1401

Acknowledgements

A.2 Angular Momentum Theory velopments. The list of textbooks and seminal articles

by James D. Louck given in the references is intended to serve this purpose, Acknowl. This contribution on angular momentum theory is ded- however inadequately. icated to Lawrence C. Biedenharn, whose tireless and Excerpts and Fig. 2.1 are reprinted from Biedenharn continuing efforts in bringing understanding and struc- and Louck [2.1] with permission of Cambridge Uni- ture to this complex subject is everywhere imprinted. versity Press. Tables 2.2–2.4 have been adapted from We also wish to acknowledge the many contribu- Edmonds [2.18] by permission of Princeton University tions of H. W. Galbraith and W. Y.C. Chen in sorting out Press. Thanks are given for this cooperation. the significance of results found in Schwinger [2.20]. The Supplement is dedicated to the memory of B.11 High Precision Calculations for Helium Brian G. Wybourne, whose contributions to symmetry by Gordon W. F. Drake techniques and angular momentum theory, both abstract The author is grateful to R. N. Hill and J. D. Mor- and applied to physical systems, was monumental. gan III for suggesting some of the material at Sect. 11.1. The author expresses his gratitude to Debi Erpen- This work was supported by the Natural Sciences and beck, whose artful mastery of TEX and scrupulous Engineering Research Council of Canada. attention to detail allowed the numerous complex re- lations to be displayed in two-column format. B.20 Thomas–Fermi Thanks are also given to Professors Brian Judd and and Other Density-Functional Theories Gordon Drake for the opportunity to make this contri- by John D. Morgan III bution. I am grateful to Cyrus Umrigar and Michael P. Teter Author’s note. It is quite impossible to attribute cred- of Cornell University for generously providing sab- its fairly in this subject because of its diverse origins batical support in the spring of 1995. I should also across all areas of physics, chemistry, and mathemat- like to thank them, as well as Elliott Lieb and Mel ics. Any attempt to do so would likely be as misleading Levy, for helpful discussions. This work was sup- as it is informative. Most of the material is rooted in ported by my National Science Foundation grant the very foundations of quantum theory itself, and the PHY-9215442. physical problems it addresses, making it still more difficult to assess unambiguous credit of ideas. Prag- B.23 Many-Body Theory of Atomic Structure matically, there is also the problem of confidence in and Processes the detailed correctness of complicated relationships, by Miron Ya. Amusia which prejudices one to cite those relationships per- This work was supported by the Israeli Science Founda- sonally checked. This accounts for the heavy use of tion under the grant 174/03. formulas from [2.1], which is, by far, the most often used source. But most of that material itself is derived B.28 Tests of Fundamental Physics from other primary sources, and an inadequate attempt by Peter J. Mohr, Barry N. Taylor was made there to indicate the broad base of origins. The authors gratefully acknowledge helpful conversa- While one might expect to find in a reference book tions with Prof. Michael Eides, Dr. Ulrich Jentschura, a comprehensive list of credits for most of the formu- Prof. Toichiro Kinoshita, and Prof. Jonathan Sapirstein. las, it has been necessary to weigh the relative merits of presenting a mature subject from a viewpoint of con- B.29 Parity Nonconserving Effects in Atoms ceptual unity versus credits for individual contributions. by Jonathan R. Sapirstein The first position was adopted. Nonetheless, there is an The work described here was carried out in collabora- obligation to indicate the origins of a subject, noting tion with S. A. Blundell and W. R. Johnson, and was those works that have been most influential in its de- supported in part by NSF grant PHY-92-04089. 1402 Acknowledgements

B.30 Atomic Clocks and Constraints on Variations We would also like to express our appreciation to all of Fundamental Constants of our scientific collaborators worldwide, both indus- by Savely G. Karshenboim, Victor Flambaum, trial and academic, for their friendship, openness, and Ekkehard Peik help over the years. Barb would like to dedicate this We are very grateful to our colleagues and to participants chapter to her father, Prof. Josef Paldus, who has been of the ACFC-2003 meeting for useful and stimulating an inspiration to her throughout her career, and with

