.net

Elmar TräbertRuhr-Universität BochumExperimentalphysik III/NB3Bochum, 44780, Germanye-mail: traebert@ep3.rub.de

Turgay UzerGeorgia Institute of TechnologySchool of Physics837 State StreetAtlanta, GA 30332-0430, USAe-mail: turgay.uzer@physics.gatech.edu

XX List of Authors

Karl VogelUniversität UlmAbteilung für QuantenphysikAlbert Einstein Allee 11Ulm, 89069, Germanye-mail: karl.vogel@uni-ulm.de

Jon C. WeisheitWashington State UniversityInstitute for Shock PhysicsPO BOX 64 28 14Pullman, WA 99164, USAe-mail: weisheit@wsu.edu

Wolfgang L. WieseNational Institute of Standards and Technology100 Bureau DriveGaithersburg, MD 20899, USAe-mail: wiese@nist.gov

Martin WilkensUniversität PotsdamInstitut für PhysikAm Neuen Palais 10Potsdam, 14469, Germanye-mail: martin.wilkens@physik.uni-potsdam.de

David R. YarkonyThe Johns Hopkins UniversityDepartment of ChemistryBaltimore, MD 21218, USAe-mail: yarkony@jhu.edu

Springer Handbook of Atomic, Molecular, and Optical PhysicsOrganization of the Handbook

Part A gathers together the mathematical methods applicable to a wideclass of problems in atomic, molecular, and optical physics. The applicationof angular momentum theory to quantum mechanics is presented. Thebasic tenet that isolated physical systems are invariant to rotations of thesystem is thereby implemented into physical theory. The powerful methodsof group theory and second quantization show how simplifications arise ifthe atomic shell is treated as a basic structural unit. The well establishedsymmetry groups of quantum mechanical Hamiltonians are extendedto the larger compact and noncompact dynamical groups. Perturbationtheory is introduced as a bridge between an exactly solvable problem anda corresponding real one, allowing approximate solutions of various systemsof differential equations. The consistent manner in which the density matrixformalism deals with pure and mixed states is developed, showing how thepreparation of an initial state as well as the details regarding the observationof the final state can be treated in a systematic way. The basic computationaltechniques necessary for accurate and efficient numerical calculationsessential to all fields of physics are outlined and a summary of relevantsoftware packages is given. The ever present one-electron solutions of thenonrelativistic Schrödinger equation and the relativistic Dirac equation forthe Coulomb potential are then summarized.

Part A Mathematical Methods2 Angular Momentum Theory3 Group Theory for Atomic Shells4 Dynamical Groups5 Perturbation Theory6 Second Quantization7 Density Matrices8 Computational Techniques9 Hydrogenic Wave Functions

Part B presents the main concepts in the theoretical and experimentalknowledge of atomic systems, including atomic structure and radiation.Ionization energies for neutral atoms and transition probabilities of selectedneutral atoms are tabulated. The computational methods needed for veryhigh precision approximations for helium are summarized. The physicaland geometrical significance of simple multipoles is examined. Thebasic nonrelativistic and relativistic theory of electrons and atoms inexternal magnetic fields is given. Various properties of Rydberg atoms inexternal fields and in collisions are investigated. The sources of hyperfinestructure in atomic and molecular spectra are outlined, and the resultingenergy splittings and isotope shifts given. Precision oscillator strengthand lifetime measurements, which provide stringent experimental testsof fundamental atomic structure calculations, are discussed. Ion beamspectroscopy is introduced, and individual applications of ion beamtechniques are detailed A basic description of neutral collisional line shapesis given, along with a discussion of radiation transfer in a confined atomicvapor. Many qualitative features of the Thomas–Fermi model are studiedand its later outgrowth into general density functional theory delineated.The Hartree–Fock and multiconfiguration Hartree–Fock theories, alongwith configuration interaction methods, are discussed in detail, and theirapplication to the calculation of various atomic properties presented.Relativistic methods for the calculation of atomic structure for generalmany-electron atoms are described. A consistent diagrammatic method forcalculating the structure of atoms and the characteristics of different atomic

Part B Atoms10 Atomic Spectroscopy11 High Precision Calculations

for Helium12 Atomic Multipoles13 Atoms in Strong Fields14 Rydberg Atoms15 Rydberg Atoms

in Strong Static Fields16 Hyperfine Structure17 Precision Oscillator Strength

and Lifetime Measurements18 Spectroscopy of Ions

Using Fast Beams and Ion Traps19 Line Shapes and Radiation Transfer20 Thomas–Fermi and Other

Density-Functional Theories21 Atomic Structure:

Multiconfiguration Hartree–FockTheories

22 Relativistic Atomic Structure23 Many-Body Theory of Atomic

Structure and Processes24 Photoionization of Atoms

XXII

processes is given. An outline of the theory of atomic photoionization andthe dynamics of the photon–atom collision process is presented. Those kindsof electron correlation that are most important in photoionization are em-phasized. The process of autoionization is treated as a quasibound stateimbedded in the scattering continuum, and a brief description of the mainelements of the theory is given. Green’s function techniques are applied tothe calculation of higher order corrections to atomic energy levels, and alsoof transition amplitudes for radiative transitions of atoms. Basic quantumelectrodynamic calculations, which are needed to explain small deviationsfrom the solution to the Schrödinger equation in simple systems, are pre-sented. Comparisons of precise measurements and theoretical predictionsthat provide tests of our knowledge of fundamental physics are made, fo-cussing on several quantitative tests of quantum electrodynamics. Precisemeasurements of parity nonconserving effects in atoms could lead to pos-sible modifications of the Standard Model, and thus uncover new physics.An approach to this fundamental problem is described. The problem of thepossible variation of the fundamental constants with time is discussed in re-lation to atomic clocks and precision frequency measurements. The mostadvanced atomic clocks are described, and the current laboratory constraintson these variations are listed.

Part B Atoms25 Autoionization26 Green’s Functions of Field Theory27 Quantum Electrodynamics28 Tests of Fundamental Physics29 Parity Nonconserving Effects

in Atoms30 Atomic Clocks and Constraints

on Variations of FundamentalConstants

Part C begins with a discussion of molecular structure from a theoreti-cal/computational perspective using the Born–Oppenheimer approximationas the point of departure. The key role that symmetry considerations playin organizing and simplifying our knowledge of molecular dynamics andspectra is described. The theory of radiative transition probabilities, whichdetermine the intensities of spectral lines, for the rotationally-resolved spec-tra of certain model molecular systems is summarized. The ways in whichmolecular photodissociation is studied in the gas phase are outlined. Theresults presented are particularly relevant to the investigation of combus-tion and atmospheric reactions. Modern experimental techniques allow thedetailed motions of the atomic constituents of a molecule to be resolved asa function of time. A brief description of the basic ideas behind these tech-niques is given, with an emphasis on gas phase molecules in collision-freeconditions. The semiclassical and quantal approaches to nonreactive scat-tering are outlined. Various quantitative approaches toward a description ofthe rates of gas phase chemical reactions are presented and then evaluatedfor their reliability and range of application. Ionic reactions in the gas phaseare also considered. Clusters, which are important in many atmospheric andindustrial processes, are arranged into six general categories, and then thephysics and chemistry common to each category is described. The most im-portant spectroscopic techniques used to study the properties of moleculesare presented in detail.

Part C Molecules31 Molecular Structure32 Molecular Symmetry and Dynamics33 Radiative Transition Probabilities34 Molecular Photodissociation35 Time-Resolved Molecular Dynamics36 Nonreactive Scattering37 Gas Phase Reactions38 Gas Phase Ionic Reactions39 Clusters40 Infrared Spectroscopy41 Laser Spectroscopy in the Submil-

limeter and Far-Infrared Regions42 Spectroscopic Techniques: Lasers43 Spectroscopic Techniques:

Cavity-Enhanced Methods44 Spectroscopic Techniques:

Ultraviolet

Part D collects together the topics and approaches used in scatteringtheory. A handy compendium of equations, formulae, and expressions forthe classical, quantal, and semiclassical approaches to elastic scatteringis given; reactive systems and model potentials are also considered. Thedependence of scattering processes on the angular orientation of thereactants and products is discussed through the analysis of scatteringexperiments which probe atomic collision theories at a fundamental level.

Part D Scattering Theory45 Elastic Scattering: Classical,

Quantal, and Semiclassical46 Orientation and Alignment

in Atomic and Molecular Collisions47 Electron–Atom, Electron–Ion,

and Electron–Molecule Collisions

XXIII

The detailed quantum mechanical techniques available to perform accuratecalculations of scattering cross sections from first principles are presented.The theory of elastic, inelastic, and ionizing collisions of electrons withatoms and atomic ions is covered and then extended to include collisionswith molecules. The standard scattering theory for electrons is extendedto include positron collisions with atomic and molecular systems. Slowcollisions of atoms or molecules within the adiabatic approximation are dis-cussed; important deviations from this model are presented in some detailfor the low energy case. The main methods in the theoretical treatment ofion-atom and atom–atom collisions are summarized with a focus on inter-mediate and high collision velocities. The molecular structure and collisiondynamics involved in ion–atom charge exchange reactions is studied. Boththe perturbative and variational capture theories of the continuum distortedwave model are presented. The Wannier theory for threshold ionization isthen developed. Studies of the energy and angular distribution of electronsejected by the impact of high-velocity atomic or ionic projectiles on atomictargets are overviewed. A useful collection of formulae, expressions, andspecific equations that cover the various approaches to electron-ion andion-ion recombination processes is given. A basic theoretical formulation ofdielectronic recombination is described, and its importance in the interpre-tation of plasma spectral emission is presented. Many of the equations usedto study theoretically the collisional properties of both charged and neutralparticles with atoms and molecules in Rydberg states are collected together;the primary approximations considered are the impulse approximation, thebinary encounter approximation, and the Born approximation. The Thomasmass-transfer process is considered from both a classical and a quantalperspective. Additional features of this process are also discussed. The the-oretical background, region of validity, and applications of the classicaltrajectory Monte Carlo method are then delineated. One-photon processesare discussed and aspects of line broadening directly related to collisionsbetween an emitting, or absorbing, atom and an electron, a neutral atom oran atomic ion are considered.

