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OnlineVersion/LNPHomepage LNPhomepage(listofavailabletitles,aimsandscope,editorialcontactsetc.): http://www.springer.de/phys/books/lnpp/ LNPonline(abstracts,full-texts,subscriptionsetc.): http://link.springer.de/series/lnpp/ S.G. Karshenboim F.S. Pavone F. Bassani M. Inguscio T.W. Ha¨nsch (Eds.) The Hydrogen Atom Precision Physics of Simple Atomic Systems 1 3 Editors Dr.SavelyG.Karshenboim Prof.F.Bassani D.I.MendeleevInstituteforMetrology ScuolaNormaleSuperiore 198005St.Petersburg,Russia PiazzadeiCavalieri and Pisa,Italy MPIforQuantumOptics 85748Garching,Germany Prof.M.Inguscio Dept.ofPhysicsandLENS Prof.F.S.Pavone UniversityofFlorence Dept.ofPhysics Florence,Italy UniversityofPerugia Perugia,Italy Prof.T.W.Ha¨nsch and MPIforQuantumOptics LENSandINFM 85748Garching,Germany UniversityofFlorence 50125Florence,Italy Coverpicture:seecontributionbyT.Yamazakiinthisvolume. LibraryofCongressCataloging-in-PublicationDataappliedfor. DieDeutscheBibliothek-CIP-Einheitsaufnahme Thehydrogenatom:precisionphysicsofsimpleatomicsystems/S.G. Karshenboim...(ed).-Berlin;Heidelberg;NewYork;Barcelona; HongKong;London;Milan;Paris;Singapore;Tokyo:Springer,2001 (Lecturenotesinphysics;570) (Physicsandastronomyonlinelibrary) ISBN3-540-41935-7 ISSN0075-8450 ISBN3-540-41935-7Springer-VerlagBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthe materialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustra- tions, recitation, broadcasting, reproduction on microfilm or in any other way, and storageindatabanks.Duplicationofthispublicationorpartsthereofispermittedonly undertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrent version,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.Violations areliableforprosecutionundertheGermanCopyrightLaw.Springer-VerlagBerlinHei- delbergNewYork amemberofBertelsmannSpringerScience+BusinessMediaGmbHhttp://www.springer.de (cid:1)c Springer-VerlagBerlinHeidelberg2001 PrintedinGermanyTheuseofgeneraldescriptivenames,registerednames,trademarks, etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuch namesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreefor generaluse. Typesetting:Camera-readybytheauthors/editor Coverdesign:design&production,Heidelberg Printedonacid-freepaper SPIN:10833154 57/3141/du-543210 Foreword by Norman F. Ramsey Studies of atomic hydrogen have been great sources for scientific discovery be- cause of that atom’s simplicity. These discoveries began with the Balmer series in1885andinclude atomicstructure,earlyquantumtheoriesoftheatom,Dirac relativistic quantum mechanics, the anomalous magnetic moment of the proton (suggesting an internal structure of the proton) and observations of failures of theDiractheorytocorrectlypredictthehydrogenhyperfinestructure,finestruc- ture andanomalousmagnetic momentofelectron.Thesefailures stimulatedthe developmentofthefirstsuccessfulrelativisticQuantumElectrodynamics(QED) with renormalization and the first successful gauge field theory. The delightful and scientifically exciting conference, Hydrogen Atom 2, in Italy on the Tuscan coast showedthat experimental studies of atomic hydrogen andcloselyrelatedatomscontinuetobesourcesofnewfundamentalinformation, as shown by the reviews and progress reports in this edition. The absolute frequency of the fundamental 1S − 2S transition in atomic hydrogen has now been measured to 1.8 parts in 1014, an improvement by a factor of 104 in the past twelve years. This improvement was made possible by a revolutionarynew approachto opticalfrequency metrology with the regularly spaced frequency comb of a mode locked femto-second multiple pulsed laser broadened in a non-linear optical fiber. Optical frequency measurement and coherent mixing experiments have now superseded microwave determination of the2S Lambshiftandhaveledtoimprovedvaluesofthefundamentalconstants, tests of the time variation of the fine structure constant, tests of cosmological variabilityoftheelectron-to-protonmassratioandtestsofQEDbymeasurement of g−2 for the electron and muon. After years of pioneering efforts atomic hydrogen has now been successfully cooled