Acknowl. discussions. whom it is an honor to share a publication in the same book. C.31 Molecular Structure by David R. Yarkony D.45 Elastic Scattering: This work has been supported in part by NSF grant CHE Classical, Quantal, and Semiclassical 94-04193, AFOSR grant F49620-93-1-0067 and DOE by M. Raymond Flannery grant DE-FG02-91ER14189 This research is supported by the U.S. Air Force Office of Scientific Research under Grant No. F49620-94-1- C.33 Radiative Transition Probabilities 0379. I wish to thank Dr. E. J. Mansky for numerous by David L. Huestis discussions on the content and form of this chapter and This work was supported by the NSF Atmospheric without whose expertise in computer typesetting this Chemistry Program, the NASA Stratospheric Chemistry chapter would not have been possible. Section, and the NASA Space Physics Division. D.54 Electron–Ion and Ion–Ion Recombination C.37 Gas Phase Reactions by M. Raymond Flannery by Eric Herbst This research is supported by the U.S. Air Force Office The author is grateful to Professor Anne B. McCoy, of Scientific Research under Grant No. F49620-94-1- Department of Chemistry, The Ohio State University, 0379. I wish to thank Dr. E. J. Mansky for numerous for a critical reading of the manuscript. discussions on the content and form of this chapter and without whose expertise in computer typesetting this C.38 Gas Phase Ionic Reactions chapter would not have been possible. by Nigel G. Adams The support of the National Science Foundation, NASA, D.56 Rydberg Collisions: Binary Encounter, and the Petroleum Research Fund-ACS for my experi- Born and Impulse Approximations mental research program is gratefully acknowledged. by Edmund J. Mansky The author thanks Prof. M. R. Flannery for many helpful C.41 Laser Spectroscopy in the Submillimeter discussions and Prof. E. W. McDaniel for access to his and Far-Infrared Regions collection of reprints. The author would also like to thank by Kenneth M. Evenson†, John M. Brown Dr. D. R. Schultz of ORNL for the time necessary to We have benefitted invaluably from the help and collab- complete this work. oration of I. G. Nolt of NASA, Langley for his assistance This work was begun at the Georgia Institute of with the detector technology, and of Kelly Chance for Technology (GIT) and completed at the Controlled his line shape fitting program and his assistance with our Fusion Atomic Data Center at Oak Ridge National Lab- studies of upper atmospheric species. oratory (ORNL). The work at GIT was supported by US AFOSR grant No. F49620-94-1-0379. The work C.43 Spectroscopic Techniques: at ORNL was supported by the Office of Fusion En- Cavity-Enhanced Methods ergy, US DOE contract No. DE-AC05-84OR21400 with by Barbara A. Paldus, Alexander A. Kachanov Lockheed-Martin Energy Systems, Inc. and by ORNL We have benefited invaluably from the collaboration Research Associates Program administered jointly by with our co-workers at Picarro, and would especially ORNL and ORISE. like to acknowledge Eric Crosson, Bruce Richman, Sze Tan, Bernard Fidric, Ed Wahl, and Herb Burkard. We E.61 Photon–Atom Interactions: Low Energy would like to extend our gratitude to Prof. Richard by Denise Caldwell, Manfred O. Krause N. Zare and Dr. Marc Levenson for their unwavering This work was supported in part by the National Science support in helping make CRDS a commercial reality. Foundation under grant PHY-9207634 and in part by Acknowledgements 1403 the US Department of Energy, Division of Chemical for numerous stimulating discussions on this exciting Sciences, under contract with Martin Marietta Energy subject. Funding by the UK Engineering and Physical Systems, Inc., DE-AC0584OR21400. Sciences Research Council (EPSRC), the Royal Society, the European Commission, and the Alexander von Hum- E.62 Photon–Atom Interactions: boldt foundation are gratefully acknowledged. Intermediate Energies by Bernd Crasemann G.86 Atoms in Dense Plasmas Acknowl. The author is indebted to Sue Mandeville for indefatiga- by Jon C. Weisheit, Michael S. Murillo ble assistance. This chapter is dedicated to the memory This work was performed under the auspices of the of Teijo Åberg. U.S. Department of Energy by the University of Cali- fornia, Los Alamos National Laboratory, under contract E.65 Ion–Atom Collisions – High Energy W-7405-Eng-36. LA-UR #04-7993. We wish to thank by Lew Cocke, Michael Schulz C. Iglesias for the results plotted in Fig. 86.2,andLos This work was supported by the Chemical Sciences Divi- Alamos colleagues P.Bradley, J. Guzik, R. Peterson, and sion, Basic Energy Sciences, Office of Energy Research, D. Saumon for providing the data plotted in Fig. 86.1. U.S. Department to Energy and by the National Science Foundation. G.87 Conduction of Electricity in Gases by Alan Garscadden F.74 Multiphoton and Strong-Field Processes This article is based on notes originally developed in co- by Multiphoton and Strong-Field Processes operation with Dr. J. C. Ingraham. Dr. R. Nagpal assisted This work was supported in part by the U.S. DOE under with an earlier version. contract number W-7405-ENG-48. G.90 Interface with Nuclear Physics F.78 Quantized Field Effects by John D. Morgan III, James S. Cohen by Matthias Freyberger, Karl Vogel, J. D.M.˙ is grateful to the Institute for Nuclear Theory of Wolfgang P. Schleich, Robert F. O’Connell the University of Washington for making it possible for We want to thank Prof. I. Bialynicki-Birula for stimulat- him to spend a productive semester there in the spring ing discussions and a critical reading of the manuscript. of 1993. This work has also been supported by National The work of RFOC was supported in part by the U.S. Science Foundation grant PHY-9215442. Army Research Office under grant No. DAAH04-94-G- 0333. G.92 Radiation Physics by Mitio Inokuti F.81 Quantum Information This work was supported by the U.S. Department of by Sir Peter L. Knight, Stefan Scheel Energy, Office of Energy Research, Office of Health We like to thank A. Beige, J. Eisert, E. A. Hinds, and Environmental Research, under Contract W-31-109- V. Kendon, W. J. Munro, M. B. Plenio, and many others ENG-38. 1405