Part D Scattering Theory48 Positron Collisions49 Adiabatic and Diabatic Collision

Processes at Low Energies50 Ion–Atom and Atom–Atom

Collisions51 Ion–Atom Charge Transfer Reactions

at Low Energies52 Continuum Distorted Wave

and Wannier Methods53 Ionization in High Energy

Ion–Atom Collisions54 Electron–Ion and Ion–Ion

Recombination55 Dielectronic Recombination56 Rydberg Collisions:

Binary Encounter, Born and ImpulseApproximations

57 Mass Transfer at High Energies:Thomas Peak

58 Classical Trajectoryand Monte Carlo Techniques

59 Collisional Broadeningof Spectral Lines

Part E focuses on the experimental aspects of scattering processes. Recentdevelopments in the field of photodetachment are reviewed, with anemphasis on accelerator-based investigations of the photodetachment ofatomic negative ions. The theoretical concepts and experimental methodsfor the scattering of low-energy photons, proceeding primarily through thephotoelectric effect, are given. The main photon–atom interaction processesin the intermediate energy range are outlined. The atomic response toinelastic photon scattering is discussed; essential aspects of radiativeand radiationless transitions are described in the two-step approximation.Advances such as cold-target recoil-ion momentum spectroscopy are alsotouched upon. Electron–atom and electron–molecule collision processes,which play a prominent role in a variety of systems, are presented. Thediscussion is limited to electron collisions with gaseous targets, wheresingle collision conditions prevail, and to low-energy impact processes.The physical principles and experimental methods used to investigate lowenergy ion–atom collisions are outlined. Inelastic processes which occur incollisions between fast, often highly charged, ions and atoms, are described.A summary of the methods commonly employed in scattering experiments

Part E Scattering Experiment60 Photodetachment61 Photon–Atom Interactions:

Low Energy62 Photon–Atom Interactions:

Intermediate Energies63 Electron–Atom

and Electron–Molecule Collisions64 Ion–Atom Scattering Experiments:

Low Energy65 Ion–Atom Collisions – High Energy66 Reactive Scattering67 Ion–Molecule Reactions

XXIV

involving neutral molecules at chemical energies is presented. Applica-tions of single-collision scattering methods to the study of reactive collisiondynamics of ionic species with neutral partners are discussed.

Part F presents a coherent collection of the main topics and issuesfound in quantum optics. Optical physics, which is concerned with thedynamical interactions of atoms and molecules with electromagneticfields, is first discussed within the context of semiclassical theories, andthen extended to a fully quantized version. The theoretical techniquesused to describe absorption and emission spectra using density matrixmethods are developed. Applications of the dark state in laser physics isbriefly mentioned. The basic concepts common to all lasers, such as gain,threshold, and electromagnetic modes of oscillation are described. Recentdevelopments in laser physics, including single-atom lasers, two-photonlasers, and the generation of attosecond pulses are also introduced. Thecurrent status of the development of different types of lasers – includingnanocavity, quantum-cascade and free-electron lasers – are summarized.The important operational characteristics, such as frequency range andoutput power, are given for each of the types of lasers described. Nonlinearprocesses arising from the modifications of the optical properties ofa medium due to the passage of intense light beams are discussed. Additionalprocesses that are enabled by the use of ultrashort or ultra-intense laserpulses are presented. The concept of coherent optical transients in atomic andmolecular systems reviewed; homogeneous and inhomogeneous relaxationin the theory are properly distinguished. Multiphoton and strong-fieldprocesses are given a theoretical description. A discussion of the generationof sub-femtosecond pulses is also included. General and specific theoriesfor the control of atomic motion by light are presented. Various traps usedfor the cooling and trapping of charged and neutral particles and theirapplications are discussed. The fundamental physics of dilute quantumdegenerate gases is outlined, especially in connection with Bose–Einsteincondensation. de Broglie optics, which concerns the propagation of matterwaves, is presented with a concentration on the underlying principles andthe illustration of these principles. The fundamentals of the quantizedelectromagnetic field and applications to the broad area of quantum opticsare discussed. A detailed description of the changes in the atom–fieldinteraction that take place when the radiation field is modified by thepresence of a cavity is given. The basic concepts needed to understandcurrent research, such as the EPR experiment, Bell’s inequalities, squeezedstates of light, the properties of electromagnetic waves in cavities, and othertopics depending on the nonlocality of light are reviewed. Applications tocryptography, tunneling times, and gravity wave detectors are included,along with recent work on “fast light” and “slow light.” Correlations andquantum superpositions which can be exploited in quantum informationprocessing and secure communication are delineated. Their link to quantumcomputing and quantum cryptography is given explicitly.

Part F Quantum Optics68 Light–Matter Interaction69 Absorption and Gain Spectra70 Laser Principles71 Types of Lasers72 Nonlinear Optics73 Coherent Transients74 Multiphoton and Strong-Field

Processes75 Cooling and Trapping76 Quantum Degenerate Gases77 De Broglie Optics78 Quantized Field Effects79 Entangled Atoms and Fields:

Cavity QED80 Quantum Optical Tests

of the Foundations of Physics81 Quantum Information

Part G is concerned with the various applications of atomic, molecular, andoptical physics. A summary of the processes that take place in photoionizedgases, collisionally ionized gases, the diffuse interstellar medium, molecularclouds, circumstellar shells, supernova ejecta, shocked regions, and the early

Part G Applications82 Applications of Atomic

and Molecular Physicsto Astrophysics

XXV

Universe are presented. The principal atomic and molecular processes thatlead to the observed cometary spectra, as well as the needs for basic atomicand molecular data in the interpretation of these spectra, are focused on.The basic methods used to understand planetary atmospheres are given.The structure of atmospheres and their interaction with solar radiation aredetailed, with an emphasis on ionospheres. Atmospheric global change isthen studied in terms of the applicable atomic and molecular processes re-sponsible for these changes. A summary of the well-known prescriptionsfor atomic structure and ionization balance, and a discussion of the modi-fied transition rates for ions in dense plasmas are given. A review of currentsimulations being used to address a wide array of issues needed to accu-rately describe atoms in dense plasmas is also presented. The main conceptsand processes of the physics and chemistry of the conduction of electricityin ionized gases are described. The physical models and laser diagnosticsused to understand combustion systems are presented. Various applicationsof atomic and molecular physics to phenomena that occur at surfaces arereviewed; particular attention is placed on the application of electron- andphoton-atom scattering processes to obtain surface specific structural andspectroscopic information. The effect of finite nuclear size on the electronicenergy levels of atoms is also detailed; and conversely, the electronic struc-ture effects in nuclear physics are discussed. A discussion of the conceptsneeded in the operation of charged particle detectors and in describing ra-diation effects is introduced. The description is restricted to fast chargedparticles. The key topics in basic radiation physics are then treated, andillustrative examples are given.

Part G Applications83 Comets84 Aeronomy85 Applications of Atomic

and Molecular Physicsto Global Change

86 Atoms in Dense Plasmas87 Conduction of Electricity in Gases88 Applications to Combustion89 Surface Physics90 Interface with Nuclear Physics91 Charged-Particle–Matter

Interactions92 Radiation Physics

XXVII

Contents

List of Tables.............................................................................................. XLVIIList of Abbreviations ................................................................................. LV

1 Units and ConstantsWilliam E. Baylis, Gordon W. F. Drake ....................................................... 11.1 Electromagnetic Units .................................................................... 11.2 Atomic Units ................................................................................. 51.3 Mathematical Constants ................................................................ 5References............................................................................................... 6

Part A Mathematical Methods

2 Angular Momentum TheoryJames D. Louck ........................................................................................ 92.1 Orbital Angular Momentum ............................................................ 122.2 Abstract Angular Momentum .......................................................... 162.3 Representation Functions .............................................................. 182.4 Group and Lie Algebra Actions ....................................................... 252.5 Differential Operator Realizations of Angular Momentum ................ 282.6 The Symmetric Rotor and Representation Functions ........................ 292.7 Wigner–Clebsch–Gordan and 3-j Coefficients ................................. 312.8 Tensor Operator Algebra................................................................. 372.9 Racah Coefficients ......................................................................... 432.10 The 9–j Coefficients ....................................................................... 472.11 Tensor Spherical Harmonics ........................................................... 522.12 Coupling and Recoupling Theory and 3n–j Coefficients .................... 542.13 Supplement on Combinatorial Foundations .................................... 602.14 Tables ........................................................................................... 69References............................................................................................... 72

3 Group Theory for Atomic ShellsBrian R. Judd .......................................................................................... 753.1 Generators .................................................................................... 753.2 Classification of Lie Algebras .......................................................... 763.3 Irreducible Representations ........................................................... 773.4 Branching Rules ............................................................................ 783.5 Kronecker Products........................................................................ 793.6 Atomic States ................................................................................ 803.7 The Generalized Wigner–Eckart Theorem ........................................ 823.8 Checks .......................................................................................... 83References............................................................................................... 84

XXVIII Contents

4 Dynamical GroupsJosef Paldus ............................................................................................ 874.1 Noncompact Dynamical Groups ...................................................... 874.2 Hamiltonian Transformation and Simple Applications ..................... 904.3 Compact Dynamical Groups ............................................................ 92References............................................................................................... 98

5 Perturbation TheoryJosef Paldus ............................................................................................ 1015.1 Matrix Perturbation Theory (PT) ...................................................... 1015.2 Time-Independent Perturbation Theory ......................................... 1035.3 Fermionic Many-Body Perturbation Theory (MBPT) .......................... 1055.4 Time-Dependent Perturbation Theory ............................................ 111References............................................................................................... 113

6 Second QuantizationBrian R. Judd .......................................................................................... 1156.1 Basic Properties............................................................................. 1156.2 Tensors ......................................................................................... 1166.3 Quasispin ...................................................................................... 1176.4 Complementarity ........................................................................... 1196.5 Quasiparticles ............................................................................... 120References............................................................................................... 121

7 Density MatricesKlaus Bartschat ....................................................................................... 1237.1 Basic Formulae .............................................................................. 1237.2 Spin and Light Polarizations .......................................................... 1257.3 Atomic Collisions ........................................................................... 1267.4 Irreducible Tensor Operators .......................................................... 1277.5 Time Evolution of State Multipoles ................................................. 1297.6 Examples ...................................................................................... 1307.7 Summary ...................................................................................... 133References............................................................................................... 133

8 Computational TechniquesDavid R. Schultz, Michael R. Strayer .......................................................... 1358.1 Representation of Functions .......................................................... 1358.2 Differential and Integral Equations ................................................ 1418.3 Computational Linear Algebra ........................................................ 1488.4 Monte Carlo Methods ..................................................................... 149References............................................................................................... 151