to a sufficiently low temperature for Bose–EinsteinCondensation (BEC) and high precision spectroscopy. Withtherecentadvancesinatomictheoriesandexperimentaltechniques,the value of the information obtained from studies of atoms that are different from but similar to atomic hydrogen have increased. These studies include atomic helium, muonic hydrogen, positronium, muonium, antihydrogen, moderate Z ions, high Z ions, antiprotonic atoms and muonic atoms. Harvard University Norman F. Ramsey October 2000 Preface Despitetheirintriguingsimplicitytwo-bodyatomicsystemssuchasthehydrogen atom continuetochallengephysicistsevenaftermorethanacenturyofresearch. Thehydrogenatomhasinspiredthedevelopmentofthefundamentaltheorieson which our modern physical understanding of the world is based. Several simple atoms have been thoroughly studied over many decades. The hydrogen atom is the simplest and experimentally best accessible of them. The understanding of its spectra was something of a Rosetta stone in unveiling the laws of Quantum Mechanics inthefirstthreedecadesofthetwentiethcenturyand–furthermore– wasthesparkthatignitedthedevelopmentofmodernQuantumElectrodynamics (QED) after the discovery of the Lamb shift and an anomaly in the hyperfine structure interval in the ground state half a century ago. The list of simple atoms accessible now includes a broad range of very dif- ferent natural and artificial systems: hydrogen, helium, muonium, positronium, various few-electron ions, muonic atoms and exotic atomic systems containing a pion, antiproton etc. While hydrogen atoms form the essential part of our universe, the unstable atoms like muonium do not exist in nature at all. The investigationofsimpleatomshasprovideduswithimportantknowledgeonfun- damental interactions between the particles these atoms consist of. Today,thesimpleatomsarestillanimportantobjectofstudy,butnowadays theyplayadifferentrole.Thetheoryofsuchatoms,boundstateQED,isafruitful training groundfor bound state Quantum Chromodymanics (QCD), the theory of strong interactions, and for few-body nuclear theory. The study of common atoms, such as hydrogen and deuterium, is opening intriguing new frontiers of higher and higher accuracy through new experimental technology, such as an entirely new approachto optical frequency metrology. In the cases of muonium, positronium, muonic atoms and multiply-charged ions, the study implies the development of new sources and new detectors. The application of spectroscopic methods is very attractive for pionic and exotic atoms, because of an extremely high (for particle physics) level of accuracy. The accurate study of some atoms (hydrogen, deuterium, muonium, helium andhydrogen-likecarbon)andsomefreeparticles(electron,proton,muon)pro- vides us with new highly accurate values of the fundamental physical constants which are important far beyond the physics of simple atoms. This publication summarizes the progress of the last twenty years and it presents the state of the art in the field. It contains material from two confer- VIII ences: Hydrogen Atom (Pisa, 1988) and Hydrogen Atom 2: Precision Physics of Simple Atomic Systems. The latter took place in Castiglione della Pescaia, Italy, from May 31–June 3, 2000.As was the case twelve years ago,it was orga- nized as a satellite meeting to the International Conference on Atomic Physics. The Hydrogen Atom 2 meeting involved more than one hundred scientists from around the world working on different aspects of the physics of simple atoms, andofferedthemtheopportunityforinterdisciplinaryexchangesbetweenatomic spectroscopy, atomic theory, nuclear and particle physics, metrology and quan- tum field theory. Most of the contributions to the Hydrogen Atom 2 meeting are presented in this publication.The book consistsoftwelve review papersdevotedto the main topics of the precision physics of simple atoms. The CD contains the electronic version of the book and, in addition, the contributed papers and a file with a scannedcopyofthe conferenceproceedingsofthe firstHydrogen Atom meeting. The study of such a simple thing as the hydrogen atom is indeed of gen- eral physical interest