About the Authors

Miron Ya. Amusia Chapter B.23

The Hebrew University Dr. Miron Amusia is a Professor of Physics at the Hebrew University of Jerusalem, Authors Racah Institute of Physics Israel, and Principal Scientist of the Ioffe Physical-Technical Institute, St-Petersburg, Jerusalem, Israel Russia. He is author and co-author of more than 400 referred papers and 9 books. His [email protected] research is in many-body theory of atoms, nuclei, molecules, clusters, and condensed matter, but primarily in atomic physics. He is Fellow of American Physical Society and a member of several professional societies and editorial boards. He received the Humboldt research award and is a member of the Russian Academy of Natural Sciences.

Nils Andersen Chapter D.46

University of Copenhagen Nils Andersen is Professor of Physics at the Niels Bohr Institute of the Niels Bohr Institute University of Copenhagen. His main activities include experimental and Copenhagen, Denmark theoretical studies of atomic collisions involving optically prepared [email protected] states. Recent research interests include cold and ultracold collisions.

Thomas Bartsch Chapter B.15 Georgia Institute of Technology Thomas Bartsch received his PhD from the University of Stuttgart, Germany, in 2002. School of Physics He is currently a postdoctoral fellow at the Georgia Institute of Technology. His Atlanta, GA, USA research is centred on applications of nonlinear dynamics to atomic and molecular [email protected] physics.

Klaus Bartschat Chapter A.7

Drake University Dr. Bartschat is the Ellis & Nelle Levitt distinguished Professor of Physics at the Department of Physics and Astronomy Department of Physics and Astronomy at Drake University. His research in theoretical Des Moines, IA, USA and computational atomic physics focuses on combining the general theory of [email protected] measurement with highly accurate numerical calculations. He is a fellow of the american physical society and has published 2 books, 30 book chapters, 10 review articles, and more than 200 papers on electron and photon collisions with atoms and ions.