9 Hydrogenic Wave FunctionsRobert N. Hill ........................................................................................... 1539.1 Schrödinger Equation .................................................................... 1539.2 Dirac Equation .............................................................................. 157

Contents XXIX

9.3 The Coulomb Green’s Function ....................................................... 1599.4 Special Functions .......................................................................... 162References............................................................................................... 170

Part B Atoms

10 Atomic SpectroscopyWilliam C. Martin, Wolfgang L. Wiese ....................................................... 17510.1 Frequency, Wavenumber, Wavelength............................................ 17610.2 Atomic States, Shells, and Configurations ....................................... 17610.3 Hydrogen and Hydrogen-Like Ions ................................................. 17610.4 Alkalis and Alkali-Like Spectra ....................................................... 17710.5 Helium and Helium-Like Ions; LS Coupling ..................................... 17710.6 Hierarchy of Atomic Structure in LS Coupling ................................... 17710.7 Allowed Terms or Levels for Equivalent Electrons............................. 17810.8 Notations for Different Coupling Schemes ....................................... 17910.9 Eigenvector Composition of Levels .................................................. 18110.10 Ground Levels and Ionization Energies for the Neutral Atoms .......... 18210.11 Zeeman Effect ............................................................................... 18310.12 Term Series, Quantum Defects, and Spectral-Line Series .................. 18410.13 Sequences .................................................................................... 18510.14 Spectral Wavelength Ranges, Dispersion of Air ................................ 18510.15 Wavelength (Frequency) Standards ................................................ 18610.16 Spectral Lines: Selection Rules, Intensities, Transition Probabilities,

f Values, and Line Strengths .......................................................... 18610.17 Atomic Lifetimes............................................................................ 19410.18 Regularities and Scaling ................................................................ 19410.19 Spectral Line Shapes, Widths, and Shifts......................................... 19510.20 Spectral Continuum Radiation ........................................................ 19610.21 Sources of Spectroscopic Data ........................................................ 197References............................................................................................... 197

11 High Precision Calculations for HeliumGordon W. F. Drake .................................................................................. 19911.1 The Three-Body Schrödinger Equation ............................................ 19911.2 Computational Methods ................................................................ 20011.3 Variational Eigenvalues ................................................................. 20511.4 Total Energies ............................................................................... 20811.5 Radiative Transitions ..................................................................... 21511.6 Future Perspectives ....................................................................... 218References............................................................................................... 218

12 Atomic MultipolesWilliam E. Baylis ...................................................................................... 22112.1 Polarization and Multipoles ........................................................... 22212.2 The Density Matrix in Liouville Space .............................................. 222

XXX Contents

12.3 Diagonal Representation: State Populations ................................... 22412.4 Interaction with Light .................................................................... 22412.5 Extensions .................................................................................... 225References............................................................................................... 226

13 Atoms in Strong FieldsS. Pedro Goldman, Mark M. Cassar ........................................................... 22713.1 Electron in a Uniform Magnetic Field .............................................. 22713.2 Atoms in Uniform Magnetic Fields .................................................. 22813.3 Atoms in Very Strong Magnetic Fields ............................................. 23013.4 Atoms in Electric Fields .................................................................. 23113.5 Recent Developments .................................................................... 233References............................................................................................... 234

14 Rydberg AtomsThomas F. Gallagher ................................................................................ 23514.1 Wave Functions and Quantum Defect Theory................................... 23514.2 Optical Excitation and Radiative Lifetimes ...................................... 23714.3 Electric Fields ................................................................................ 23814.4 Magnetic Fields ............................................................................. 24114.5 Microwave Fields ........................................................................... 24214.6 Collisions ...................................................................................... 24314.7 Autoionizing Rydberg States .......................................................... 244References............................................................................................... 245

15 Rydberg Atoms in Strong Static FieldsThomas Bartsch, Turgay Uzer.................................................................... 24715.1 Scaled-Energy Spectroscopy ........................................................... 24815.2 Closed-Orbit Theory ....................................................................... 24815.3 Classical and Quantum Chaos ......................................................... 24915.4 Nuclear-Mass Effects ..................................................................... 251References............................................................................................... 251

16 Hyperfine StructureGuy T. Emery............................................................................................ 25316.1 Splittings and Intensities ............................................................... 25416.2 Isotope Shifts ................................................................................ 25616.3 Hyperfine Structure ....................................................................... 258References............................................................................................... 259

17 Precision Oscillator Strength and Lifetime MeasurementsLorenzo J. Curtis....................................................................................... 26117.1 Oscillator Strengths ....................................................................... 26217.2 Lifetimes ....................................................................................... 264References............................................................................................... 268

Contents XXXI

18 Spectroscopy of Ions Using Fast Beams and Ion TrapsEric H. Pinnington, Elmar Träbert ............................................................. 26918.1 Spectroscopy Using Fast Ion Beams ................................................ 26918.2 Spectroscopy Using Ion Traps ......................................................... 272References............................................................................................... 277

19 Line Shapes and Radiation TransferAlan Gallagher ........................................................................................ 27919.1 Collisional Line Shapes .................................................................. 27919.2 Radiation Trapping ........................................................................ 287References............................................................................................... 292

20 Thomas–Fermi and Other Density-Functional TheoriesJohn D. Morgan III ................................................................................... 29520.1 Thomas–Fermi Theoryand Its Extensions ........................................ 29620.2 Nonrelativistic Energies of Heavy Atoms ......................................... 30020.3 General Density Functional Theory ................................................. 30120.4 Recent Developments .................................................................... 303References............................................................................................... 304

21 Atomic Structure: Multiconfiguration Hartree–Fock TheoriesCharlotte F. Fischer .................................................................................. 30721.1 Hamiltonians: Schrödinger and Breit–Pauli .................................... 30721.2 Wave Functions: LS and LSJ Coupling .............................................. 30821.3 Variational Principle ...................................................................... 30921.4 Hartree–Fock Theory...................................................................... 30921.5 Multiconfiguration Hartree–Fock Theory ......................................... 31321.6 Configuration Interaction Methods ................................................. 31621.7 Atomic Properties .......................................................................... 31821.8 Summary ...................................................................................... 322References............................................................................................... 322

22 Relativistic Atomic StructureIan P. Grant ............................................................................................ 32522.1 Mathematical Preliminaries ........................................................... 32622.2 Dirac’s Equation ............................................................................ 32822.3 QED: Relativistic Atomic and Molecular Structure ............................. 32922.4 Many-Body Theory For Atoms ........................................................ 33422.5 Spherical Symmetry ....................................................................... 33722.6 Numerical Approximation of Central Field Dirac Equations............... 34422.7 Many-Body Calculations ................................................................ 35022.8 Recent Developments .................................................................... 354References............................................................................................... 355

23 Many-Body Theory of Atomic Structure and ProcessesMiron Ya. Amusia .................................................................................... 35923.1 Diagrammatic Technique ............................................................... 360

XXXII Contents

23.2 Calculation of Atomic Properties ..................................................... 36523.3 Concluding Remarks ...................................................................... 375References............................................................................................... 376

24 Photoionization of AtomsAnthony F. Starace................................................................................... 37924.1 General Considerations .................................................................. 37924.2 An Independent Electron Model ..................................................... 38224.3 Particle–Hole Interaction Effects .................................................... 38424.4 Theoretical Methods for Photoionization ........................................ 38624.5 Recent Developments .................................................................... 38724.6 Future Directions ........................................................................... 388References............................................................................................... 388

25 AutoionizationAaron Temkin, Anand K. Bhatia ............................................................... 39125.1 Introduction ................................................................................. 39125.2 The Projection Operator Formalism ................................................. 39225.3 Forms of P and Q ........................................................................... 39325.4 Width, Shift, and Shape Parameter ................................................ 39425.5 Other Calculational Methods .......................................................... 39625.6 Related Topics ............................................................................... 398References............................................................................................... 399

26 Green’s Functions of Field TheoryGordon Feldman, Thomas Fulton .............................................................. 40126.1 The Two-Point Green’s Function .................................................... 40226.2 The Four-Point Green’s Function .................................................... 40526.3 Radiative Transitions ..................................................................... 40626.4 Radiative Corrections ..................................................................... 408References............................................................................................... 411

27 Quantum ElectrodynamicsJonathan R. Sapirstein ............................................................................. 41327.1 Covariant Perturbation Theory........................................................ 41327.2 Renormalization Theory and Gauge Choices .................................... 41427.3 Tests of QED in Lepton Scattering .................................................... 41627.4 Electron and Muon g Factors .......................................................... 41627.5 Recoil Corrections .......................................................................... 41827.6 Fine Structure ............................................................................... 42027.7 Hyperfine Structure ....................................................................... 42127.8 Orthopositronium Decay Rate ......................................................... 42227.9 Precision Tests of QED in Neutral Helium ......................................... 42327.10 QED in Highly Charged One-Electron Ions ........................................ 42427.11 QED in Highly Charged Many-Electron Ions ..................................... 425References............................................................................................... 427

Contents XXXIII

28 Tests of Fundamental PhysicsPeter J. Mohr, Barry N. Taylor ................................................................... 42928.1 Electron g-Factor Anomaly ............................................................. 42928.2 Electron g-Factor in 12C5+ and 16O7+ .............................................. 43228.3 Hydrogen and Deuterium Atoms .................................................... 437References............................................................................................... 445

29 Parity Nonconserving Effects in AtomsJonathan R. Sapirstein ............................................................................. 44929.1 The Standard Model ...................................................................... 45029.2 PNC in Cesium ............................................................................... 45129.3 Many-Body Perturbation Theory .................................................... 45129.4 PNC Calculations ............................................................................ 45229.5 Recent Developments .................................................................... 45329.6 Comparison with Experiment ......................................................... 453References............................................................................................... 454

30 Atomic Clocks and Constraintson Variations of Fundamental ConstantsSavely G. Karshenboim, Victor Flambaum, Ekkehard Peik .......................... 45530.1 Atomic Clocks and Frequency Standards ......................................... 45630.2 Atomic Spectra and their Dependence on the Fundamental

Constants ...................................................................................... 45930.3 Laboratory Constraints on Time the Variations

of the Fundamental Constants ....................................................... 46030.4 Summary ...................................................................................... 462References............................................................................................... 462

Part C Molecules

31 Molecular StructureDavid R. Yarkony ..................................................................................... 46731.1 Concepts ....................................................................................... 46831.2 Characterization of Potential Energy Surfaces.................................. 47031.3 Intersurface Interactions: Perturbations ......................................... 47631.4 Nuclear Motion ............................................................................. 48031.5 Reaction Mechanisms: A Spin-Forbidden Chemical Reaction............ 48431.6 Recent Developments .................................................................... 486References............................................................................................... 486