for a broad audience, while any conference proceedings reporting detailed information in the field may only be of interest to a nar- rower community. As a result of this, we decided to put the review papers into book form, while the contributed papers based on progress reports and poster presentations have been put onto the compact disk. We gratefully acknowledge Springer-Verlag for their understanding of the special nature of this endeavour and their agreement to promote the book+CD edition. Support from the Max-Planck-Institut fu¨r Quantenoptik (MPQ), the Euro- peanLaboratoryforNon-LinearSpectroscopy(LENS),D.I.MendeleevInstitute forMetrology(VNIIM)isgratefullyacknowledgedbytheorganizingcommittee. Our special thanks go to Ju¨rgen Kluge and Klaus Jungmann for their help in organizing the meeting. The Hydrogen Atom meeting of 2000was the second in the series and we, as the meeting chairmen, would like to gratefully acknowledge efforts by F. Bas- sani, M. Inguscio and T. W. H¨ansch, who initiated the meeting series and gave essential support in the organizationof the second Hydrogen meeting. Garching, Germany Savely G. Karshenboim November, 2000 Francesco S. Pavone Contents Introduction to Simple Atoms Savely G. Karshenboim, Francesco S. Pavone.......................... 1 Part I Hydrogen and Helium Precision Spectroscopy of Atomic Hydrogen F. Biraben, T.W. Ha¨nsch, M. Fischer, M. Niering, R. Holzwarth, J. Reichert, Th. Udem, M. Weitz, B. de Beauvoir, C. Schwob, L. Jozefowski, L. Hilico, F. Nez, L. Julien, O. Acef, J.-J. Zondy, A. Clairon 17 Ultracold Hydrogen Lorenz Willmann, Daniel Kleppner .................................. 42 Review of High Precision Theory and Experiment for Helium Gordon W. F. Drake ............................................... 57 Part II Positronium and Muonium Spectroscopy of the Muonium Atom Klaus-Peter Jungmann ............................................. 81 Experimental Tests of QED in Positronium: Recent Advances Ralph S. Conti, Richard S. Vallery, David W. Gidley, Jason J. Engbrecht, Mark Skalsey, Paul W. Zitzewitz ..................................... 103 Part III Fundamental Constants and Frequency Metrology A New Type of Frequency Chain and Its Application to Fundamental Frequency Metrology Thomas Udem, Jo¨rg Reichert, Ronald Holzwarth, Scott Diddams, David Jones, Jun Ye, Steven Cundiff, Theodor H¨ansch, John Hall ....... 125 Fundamental Constants and the Hydrogen Atom Peter J. Mohr, Barry N. Taylor ..................................... 145 X Contents Present Status of g−2 of Electron and Muon Toichiro Kinoshita ................................................. 157 Part IV Few-Electron Highly-Charged Ions Laser Spectroscopy of Hydrogen-Like and Helium-Like Ions Edmund G. Myers ................................................. 179 The g Factor of Hydrogenic Ions: A Test of Bound State QED G. Werth, H. Ha¨ffner, N. Hermanspahn, H.-J. Kluge, W. Quint, J. Verdu´ 204 Part V Exotic Atoms Elementary Relativistic Atoms Leonid Nemenov ................................................... 223 Antiprotonic Helium – An Exotic Hydrogenic Atom Toshimitsu Yamazaki .............................................. 246 Appendix: Abstracts of Contributed Papers Edited by S. G. Karshenboim and F. S. Pavone ........................ 266 Subject Index ................................................... 285 Author Index.................................................... 290 Contributed Papers (on CD only) Part VI Hydrogen and Helium Towards a Precise Measurement of the He+ 2S Lamb Shift S. A. Burrows, S. Gu´erandel, E. A. Hinds, F. Lison, M. G. Boshier...... 303 High Precision Measurements on Helium at 1083 nm Pablo Cancio Pastor, Paolo De Natale, Giovanni Giusfredi, Francesco S. Pavone, Massimo Inguscio............................... 314 Absolute Frequency Measurement of the 1S-3S Transition in Hydrogen Ga¨etan Hagel, R´emy Battesti, Catherine Schwob, Francois Nez, Lucile Julien, Francois Biraben, Ouali Acef, Jean-Jacques Zondy, Andr´e Clairon . 328 2s Hyperfine Structure in Hydrogen Atom and Helium-3 Ion Savely G. Karshenboim ............................................ 335