William E. Baylis Chapters 1, B.12

University of Windsor Professor Baylis earned degrees in physics from Duke (B.Sc.), Department of Physics the University of Illinois (M.Sc.), and the Technical University of Windsor, ON, Canada Munich (D.Sc.). He has authored two books, edited or co-edited four [email protected] more, contributed 28 chapters to other volumes, and published over a hundred journal articles. His publications are in theoretical physics and emphasize atomic and molecular structure, atomic collisions, and interactions with radiation. His most recent work concerns relativistic dynamics, the photon position operator and wave function, and applications of Clifford algebra, especially to the quantum - classical interface. He is a fellow of the American Physical Society, past chair of the Divisions of Atomic and Molecular Physics and of Theoretical Physics of the Canadian Association of Physicists, a member of the international editorial boards of the Springer Series of Atomic, Optical, and Plasma Physics and of the journal Advances in Applied Clifford Algebras. He is currently a University Professor at the University of Windsor. 1406 About the Authors

Anand K. Bhatia Chapter B.25

NASA Goddard Space Flight Center Dr. Bhatia received his Ph.D. in theoretical physics from the University Laboratory for Astronomy & Solar Physics of Maryland in 1963. Since then he has been at Goddard Space Flight Greenbelt, MD, USA Center. He has published a large number of papers in refereed journals [email protected] on various topics in atomic and astrophysics: scattering of electrons and positrons from atoms, muonic fusion, polarizabilities of two-electron Authors systems, Lamb shift, Rydberg states, excitation of ions etc. He is a Fellow of the American Physical Society.

Hans Bichsel Chapter G.91 University of Washington Professor Hans Bichsel has worked on the interactions of fast charged particles with Center for Experimental Nuclear Physics matter for over 50 years. Some of his measurements are the most accurate of their and Astrophysics (CENPA) type. At present he is studying the methods of particle identification for the time Seattle, WA, USA projection chambers at STAR and ALICE. Earlier he worked in nuclear physics and [email protected] developed neutron radiation therapy in Seattle.

John M. Brown Chapter C.41

University of Oxford Professor Brown obtained his Ph.D. degree from the University of Physical and Theoretical Chemistry Cambridge in 1966. Before moving to Oxford in 1983, he was Laboratory a Lecturer in the Department of Chemistry at Southampton University. Oxford, England He is a high-resolution, gas-phase spectroscopist with a special interest [email protected] in free radical species. In addition to experimental studies at all wavelengths from microwave to the ultraviolet, he is interested in the development of theoretical models to describe the experimental results.

Henry Buijs Chapter C.40

ABB Bomem Inc. Henry Buijs founded ABB Bomem Inc. in 1973 to bring to market state Québec, Canada of the art Fourier Transform spectrometers. He received his Ph.D. from [email protected] the University of British Columbia. He has interest in spectroscopic measurement in the atmosphere for Ozone chemistry, meteorological sounding and climate change assessment. ABB Bomem Inc. is leader in FT spectrometers for satellite based sensors and industrial process monitoring solutions.

Philip Burke Chapter D.47 The Queen’s University of Belfast Phil Burke is Emeritus Professor of Mathematical Physics at the Queen’s University Department of Applied Mathematics and of Belfast, having been Professor at Queen’s from 1967 until 1998. His research Theoretical Physics interests are the theory of atomic, molecular, and optical physics and their Belfast, Northern Ireland, UK applications. He was awarded the Guthrie Medal and Prize in 1994 and the David [email protected] Bates Prize in 2000. He is a Fellow of the Royal Society.