32 Molecular Symmetry and DynamicsWilliam G. Harter ..................................................................................... 49132.1 Dynamics and Spectra of Molecular Rotors ...................................... 49132.2 Rotational Energy Surfaces and Semiclassical

Rotational Dynamics...................................................................... 49432.3 Symmetry of Molecular Rotors ........................................................ 498

XXXIV Contents

32.4 Tetrahedral-Octahedral Rotational Dynamics and Spectra ............... 49932.5 High Resolution Rovibrational Structure ......................................... 50332.6 Composite Rotors and Multiple RES ................................................. 507References............................................................................................... 512

33 Radiative Transition ProbabilitiesDavid L. Huestis ....................................................................................... 51533.1 Overview....................................................................................... 51533.2 Molecular Wave Functions in the Rotating Frame ............................ 51633.3 The Energy–Intensity Model ........................................................... 51833.4 Selection Rules .............................................................................. 52133.5 Absorption Cross Sections and Radiative Lifetimes........................... 52433.6 Vibrational Band Strengths ............................................................ 52533.7 Rotational Branch Strengths .......................................................... 52633.8 Forbidden Transitions .................................................................... 53033.9 Recent Developments .................................................................... 531References............................................................................................... 532

34 Molecular PhotodissociationAbigail J. Dobbyn, David H. Mordaunt, Reinhard Schinke .......................... 53534.1 Observables .................................................................................. 53734.2 Experimental Techniques ............................................................... 53934.3 Theoretical Techniques .................................................................. 54034.4 Concepts in Dissociation ................................................................ 54134.5 Recent Developments .................................................................... 54334.6 Summary ...................................................................................... 544References............................................................................................... 545

35 Time-Resolved Molecular DynamicsVolker Engel ............................................................................................ 54735.1 Pump–Probe Experiments ............................................................. 54835.2 Theoretical Description .................................................................. 54835.3 Applications .................................................................................. 55035.4 Recent Developments .................................................................... 551References............................................................................................... 552

36 Nonreactive ScatteringDavid R. Flower ....................................................................................... 55536.1 Definitions .................................................................................... 55536.2 Semiclassical Method..................................................................... 55636.3 Quantal Method ............................................................................ 55636.4 Symmetries and Conservation Laws ................................................ 55736.5 Coordinate Systems ....................................................................... 55736.6 Scattering Equations...................................................................... 55836.7 Matrix Elements ............................................................................ 558References............................................................................................... 560

Contents XXXV

37 Gas Phase ReactionsEric Herbst ............................................................................................... 56137.1 Normal Bimolecular Reactions ....................................................... 56337.2 Association Reactions .................................................................... 57037.3 Concluding Remarks ...................................................................... 572References............................................................................................... 573

38 Gas Phase Ionic ReactionsNigel G. Adams ........................................................................................ 57538.1 Overview....................................................................................... 57538.2 Reaction Energetics ....................................................................... 57638.3 Chemical Kinetics .......................................................................... 57838.4 Reaction Processes ........................................................................ 57838.5 Electron Attachment ...................................................................... 58238.6 Recombination.............................................................................. 583References............................................................................................... 585

39 ClustersMary L. Mandich ...................................................................................... 58939.1 Metal Clusters................................................................................ 59039.2 Carbon Clusters ............................................................................. 59339.3 Ionic Clusters................................................................................. 59639.4 Semiconductor Clusters .................................................................. 59739.5 Noble Gas Clusters ......................................................................... 59939.6 Molecular Clusters ......................................................................... 60239.7 Recent Developments .................................................................... 603References............................................................................................... 604

40 Infrared SpectroscopyHenry Buijs .............................................................................................. 60740.1 Intensities of Infrared Radiation .................................................... 60740.2 Sources for IR Absorption Spectroscopy ........................................... 60840.3 Source, Spectrometer, Sample and Detector Relationship ................ 60840.4 Simplified Principle of FTIR Spectroscopy ........................................ 60840.5 Optical Aspects of FTIR Technology .................................................. 61140.6 The Scanning Michelson Interferometer .......................................... 61240.7 Recent Developments .................................................................... 61340.8 Conclusion .................................................................................... 613References............................................................................................... 613

41 Laser Spectroscopy in the Submillimeterand Far-Infrared RegionsKenneth M. Evenson†, John M. Brown....................................................... 61541.1 Experimental Techniques using Coherent SM-FIR Radiation ............. 61641.2 Submillimeter and FIR Astronomy .................................................. 62041.3 Upper Atmospheric Studies ............................................................ 620References............................................................................................... 621

XXXVI Contents

42 Spectroscopic Techniques: LasersPaul Engelking ........................................................................................ 62342.1 Laser Basics ................................................................................... 62342.2 Laser Designs ................................................................................ 62542.3 Interaction of Laser Light with Matter............................................. 62842.4 Recent Developments .................................................................... 630References............................................................................................... 631

43 Spectroscopic Techniques: Cavity-Enhanced MethodsBarbara A. Paldus, Alexander A. Kachanov ............................................... 63343.1 Limitations of Traditional Absorption Spectrometers ....................... 63343.2 Cavity Ring-Down Spectroscopy ..................................................... 63443.3 Cavity Enhanced Spectroscopy ........................................................ 63643.4 Extensions to Solids and Liquids .................................................... 639References............................................................................................... 640

44 Spectroscopic Techniques: UltravioletGlenn Stark, Peter L. Smith ....................................................................... 64144.1 Light Sources ................................................................................. 64244.2 VUV Lasers ..................................................................................... 64544.3 Spectrometers ............................................................................... 64744.4 Detectors ...................................................................................... 64844.5 Optical Materials ........................................................................... 651References............................................................................................... 652

Part D Scattering Theory

45 Elastic Scattering: Classical, Quantal, and SemiclassicalM. Raymond Flannery .............................................................................. 65945.1 Classical Scattering Formulae ......................................................... 65945.2 Quantal Scattering Formulae .......................................................... 66445.3 Semiclassical Scattering Formulae .................................................. 67545.4 Elastic Scattering in Reactive Systems ............................................. 68345.5 Results for Model Potentials ........................................................... 684References............................................................................................... 689

46 Orientation and Alignment in Atomicand Molecular CollisionsNils Andersen .......................................................................................... 69346.1 Collisions Involving Unpolarized Beams .......................................... 69446.2 Collisions Involving Spin-Polarized Beams ...................................... 69946.3 Example ....................................................................................... 70246.4 Recent Developments .................................................................... 70346.5 Summary ...................................................................................... 703References............................................................................................... 703

Contents XXXVII

47 Electron–Atom, Electron–Ion, and Electron–Molecule CollisionsPhilip Burke ............................................................................................ 70547.1 Electron–Atom and Electron–Ion Collisions ..................................... 70547.2 Electron–Molecule Collisions .......................................................... 72047.3 Electron–Atom Collisions in a Laser Field ........................................ 723References............................................................................................... 727

48 Positron CollisionsRobert P. McEachran, Allan Stauffer.......................................................... 73148.1 Scattering Channels ....................................................................... 73148.2 Theoretical Methods ...................................................................... 73348.3 Particular Applications ................................................................... 73548.4 Binding of Positrons to Atoms ........................................................ 73748.5 Reviews ........................................................................................ 738References............................................................................................... 738

49 Adiabatic and Diabatic Collision Processes at Low EnergiesEvgueni E. Nikitin .................................................................................... 74149.1 Basic Definitions ........................................................................... 74149.2 Two-State Approximation .............................................................. 74349.3 Single-Passage Transition Probabilities: Analytical Models .............. 74649.4 Double-Passage Transition Probabilities and Cross Sections ............. 74949.5 Multiple-Passage Transition Probabilities ....................................... 751References............................................................................................... 752

50 Ion–Atom and Atom–Atom CollisionsA. Lewis Ford, John F. Reading ................................................................. 75350.1 Treatment of Heavy Particle Motion ................................................ 75450.2 Independent-Particle Models

Versus Many-Electron Treatments .................................................. 75550.3 Analytical Approximations Versus Numerical Calculations ................ 75650.4 Description of the Ionization Continuum ........................................ 758References............................................................................................... 759

51 Ion–Atom Charge Transfer Reactions at Low EnergiesMuriel Gargaud, Ronald McCarroll ............................................................ 76151.1 Molecular Structure Calculations..................................................... 76251.2 Dynamics of the Collision ............................................................... 76551.3 Radial and Rotational Coupling Matrix Elements ............................. 76651.4 Total Electron Capture Cross Sections .............................................. 76751.5 Landau–Zener Approximation ........................................................ 76951.6 Differential Cross Sections .............................................................. 76951.7 Orientation Effects ......................................................................... 77051.8 New Developments........................................................................ 772References............................................................................................... 772

XXXVIII Contents

52 Continuum Distorted Wave and Wannier MethodsDerrick Crothers, Fiona McCausland, John Glass, Jim F. McCann,Francesca O’Rourke, Ruth T. Pedlow.......................................................... 77552.1 Continuum Distorted Wave Method ................................................ 77552.2 Wannier Method ........................................................................... 781References............................................................................................... 786

53 Ionization in High Energy Ion–Atom CollisionsJoseph H. Macek, Steven T. Manson .......................................................... 78953.1 Born Approximation ...................................................................... 78953.2 Prominent Features ....................................................................... 79253.3 Recent Developments .................................................................... 796References............................................................................................... 796

54 Electron–Ion and Ion–Ion RecombinationM. Raymond Flannery .............................................................................. 79954.1 Recombination Processes ............................................................... 80054.2 Collisional-Radiative Recombination .............................................. 80154.3 Macroscopic Methods .................................................................... 80354.4 Dissociative Recombination ........................................................... 80754.5 Mutual Neutralization.................................................................... 81054.6 One-Way Microscopic Equilibrium Current, Flux,

and Pair-Distributions ................................................................... 81154.7 Microscopic Methods for Termolecular

Ion–Ion Recombination ................................................................. 81254.8 Radiative Recombination ............................................................... 81754.9 Useful Quantities ........................................................................... 824References............................................................................................... 824

55 Dielectronic RecombinationMichael S. Pindzola, Donald C. Griffin, Nigel R. Badnell ............................. 82955.1 Theoretical Formulation ................................................................. 83055.2 Comparisons with Experiment........................................................ 83155.3 Radiative-Dielectronic Recombination Interference ........................ 83255.4 Dielectronic Recombinationin Plasmas ........................................... 833References............................................................................................... 833