Denise Caldwell Chapter E.61

National Science Foundation Dr. Caldwell is the Program Director for the Atomic, Molecular, Optical, and Plasma Physics Division Physics program at the National Science Foundation. She was awarded her Ph.D. by Arlington, VA, USA Columbia University in 1976. She then held a postdoc at the University of Bielefeld [email protected] and a junior faculty position at Yale University. In 1985 she joined the faculty at the University of Central Florida, where she maintained a research program on atomic photoionization using synchrotron radiation. In 1998 she left full-time academia to become a permanent staff member of the NSF. She is a Fellow of the American Physical Society. About the Authors 1407

Mark M. Cassar Chapter B.13

University of Windsor Mark M. Cassar received his Ph.D. from the University of Windsor, Department of Physics Canada in 2003. His research focuses on high-precision theoretical Windsor, ON, Canada calculations for the energy level structure of three-body atomic and [email protected] molecular systems. Authors

Kelly Chance Chapter G.85

Harvard-Smithsonian Center for Dr. Chance heads the Atomic and Molecular Physics Division of the Astrophysics Harvard-Smithsonian Center for Astrophysics. His current research Cambridge, MA, USA applies molecular spectroscopy, structure and dynamics to studies of [email protected] planetary atmospheres, with emphasis on satellite-based measurements of Earth’s ozone layer composition and lower atmospheric pollution. Recent accomplishments include global measurements of tropospheric ozone, volatile organic compounds, and nitrogen oxides.

Raymond Y. Chiao Chapter F.80 366 Leconte Hall Professor Chiao was awarded his Ph.D. by MIT in 1965. He has been Professor of U.C. Berkeley Physics at Berkeley since 1977. His research interests are: Nonlinear and quantum Berkeley, CA, USA optics; low temperature physics as applied to astrophysics; the relationship between [email protected] general relativity and macroscopic quantum matter. He is writing a book with J. C. Garrison on Quantum Optics.

James S. Cohen Chapter G.90

Los Alamos National Laboratory Dr. Cohen is Group Leader of the Atomic and Optical Theory Group in Atomic and Optical Theory the Theoretical Division of Los Alamos National Laboratory and Los Alamos, NM, USA a Fellow of the American Physical Society. He received a Ph.D. in [email protected] Physics from Rice University in 1973. His general area of research is theoretical atomic and molecular physics, with special interest in exotic muonic and antiprotonic species.

Bernd Crasemann Chapter E.62

University of Oregon Bernd Crasemann is Professor Emeritus of Physics in the University Department of Physics of Oregon and Editor of Physical Review, Atomic, Molecular, and Eugene, OR, USA Optical Physics since 1993. He received his early education in Chile [email protected] and a Ph.D. from the University of California at Berkeley. His work is in experimental and theoretical atomic inner-shell physics, particularly as explored with synchrotron radiation.

David R. Crosley Chapter G.88 SRI International For most of his career, David R. Crosley has developed and used laser-induced Molecular Physics Laboratory fluorescence to study small free radicals. This research includes fundamental Menlo Park, CA, USA spectroscopic and energy transfer studies, as well as applications to combustion, [email protected] atmospheric chemistry,and environmental monitoring. Notable among these are studies of OH, NH, and CH. He is a Fellow of the APS and AAAS.

Derrick Crothers Chapter D.52

Queen’s University Belfast Derrick Crothers is Professor of Theoretical Physics (Personal chair). He researches Department of Applied Mathematics and in atomic, molecular, optical, and condensed matter physics. Topics include Theoretical Physics heavy-particle collisions, threshold phenomena, dielectrics and ferromagnetics. Belfast, Northern Ireland, UK He was awarded an Honorary Professorship in Physics by St Petersburg State [email protected] University in 2003. 1408 About the Authors

Lorenzo J. Curtis Chapter B.17

University of Toledo Lorenzo J. Curtis is a Distinguished University Professor of Physics at Department of Physics and Astronomy the University of Toledo. He received his Ph.D. from the University of Toledo, OH, USA Michigan in 1963 and was awarded the degree Philosophiae Doctorem [email protected] Honoris Causa by the University of Lund in 1999. His research involves time-resolved atomic spectroscopy and the structure of highly ionized Authors atoms. He is the author of over 200 scientific articles and a textbook on atomic structure,. He is an editor of Physica Scripta and a Member of the Editorial Board of Physical Review A.