56 Rydberg Collisions: Binary Encounter,Born and Impulse ApproximationsEdmund J. Mansky................................................................................... 83556.1 Rydberg Collision Processes ............................................................ 83656.2 General Properties of Rydberg States .............................................. 83656.3 Correspondence Principles ............................................................. 83956.4 Distribution Functions ................................................................... 84056.5 Classical Theory ............................................................................. 84156.6 Working Formulae for Rydberg Collisions ........................................ 84256.7 Impulse Approximation ................................................................. 845

Contents XXXIX

56.8 Binary Encounter Approximation ................................................... 85256.9 Born Approximation ...................................................................... 856References............................................................................................... 860

57 Mass Transfer at High Energies: Thomas PeakJames H. McGuire, Jack C. Straton, Takeshi Ishihara .................................. 86357.1 The Classical Thomas Process .......................................................... 86357.2 Quantum Description ..................................................................... 86457.3 Off-Energy-Shell Effects ................................................................. 86657.4 Dispersion Relations ...................................................................... 86657.5 Destructive Interference of Amplitudes ........................................... 86757.6 Recent Developments .................................................................... 867References............................................................................................... 868

58 Classical Trajectory and Monte Carlo TechniquesRonald E. Olson ....................................................................................... 86958.1 Theoretical Background ................................................................. 86958.2 Region of Validity .......................................................................... 87158.3 Applications .................................................................................. 87158.4 Conclusions ................................................................................... 874References............................................................................................... 874

59 Collisional Broadening of Spectral LinesGillian Peach ........................................................................................... 87559.1 Impact Approximation ................................................................... 87559.2 Isolated Lines ................................................................................ 87659.3 Overlapping Lines .......................................................................... 88059.4 Quantum-Mechanical Theory ......................................................... 88259.5 One-Perturber Approximation........................................................ 88559.6 Unified Theories and Conclusions ................................................... 888References............................................................................................... 888

Part E Scattering Experiments

60 PhotodetachmentDavid J. Pegg .......................................................................................... 89160.1 Negative Ions ................................................................................ 89160.2 Photodetachment ......................................................................... 89260.3 Experimental Procedures ............................................................... 89360.4 Results .......................................................................................... 895References............................................................................................... 898

61 Photon–Atom Interactions: Low EnergyDenise Caldwell, Manfred O. Krause .......................................................... 90161.1 Theoretical Concepts ...................................................................... 90161.2 Experimental Methods ................................................................... 907

XL Contents

61.3 Additional Considerations .............................................................. 911References............................................................................................... 912

62 Photon–Atom Interactions: Intermediate EnergiesBernd Crasemann .................................................................................... 91562.1 Overview....................................................................................... 91562.2 Elastic Photon-Atom Scattering ...................................................... 91662.3 Inelastic Photon-Atom Interactions ................................................ 91862.4 Atomic Response to Inelastic Photon-Atom Interactions .................. 91962.5 Threshold Phenomena ................................................................... 923References............................................................................................... 925

63 Electron–Atom and Electron–Molecule CollisionsSandor Trajmar, William J. McConkey, Isik Kanik ....................................... 92963.1 Basic Concepts .............................................................................. 92963.2 Collision Processes ......................................................................... 93363.3 Coincidence and Superelastic Measurements .................................. 93663.4 Experiments with Polarized Electrons ............................................. 93863.5 Electron Collisions with Excited Species .......................................... 93963.6 Electron Collisions in Traps ............................................................. 93963.7 Future Developments .................................................................... 940References............................................................................................... 940

64 Ion–Atom Scattering Experiments: Low EnergyRonald Phaneuf ...................................................................................... 94364.1 Low Energy Ion–Atom Collision Processes ....................................... 94364.2 Experimental Methods

for Total Cross Section Measurements ............................................. 94564.3 Methods for State and Angular Selective Measurements .................. 947References............................................................................................... 948

65 Ion–Atom Collisions – High EnergyLew Cocke, Michael Schulz ........................................................................ 95165.1 Basic One-Electron Processes ......................................................... 95165.2 Multi-Electron Processes ................................................................ 95765.3 Electron Spectra in Ion–Atom Collisions .......................................... 95965.4 Quasi-Free Electron Processes in Ion–Atom Collisions ...................... 96165.5 Some Exotic Processes ................................................................... 962References............................................................................................... 963

66 Reactive ScatteringArthur G. Suits, Yuan T. Lee ...................................................................... 96766.1 Experimental Methods ................................................................... 96766.2 Experimental Configurations .......................................................... 97166.3 Elastic and Inelastic Scattering ....................................................... 97666.4 Reactive Scattering ........................................................................ 97866.5 Recent Developments .................................................................... 980References............................................................................................... 980

Contents XLI

67 Ion–Molecule ReactionsJames M. Farrar ....................................................................................... 98367.1 Instrumentation ............................................................................ 98567.2 Kinematic Analysis ........................................................................ 98567.3 Scattering Cross Sections ................................................................ 98767.4 New Directions: Complexity and Imaging ........................................ 991References............................................................................................... 992

Part F Quantum Optics

68 Light–Matter InteractionPierre Meystre .......................................................................................... 99768.1 Multipole Expansion ...................................................................... 99768.2 Lorentz Atom ................................................................................ 99968.3 Two-Level Atoms ........................................................................... 100068.4 Relaxation Mechanisms ................................................................. 100368.5 Rate Equation Approximation ........................................................ 100568.6 Light Scattering ............................................................................. 1006References............................................................................................... 1007

69 Absorption and Gain SpectraStig Stenholm .......................................................................................... 100969.1 Index of Refraction ........................................................................ 100969.2 Density Matrix Treatment of the Two-Level Atom ............................ 101069.3 Line Broadening ............................................................................ 101169.4 The Rate Equation Limit ................................................................. 101369.5 Two-Level Doppler-Free Spectroscopy ............................................ 101569.6 Three-Level Spectroscopy............................................................... 101669.7 Special Effects in Three-Level Systems ............................................ 101869.8 Summary of the Literature ............................................................. 1020References............................................................................................... 1020

70 Laser PrinciplesPeter W. Milonni ...................................................................................... 102370.1 Gain, Threshold, and Matter–Field Coupling ................................... 102370.2 Continuous Wave, Single-Mode Operation ...................................... 102570.3 Laser Resonators ........................................................................... 102870.4 Photon Statistics ........................................................................... 103070.5 Multi-Mode and Pulsed Operation ................................................. 103170.6 Instabilities and Chaos .................................................................. 103370.7 Recent Developments .................................................................... 1033References............................................................................................... 1034

71 Types of LasersRichard C. Powell ..................................................................................... 103571.1 Gas Lasers ..................................................................................... 103671.2 Solid State Lasers........................................................................... 1039

XLII Contents

71.3 Semiconductor Lasers .................................................................... 104371.4 Liquid Lasers ................................................................................. 104471.5 Other Types of Lasers ..................................................................... 104571.6 Recent Developments .................................................................... 1046References............................................................................................... 1048

72 Nonlinear OpticsAlexander L. Gaeta, Robert W. Boyd.......................................................... 105172.1 Nonlinear Susceptibility ................................................................. 105172.2 Wave Equation in Nonlinear Optics................................................. 105472.3 Second-Order Processes ................................................................. 105672.4 Third-Order Processes .................................................................... 105772.5 Stimulated Light Scattering ............................................................ 105972.6 Other Nonlinear Optical Processes .................................................. 1061References............................................................................................... 1062

73 Coherent TransientsJoseph H. Eberly, Carlos R. Stroud Jr.......................................................... 106573.1 Optical Bloch Equations ................................................................. 106573.2 Numerical Estimates of Parameters ................................................ 106673.3 Homogeneous Relaxation .............................................................. 106673.4 Inhomogeneous Relaxation ........................................................... 106873.5 Resonant Pulse Propagation .......................................................... 106973.6 Multi-Level Generalizations ........................................................... 107173.7 Disentanglement and “Sudden Death” of Coherent Transients ........ 1074References............................................................................................... 1076

74 Multiphoton and Strong-Field ProcessesKenneth C. Kulander, Maciej Lewenstein ................................................... 107774.1 Weak Field Multiphoton Processes .................................................. 107874.2 Strong-Field Multiphoton Processes ............................................... 108074.3 Strong-Field Calculational Techniques ............................................ 1086References............................................................................................... 1088

75 Cooling and TrappingJuha Javanainen ..................................................................................... 109175.1 Notation ....................................................................................... 109175.2 Control of Atomic Motion by Light .................................................. 109275.3 Magnetic Trap for Atoms ................................................................ 109975.4 Trapping and Cooling of Charged Particles ...................................... 109975.5 Applications of Cooling and Trapping ............................................. 1103References............................................................................................... 1105

76 Quantum Degenerate GasesJuha Javanainen ..................................................................................... 110776.1 Elements of Quantum Field Theory ................................................. 110776.2 Basic Properties of Degenerate Gases ............................................. 1110

Contents XLIII

76.3 Experimental ................................................................................ 111576.4 BEC Superfluid ............................................................................... 111776.5 Current Active Topics...................................................................... 1119References............................................................................................... 1123

77 De Broglie OpticsCarsten Henkel, Martin Wilkens ................................................................ 112577.1 Overview....................................................................................... 112577.2 Hamiltonian of de Broglie Optics .................................................... 112677.3 Principles of de Broglie Optics ........................................................ 112977.4 Refraction and Reflection .............................................................. 113177.5 Diffraction .................................................................................... 113377.6 Interference .................................................................................. 113577.7 Coherence of Scalar Matter Waves .................................................. 1137References............................................................................................... 1139

78 Quantized Field EffectsMatthias Freyberger, Karl Vogel, Wolfgang P. Schleich, Robert F. O’Connell 114178.1 Field Quantization ......................................................................... 114278.2 Field States ................................................................................... 114278.3 Quantum Coherence Theory ........................................................... 114678.4 Photodetection Theory................................................................... 114778.5 Quasi-Probability Distributions ...................................................... 114878.6 Reservoir Theory ............................................................................ 115178.7 Master Equation ............................................................................ 115278.8 Solution of the Master Equation ..................................................... 115478.9 Quantum Regression Hypothesis .................................................... 115678.10 Quantum Noise Operators .............................................................. 115778.11 Quantum Monte Carlo Formalism ................................................... 115978.12 Spontaneous Emission in Free Space .............................................. 115978.13 Resonance Fluorescence ................................................................ 116078.14 Recent Developments .................................................................... 1162References............................................................................................... 1163

79 Entangled Atoms and Fields: Cavity QEDDieter Meschede, Axel Schenzle ................................................................. 116779.1 Atoms and Fields ........................................................................... 116779.2 Weak Coupling in Cavity QED .......................................................... 116979.3 Strong Coupling in Cavity QED ......................................................... 117379.4 Strong Coupling in Experiments ..................................................... 117479.5 Microscopic Masers and Lasers ....................................................... 117579.6 Micromasers.................................................................................. 117879.7 Quantum Theory of Measurement .................................................. 118079.8 Applications of Cavity QED .............................................................. 1181References............................................................................................... 1182

XLIV Contents

80 Quantum Optical Tests of the Foundations of PhysicsAephraim M. Steinberg, Paul G. Kwiat, Raymond Y. Chiao ......................... 118580.1 The Photon Hypothesis .................................................................. 118680.2 Quantum Properties of Light .......................................................... 118680.3 Nonclassical Interference ............................................................... 118880.4 Complementarity and Coherence.................................................... 119180.5 Measurements in Quantum Mechanics ........................................... 119380.6 The EPR Paradox and Bell’s Inequalities ......................................... 119580.7 Quantum Information.................................................................... 120080.8 The Single-Photon Tunneling Time ................................................. 120280.9 Gravity and Quantum Optics .......................................................... 1206References............................................................................................... 1207

81 Quantum InformationPeter L. Knight, Stefan Scheel ................................................................... 121581.1 Quantifying Information ................................................................ 121681.2 Simple Quantum Protocols ............................................................. 121881.3 Unitary Transformations ................................................................ 122181.4 Quantum Algorithms ..................................................................... 122281.5 Error Correction ............................................................................. 122381.6 The DiVincenzo Checklist ................................................................ 122481.7 Physical Implementations .............................................................. 122581.8 Outlook ......................................................................................... 1227References............................................................................................... 1228

Part G Applications

82 Applications of Atomic and Molecular Physics to AstrophysicsAlexander Dalgarno, Stephen Lepp ........................................................... 123582.1 Photoionized Gas .......................................................................... 123582.2 Collisionally Ionized Gas ................................................................ 123782.3 Diffuse Molecular Clouds ................................................................ 123882.4 Dark Molecular Clouds ................................................................... 123982.5 Circumstellar Shells and Stellar Atmospheres .................................. 124182.6 Supernova Ejecta ........................................................................... 124282.7 Shocked Gas.................................................................................. 124382.8 The Early Universe ......................................................................... 124482.9 Recent Developments .................................................................... 124482.10 Other Reading ............................................................................... 1245References............................................................................................... 1245

83 CometsPaul D. Feldman ...................................................................................... 124783.1 Observations ................................................................................. 124783.2 Excitation Mechanisms .................................................................. 125083.3 Cometary Models ........................................................................... 125483.4 Summary ...................................................................................... 1256References............................................................................................... 1257

Contents XLV

84 AeronomyJane L. Fox .............................................................................................. 125984.1 Basic Structure of Atmospheres ...................................................... 125984.2 Density Distributions of Neutral Species .......................................... 126484.3 Interaction of Solar Radiation with the Atmosphere ........................ 126584.4 Ionospheres .................................................................................. 127184.5 Neutral, Ion and Electron Temperatures ......................................... 128184.6 Luminosity .................................................................................... 128484.7 Planetary Escape ........................................................................... 1287References............................................................................................... 1290

85 Applications of Atomic and Molecular Physicsto Global ChangeKate P. Kirby, Kelly Chance ....................................................................... 129385.1 Overview....................................................................................... 129385.2 Atmospheric Models and Data Needs .............................................. 129485.3 Tropospheric Warming/Upper Atmosphere Cooling .......................... 129585.4 Stratospheric Ozone ....................................................................... 129885.5 Atmospheric Measurements ........................................................... 1300References............................................................................................... 1301

86 Atoms in Dense PlasmasJon C. Weisheit, Michael S. Murillo ............................................................ 130386.1 The Dense Plasma Environment ..................................................... 130586.2 Atomic Models and Ionization Balance ........................................... 130886.3 Elementary Processes .................................................................... 131186.4 Simulations................................................................................... 1313References............................................................................................... 1316

87 Conduction of Electricity in GasesAlan Garscadden ..................................................................................... 131987.1 Electron Scattering and Transport Phenomena ................................ 132087.2 Glow Discharge Phenomena .......................................................... 132787.3 Atomic and Molecular Processes ..................................................... 132887.4 Electrical Discharge in Gases: Applications ...................................... 133087.5 Conclusions ................................................................................... 1333References............................................................................................... 1333

88 Applications to CombustionDavid R. Crosley ....................................................................................... 133588.1 Combustion Chemistry ................................................................... 133688.2 Laser Combustion Diagnostics ........................................................ 133788.3 Recent Developments .................................................................... 1342References............................................................................................... 1342

XLVI Contents

89 Surface PhysicsErik T. Jensen ........................................................................................... 134389.1 Low Energy Electrons and Surface Science ....................................... 134389.2 Electron–Atom Interactions ........................................................... 134489.3 Photon–Atom Interactions ............................................................. 134689.4 Atom–Surface Interactions ............................................................. 135189.5 Recent Developments .................................................................... 1352References............................................................................................... 1353

90 Interface with Nuclear PhysicsJohn D. Morgan III, James S. Cohen .......................................................... 135590.1 Nuclear Size Effects in Atoms .......................................................... 135690.2 Electronic Structure Effects in Nuclear Physics ................................. 135890.3 Muon-Catalyzed Fusion ................................................................. 1359References............................................................................................... 1369

91 Charged-Particle–Matter InteractionsHans Bichsel ............................................................................................ 137391.1 Experimental Aspects .................................................................... 137491.2 Theory of Cross Sections ................................................................. 137691.3 Moments of the Cross Section ......................................................... 137891.4 Energy Loss Straggling ................................................................... 138191.5 Multiple Scattering and Nuclear Reactions ...................................... 138491.6 Monte Carlo Calculations ................................................................ 138491.7 Detector Conversion Factors ........................................................... 1385References............................................................................................... 1385

92 Radiation PhysicsMitio Inokuti ........................................................................................... 138992.1 General Overview .......................................................................... 138992.2 Radiation Absorption and its Consequences.................................... 139092.3 Electron Transport and Degradation ............................................... 139292.4 Connections with Related Fields of Research................................... 139792.5 Supplement .................................................................................. 1397References............................................................................................... 1398

Acknowledgements ................................................................................... 1401About the Authors ..................................................................................... 1405Detailed Contents ...................................................................................... 1425Subject Index ............................................................................................. 1471

XLVII

List of Tables

1 Units and ConstantsTable 1.1 Table of physical constants. Uncertainties are given in

parentheses ......................................................................... 2Table 1.2 The correlation coefficients of a selected group of constants

based on the 2002 CODATA ..................................................... 3Table 1.3 Conversion factors for various physical quantities .................. 4Table 1.4 Physical quantities in atomic units with

�= e = me = 4πε0 = 1, and α−1 = 137.035 999 11(46) ............... 5Table 1.5 Values of e, π, Euler’s constant γ , and the Riemann zeta

function ζ(n) ........................................................................ 6

Part A Mathematical Methods

2 Angular Momentum TheoryTable 2.1 The solid and spherical harmonics Ylm, and the tensor

harmonics T kµ (labeled by k = l and µ= m) for l = 0, 1, 2, 3,

and 4 ................................................................................... 69Table 2.2 The 3– j coefficients for all M’s= 0, or J3 = 0, 1

2 ..................... 69Table 2.3 The 3– j coefficients for J3 = 1, 3

2 , 2 ........................................ 70Table 2.4 The 6– j coefficients for d = 0, 1

2 , 1,32 , 2, with s = a+b+ c ....... 71

3 Group Theory for Atomic ShellsTable 3.1 Generators of the Lie groups for the atomic l shell ................. 77Table 3.2 Dimensions D of the irreducible representations ([irre]IR’s) of

various Lie groups ................................................................. 78Table 3.3 Eigenvalues of Casimir’s operator C for groups used in the

atomic l shell ....................................................................... 79Table 3.4 The states of the d shell ........................................................ 81

Part B Atoms

10 Atomic SpectroscopyTable 10.1 Atomic structural hierarchy in L S coupling and names for the

groups of all transitions between structural entities ............... 178Table 10.2 Allowed J values for lN

j equivalent electrons ( jj) coupling ...... 178Table 10.3 Ground levels and ionization energies for the neutral atoms . 182Table 10.4 Selection rules for discrete transitions ................................... 187Table 10.5 Wavelengths λ, upper energy levels Ek, statistical weights gi

and gk of lower and upper levels, and transition probabilitiesAki for persistent spectral lines of neutral atoms .................... 187

XLVIII List of Tables

Table 10.6 Conversion relations between S and Aki for forbiddentransitions............................................................................ 192

Table 10.7 Relative strengths for lines of multiplets in L S coupling ......... 193Table 10.8 Some transitions of the main spectral series of hydrogen ....... 195Table 10.9 Values of Stark-broadening parameter α1/2 of the Hβ line of

hydrogen (4861 Å) for various temperatures and electrondensities .............................................................................. 196

11 High Precision Calculations for HeliumTable 11.1 Formulas for the radial integrals

I0(a, b, c;α, β)= 〈ra1 rb

2rc12 e−αr1−βr2〉rad and

I log0 (a, b, c;α, β)= 〈ra

1 rb2rc

12ln r12 e−αr1−βr2〉rad ........................... 203Table 11.2 Nonrelativistic eigenvalue coefficients ε0 and ε1 for helium .... 205Table 11.3 Eigenvalue coefficients ε2 for helium ..................................... 207Table 11.4 Values of the reduced electron mass ratio µ/M ...................... 207Table 11.5 Nonrelativistic eigenvalues E = ε0+ (µ/M)ε1+ (µ/M)2ε2 for

helium-like ions................................................................... 207Table 11.6 Expectation values of various operators for He-like ions for

the case M =∞.................................................................... 208Table 11.7 Total ionization energies for 4He, calculated with

RM = 3 289 391 006.715 MHz ................................................... 210Table 11.8 QED corrections to the ionization energy included in Table 11.7

for the S- and P-states of helium ......................................... 211Table 11.9 Quantum defects for the total energies of helium with the

∆Wn term subtracted (11.54) .................................................. 212Table 11.10 Formulas for the hydrogenic expectation value

〈r− j〉 ≡ 〈nl|r− j |nl〉 ................................................................. 214Table 11.11 Oscillator strengths for helium............................................... 216Table 11.12 Singlet–triplet mixing angles for helium ................................ 217

13 Atoms in Strong FieldsTable 13.1 Relativistic ground state binding energy −Egs/Z2 and finite

nuclear size correction δEnuc/Z2 of hydrogenic atoms forvarious magnetic fields B ...................................................... 230

Table 13.2 Relativistic binding energy −E2S,−1/2 for the 2S1/2(mj =− 1

2

)

and −E2P,−1/2 for the 2P1/2(m j =− 1

2

)excited states of

hydrogen in an intense magnetic field B ............................... 231Table 13.3 Relativistic corrections δE = (E− ENR)/|ER| to the

nonrelativistic energies ENR for the ground state and n = 2excited states of hydrogen in an intense magnetic field B ...... 231

Table 13.4 Relativistic dipole polarizabilities for the ground stateof hydrogenic atoms ............................................................. 233

17 Precision Oscillator Strength and Lifetime MeasurementsTable 17.1 Measured np 2PJ lifetimes..................................................... 266

List of Tables XLIX

21 Atomic Structure: Multiconfiguration Hartree–Fock TheoriesTable 21.1 The effective quantum number and quantum defect

parameters of the 2snd Rydberg series in Be .......................... 312Table 21.2 Observed and Hartree–Fock ionization potentials for

the ground states of neutral atoms, in eV .............................. 313Table 21.3 Comparison of theoretical and experimental energies for Be

1s22s2 1S in hartrees ............................................................. 317Table 21.4 Specific mass shift parameter and electron density at the

nucleus as a function of the active set ................................... 319Table 21.5 MCHF Hyperfine constants for the 1s22s2p 1P state

of B II .................................................................................. 320Table 21.6 Convergence of transition data for the

1s22s22p2Po → 1s22s2p2 2D transition in Boron withincreasing active set ............................................................. 322

22 Relativistic Atomic StructureTable 22.1 Relativistic angular density functions .................................... 339Table 22.2 Nonrelativistic angular density functions ............................... 339Table 22.3 Spectroscopic labels and angular quantum numbers .............. 340Table 22.4 Radial moments 〈ρs〉 ............................................................. 342Table 22.5 j N configurational states in the seniority scheme .................. 351

25 AutoionizationTable 25.1 Test of sum rule (25.15) for the lowest He− (1s2s2 2S)

autodetachment state ([25.4]) ............................................... 393Table 25.2 Comparison of methods for calculating the energy

of the lowest He− (1s2s2 2S) autodetachment state ................ 393Table 25.3 Energies Es of the He(2s2p1P0) autoionization states below

He+ (n = 2) threshold from the variational calculationsof O’Malley and Geltman [25.13] ............................................ 394

Table 25.4 Comparison of high precision calculations with experimentfor the resonance parameters of the He(1P0) resonancesbelow the n = 2 threshold ..................................................... 396

Table 25.5 Comparison of resonance parameters obtainedfrom different methods for calculating 1De states in H− ......... 397

Table 25.6 Resonance energies EF (Ry) and widths (eV) for 1P statesof He below n = 2 threshold (−1 Ry) of He+ ........................... 398

27 Quantum ElectrodynamicsTable 27.1 Contributions to of C2 in Yennie gauge .................................. 417

28 Tests of Fundamental PhysicsTable 28.1 Theoretical contributions and total for the g-factor

of the electron in hydrogenic carbon 12 based on the 2002recommended values of the constants................................... 433

L List of Tables

Table 28.2 Theoretical contributions and total for the g-factorof the electron in hydrogenic oxygen 16 based on the 2002recommended values of the constants................................... 433

Table 28.3 Relevant Bethe logarithms ln k0(n, l) ...................................... 439Table 28.4 Values of the function GSE(α) ............................................... 440Table 28.5 Values of the function G(1)VP(α) ............................................... 441Table 28.6 Values of N .......................................................................... 442Table 28.7 Values of bL and B60 ............................................................. 442Table 28.8 Measured transition frequencies ν in hydrogen ...................... 445

30 Atomic Clocks and Constraintson Variations of Fundamental ConstantsTable 30.1 Limits on possible time variation of frequencies of different

transitions in SI units ............................................................ 459Table 30.2 Magnetic moments and relativistic corrections for atoms

involved in microwave standards .......................................... 460Table 30.3 Limits on possible time variation of the frequencies

of different transitions and their sensitivity to variationsin α due to relativistic corrections ......................................... 460

Table 30.4 Model-independent laboratory constraints on the possibletime variations of natural constants ...................................... 461

Table 30.5 Model-dependent laboratory constraints on possible timevariations of fundamental constants ..................................... 462

Part C Molecules

32 Molecular Symmetry and DynamicsTable 32.1 Tunneling energy eigensolutions ........................................... 497Table 32.2 Character table for symmetry group C2 .................................. 498Table 32.3 Character table for symmetry group D2 .................................. 498Table 32.4 Character table for symmetry group O ................................... 500Table 32.5 Eigenvectors and eigenvalues of the tunneling matrix for the

(A1, E, T1) cluster with K = 28 .............................................. 503Table 32.6 Spin − 1

2 basis states for SiF4 rotating about a C4 symmetryaxis ...................................................................................... 506

38 Gas Phase Ionic ReactionsTable 38.1 Examples illustrating the range of ionic reactions that can

occur in the gas phase .......................................................... 576

42 Spectroscopic Techniques: LasersTable 42.1 Fixed frequency lasers .......................................................... 627Table 42.2 Approximate tuning ranges for tunable lasers ........................ 627

44 Spectroscopic Techniques: UltravioletTable 44.1 Representative third-order frequency conversion schemes for

generation of tunable coherent VUV light .............................. 647

List of Tables LI

Part D Scattering Theory

45 Elastic Scattering: Classical, Quantal, and SemiclassicalTable 45.1 Model interaction potentials ................................................. 685

46 Orientation and Alignment in Atomicand Molecular CollisionsTable 46.1 Summary of cases of increasing complexity,

and the orientation and alignment parameters necessaryfor unpolarized beams .......................................................... 698

Table 46.2 Summary of cases of increasing complexity for spin-polarizedbeams .................................................................................. 702

49 Adiabatic and Diabatic Collision Processes at Low EnergiesTable 49.1 Selection rules for the coupling between diabatic

and adiabatic states of a diatomic quasimolecule(w= g, u; σ =+,−) .............................................................. 745

Table 49.2 Selection rules for dynamic coupling between adiabaticstates of a system of three atoms .......................................... 746

56 Rydberg Collisions: Binary Encounter,Born and Impulse ApproximationsTable 56.1 General n-dependence of characteristic properties

of Rydberg states .................................................................. 837Table 56.2 Coefficients C(ni i → n f f ) in the Born capture cross section

formula (56.284) ................................................................... 860Table 56.3 Functions F(ni i → n f f ; x) in the Born capture cross section

formula (56.284) ................................................................... 860

Part E Scattering Experiments

62 Photon–Atom Interactions: Intermediate EnergiesTable 62.1 Nomenclature for vacancy states ........................................... 920

66 Reactive ScatteringTable 66.1 Collision numbers for coupling between different modes ....... 968

Part F Quantum Optics

71 Types of LasersTable 71.1 Categories of lasers ............................................................... 1035

75 Cooling and TrappingTable 75.1 Laser cooling parameters for the lowest S1/2–P3/2 transition

of hydrogen and most alkalis (the D2 line) ............................ 1092

LII List of Tables

81 Quantum InformationTable 81.1 BB84 protocol for secret key distribution ............................... 1219

Part G Applications

82 Applications of Atomic and Molecular Physics to AstrophysicsTable 82.1 Molecules observed in interstellar clouds ............................... 1240

84 AeronomyTable 84.1 Homopause characteristics of planets and satellites ............... 1260Table 84.2 Molecular weights and fractional composition of dry air

in the terrestrial atmosphere ................................................ 1261Table 84.3 Composition of the lower atmospheres of Mars

and Venus ............................................................................ 1262Table 84.4 Composition of the lower atmospheres of Jupiter

and Saturn ........................................................................... 1263Table 84.5 Composition of the lower atmospheres of Uranus

and Neptune ........................................................................ 1263Table 84.6 Composition of the lower atmosphere of Titan ....................... 1263Table 84.7 Composition of the atmosphere of Triton ............................... 1263Table 84.8 Number densities of species at the surface of Mercury ............ 1264Table 84.9 Ionization potentials (IP) of common atmospheric species ...... 1273Table 84.10 Exobase properties of the planets ......................................... 1289

86 Atoms in Dense PlasmasTable 86.1 Some plasma quantities that depend on its ionization

balance ................................................................................ 1308

88 Applications to CombustionTable 88.1 Combustion chemistry intermediates detectable

by laser-induced fluorescence .............................................. 1339

90 Interface with Nuclear PhysicsTable 90.1 Resonant (quasiresonant if negative) collision energies εres

(in meV) calculated using (90.35) ........................................... 1365Table 90.2 Comparison of sticking values ............................................... 1368

91 Charged-Particle–Matter InteractionsTable 91.1 The coefficient τ(β)= M0β

2/(NZkR) for pions withMπ = 139.567 MeV/c2, calculated in the FVP approximation .... 1378

Table 91.2 Calculated most probable energy loss ∆mp of pions withZ1 =±1 and kinetic energy T passing through a distance xof argon gas

(at 760 Torr, 293 K, �= 1.66 g/dm3

)..................... 1381

Table 91.3 Calculated values of Γ (fwhm) of the straggling function F(∆)(see Table 91.2) ..................................................................... 1382

List of Tables LIII

92 Radiation PhysicsTable 92.1 The mean number N j of initial species produced in molecular

hydrogen upon complete degradation of an incident electronat 10 keV, and the energy absorbed Eabs ............................... 1391

Table 92.2 Condensed matter effects ...................................................... 1396

LV

List of Abbreviations

2P/2H two-particle/two-hole

A

AA average atomACT activated complex theoryADDS angular distribution by Doppler

spectroscopyADO average dipole orientationAES Auger electron spectroscopyAI adiabatic ionizationAL absorption lossALS advanced light sourceAMO atomic, molecular, and opticalANDC arbitrarily normalized decay curveAO atomic orbitalAOM acoustooptic modulatorAS active spaceASD atomic spectra databaseASF atomic state functionsATI above threshold ionizationAU absorbance units

B

BEA binary encounter approximationBEC Bose–Einstein condensate

(or condensation)BF body-fixedBI Bell’s inequalityBL Bethe logBO Born–OppenheimerBS Bethe–SalpeterBW Brillouin–Wigner

C

CARS coherent anti-Stokes Raman scatteringCAS complete active spaceCASPT complete active space perturbation

theoryCAUGA Clifford algebra unitary group approachCC coupled clusterCCA coupled cluster approximationCCC convergent close couplingCCD coupled cluster doublesCCO coupled-channels opticalCDW continuum distorted waveCEAS cavity enhanced absorption spectroscopyCES cavity enhanced spectroscopyCES constant energy surface

CETS cavity enhanced transmissionspectroscopy

CFCP free–free molecular Franck–CondonCG Clebsch–GordanCH Clauser–HorneCI configuration interactionCIS constant ionic stateCL constant logCM center-of-massCMA cylindrical mirror analyzerCOA classical oscillator approximationCODATA Committee on Data for Science and

TechnologyCOIL chemical-oxygen-iodineCOLTRIMS cold-target recoil-ion momentum

spectroscopyCP central potentialCPA chirped-pulsed-amplificationCQC classical-quantal couplingCRDS cavity ring-down spectroscopyCSDA continuous slowing down approximationCSF configurational state functionsCTF common translation factorCTMC classical trajectory Monte CarloCW continuous waveCW-CRDS continuous-Wave Cavity Ring-Down

SpectroscopyCX charge exchangeCXO Chandra X-ray Observatory

D

DB detailed balanceDCS differential cross sectionsDDCS doubly differential cross sectionsDF Dirac–FockDFB distributed feedbackDFS decoherence free subspaceDFT discrete Fourier transformDFWM degenerate four wave mixingDLR dielectronic recombinationDODS different orbitals for different spinsDR dielectronic recombinationDSPB distorted wave strong potential Born

approximation

E

EA excitation-autoionizationEBIT electron beam ion trapsEBS eikonal Born series

LVI List of Abbreviations

ECP effective core potentialECS exterior complex scalingEEDF electron energy distribution functionsEOM equation of motionEPR Einstein–Podolsky–RosenESM elastic scattering modelESR experimental storage ringEUV extreme ultravioletEW-CRDS evanescent-wave CRDSEXAFS extended X-ray absorption fine structure

F

FBA first Born approximationFCPC full-core plus correlationFEL free-electron lasersFFT fast Fourier transformFID free induction decayFIR far-infraredFM frequency modulationFOTOS first-order theory for oscillator strengthsFS fine-structureFT Fourier transformFTIR Fourier transform infrared spectroscopyFTMS Fourier transform mass spectrometryFTS Fourier transform spectroscopyFUSE far ultraviolet spectroscopic explorerFUV far ultravioletFVP Fermi virtual photonFWHM full width at half maximum

G

GBT generalized Brillouin’s TheoremGFA Green’s function approachGGA generalized gradient approximationGHZ Greenberger, Horne, ZeilingerGI gauge invariantGIB guided ion beamGOME global ozone monitoring experimentGOS generalized oscillator strengthGPE Gross–Pitaevskii equationGRPAE generalized random phase

approximationwith exchange

H

HEDP high energy-density physicsHF Hartree–Fock equationsHF Hellman–FeynmanHG harmonic generationHOM Hong–Ou–MandelHREELS high resolution electron energy loss

spectroscopyHRTOF H-atom Rydberg time-of-flightHUM Hylleraas–Undheim–MacDonald

theorem

I

IC intermediate couplingICF inertial confinement fusionICOS integrated cavity output spectroscopyICSLS international conference on spectral line

shapesIERM intermediate energy R-matrixIPCC intergovernmental panel on climate

changeIPES inverse photoemission spectroscopyIPIR independent-processes and

isolated-resonanceIPM independent particle modelIPP impact parameter pictureIR irreducible representationsIR infraredIRI international reference ionosphereIRREP irreducable representationISO infrared space observatory

J

JB Jeffrey–Born

K

KS Kohn–ShamKTA potassium titanyl arsenateKTP potassium titanyl phosphate

L

LieA Lie algebrasLA linear algebraicL-CETS locked cavity enhanced transmission

spectroscopyLDA local density approximationLEED low energy electron diffractionLER laser electric resonanceLG Lie groupsLHC left-hand circularLHV local hidden variableLIF laser-induced-fluorescenceLIGO laser interferometer gravitational-wave

observatoryLISA laser interferometer space antennaLL Landau–LifshitzLM Levenberg–MarquardtLMR laser magnetic resonanceLPT laser photodetachment thresholdLRL Laplace–Runge–LenzLTE local thermodynamic

equilibriumLYP Lee, Yang, and ParrLZ Landau–Zener

List of Abbreviations LVII

M

MBE molecular beam epitaxyMCP microchannel plateMDAL minimum detectable absorption lossMBPT many-body perturbation theoryMCDHF multiconfigurational Dirac–Hartree–FockMCHF multiconfiguration Hartree–FockMCSCF multiconfigurational self-consistent fieldMEMS microelectromechanical systemsMFP mean free pathMIGO matter–wave interferometric

gravitational-wave observatoryMIM metal-insulator-metalMKSA meters, kilograms, seconds, and amperesMM Massey–MohrMMCDF multichannel multiconfiguration

Dirac–FockMO molecular orbitalMOPA master oscillator power amplifierMOT magneto-optical trapMOX molecular orbital X-radiationMP2 second order Møller–Plesset perturbation

theoryMP3 third order Møller–Plesset perturbation

theoryMPI multiphoton ionizationMQDT multichannel quantum defect theoryMR multireferenceMR-SDCI multireference singles/doubles

configuration interactionMUV middle ultraviolet

N

NAR nonadiabatic regionNEP noise-equivalent powerNEXAFS near-edge X-ray absorption fine structureNDIR non-dispersive infraredNFS nonfine-structureNICE-OHMS noise-immune, cavity-enhanced optical

heterodyne molecular spectroscopyNIM normal incidence monochromatorNIST National Institute of Standards and

TechnologyNMR nuclear magnetic resonance systemsNNS nearest-neighbor energy level spacingsNR nonrelativisticNRQED NR quantum electrodynamics

O

OAO-2 orbiting astronomical observatoryOB ordinary BremsstrahlungOBE optical Bloch equationsOBK Oppenheimer–Brinkman–Kramers

OCP one-component plasmaOHCE one-and-a-half centered expansionOMI ozone monitoring instrumentOPO optical parametric oscillator

P

P-CRDS pulsed-cavity ringdown spectroscopyPADDS angular distribution by Doppler

spectroscopyPAH polycyclic aromatic hydrocarbonPBS polarizing beam splittersPCDW projectile continuum distorted wave

approximationPDM phase diffusion modelPEC potential energy curvesPES photoelectron spectroscopyPES potential energy surfacePH/HP particle–hole/hole–particlePI photoionizationPID particle identificationPIMC path-integral Monte CarloPMT photomultiplier tubesPNC parity nonconservationPPT positive partial transposesPR polarization radiationPSD postion senitive detectorsPSS perturbed stationary statePT perturbation theoryPWBA plane wave Born approximationPZT piezo-electric transducer

Q

QCD quantum chromodynamicsQED quantum electrodynamicsQIP quantum information processingQKD quantum key distributionQMC quantum Monte CarloQND quantum nondemolitionQS quasistaticQSS quasi-steady state

R

RATIP relativistic atomic transition andionization properties

RDC ring-down cavityREADI resonant excitation auto-double ionizationREC radiative electron captureREDA resonant excitation double autoionizationREMPI resonance-enhanced multiphoton

ionizationRES rotational energy surfaceRHC right-hand circularRHIC relativistic heavy ion collider

LVIII List of Abbreviations

RIMS recoil-ion momentum spectroscopyRMI relativistic mass increaseRMPS R-matrix with pseudostatesRNA Raman–Nath approximationRPA random-phase approximationRPA retarding potential analyzerRPAE random phase approximation with

exchangeRR radiative recombinationRRKM Rampsberger–Rice–Karplus–MarcusRSE radial Schrödinger equationRSPT Rayleigh–Schrödinger perturbation

theoryRT Ramsauer–TownsendRTE resonant transfer and excitationRWA rotating wave approximation

S

SA-MCSCF state averaged multiconfigurationself-consistent field

SACM statistical adiabatic channel modelSBS stimulated Brillouin scatteringSCA semiclassical approximationSCF self-consistent fieldSCIAMACHY scanning imaging absorption

spectrometer for atmosphericchartography

SD spin-dependentSD single and doubleSDS singly differential cross sectionSDTQ single, double, triple, quadrupleSE Schrödinger equationSEP stimulated emission pumpSEPE simultaneous electron photon

excitationSEXAFS surface extended X-ray absorption fine

structureSF space-fixedSI spin-independentSIAM Society for Industrial and Applied

MathematicsSM submillimeterSM-FIR submillimeter far-infraredSMS specific mass shiftSOHO solar and heliospheric observatorySP stationary phaseSPA stationary phase approximationsSQL standard quantum limitSQUID superconducting quantum interference

detectorSR synchrotron radiationSRS stimulated Raman scatteringSS strong-short

STIRAP stimulated Raman adiabatic passageSTO Slater type orbitalSTP standard temperature and pressure

T

TCDW target continuum distorted waveTDCS triply differential cross sectionTDHF time-dependent Hartree–FockTDS thermal desorption spectroscopyTDSE time dependent Schrödinger equationTEA transverse-excitation-atmospheric-

pressureTF toroidal fieldTOF time-of-flightTOP time orbiting potentialTPA two-photon absorptionTSR test storage ringTuFIR tunable far-infrared

U

UGA unitary group approachUHF unrestricted Hartree–FockUPS ultraviolet photoelectron spectroscopyUV ultravioletUV-VIS ultraviolet-visible

V

VASP Vienna ab-initio simulation packageVCSEL vertical-cavity surface-emitting laserVECSEL vertical external cavity surface-emitting

laserVES vibrational energy surfacesVUV vacuum ultraviolet

W

WCG Wigner–Clebsch–GordanWDM warm dense matterWKB Wentzel, Kramers, BrillouinWL weak-longWMAP Wilkinson microwave anisotropy

probeWPMD wavepacket molecular dynamics

X

XPS X-ray photoelectron spectroscopy

Y

YAG Yttrium Aluminum Garnet