Gordon W. F. Drake Chapters 1, B.11

University of Windsor Dr. Gordon W.F. Drake is a Professor of Physics and Department Head at the Department of Physics University of Windsor, Canada. He received his Ph.D. degree from York University Windsor, ON, Canada in Toronto. His research on high precision calculations and QED theory for helium [email protected] and other few-body atomic systems has resulted in over 150 refereed journal articles, and numerous other review articles and book chapters. He is a Fellow of the American Physical Society and the Royal Society of Canada, and has been awarded numerous prizes and distinctions for his research. He is currently the Editor of the Canadian Journal of Physics, and an Associate Editor for Physical Review A, as well as Editor of the current volume, and Co-Editor-in-Chief of the Springer Series on Atomic, Optical, and Plasma Physics. He has served as President of the Canadian Association of Physicists, and as Chair of the Division of Atomic, Molecular, and Optical Physics of the American Physical Society.

Joseph H. Eberly Chapter F.73

University of Rochester Joseph H. Eberly is Andrew Carnegie Professor of Physics and Department of Physics and Astronomy Professor of Optics at the University of Rochester. He earned his Ph.D. and Institute of Optics from Stanford University. He held the APS Chair of the Division of Rochester, NY, USA Laser Science from 1996–97 and was Divisional Councilor from [email protected] 2003–2005. Eberly is OSA Vice President and its President in 2007. He is Foreign Member of the Academy of Science of Poland and received numerous awards such as the Charles Hard Townes Award in 1994, the Smoluchowski Medal in 1987, and the Humboldt Preis in 1984. He has published more than 300 research and review papers and several books in the areas of quantum optics, cavity QED and photon–atom interactions, evolution of coherence and quantum entanglement, high-field atomic physics, and nonlinear propagation of short optical pulses.

Guy T. Emery Chapter B.16

Bowdoin College Guy Emery was on the Brookhaven National Laboratory Staff, and Department of Physics taught physics at Indiana University and later Bowdoin College Brunswick, ME, USA (Brunswick, ME). He was a visiting scientist at the Universities of [email protected] Groningen and Osaka. His research has been in nuclear structure and reactions, the intersections of nuclear physics with atomic physics and particle physics, and in the history of physics.

Volker Engel Chapter C.35 Universität Würzburg Volker Engel studied Physics at the University of Göttingen and worked as Institut für Physikalische Chemie a post-doctoral associate at the University of California, Santa Barbara. After his Würzburg, Germany Habilitation in Physics (1993, University of Freiburg) he was appointed Professor in [email protected] 1994 at the University of Würzburg. His research interests are in the time-dependent quantum theory of atomic and molecular dynamics in laser fields. About the Authors 1409

James M. Farrar Chapter E.67

University of Rochester James M. Farrar received his Ph.D. degree at the University of Chicago Department of Chemistry in 1974 working under the direction of Professor Yuan-Tseh Lee. Prior Rochester, NY, USA to joining the faculty at the University of Rochester, he was [email protected] a postdoctoral fellow in the laboratory of Professor Bruce H. Mahan at the University of California at Berkeley. He has had a long-term interest in molecular beam studies of the dynamics of chemical reactions, and Authors his current interests include low energy ion-molecule collisions and electronic spectroscopy of size-selected clusters ions. He is a Fellow of the American Physical Society.

Paul D. Feldman Chapter G.83

The Johns Hopkins University Dr. Feldman is Professor of Physics and Astronomy at the Johns Hopkins University Department of Physics and Astronomy where he has been since 1967. He received his Ph.D. in physics from Columbia Baltimore, MD, USA University in 1964. His recent work has been in space ultraviolet astronomy and [email protected] spectroscopy with a focus on the study of the atmospheres of comets and planets and of the Earth’s upper atmosphere.

Victor Flambaum Chapter B.30

University of New South Wales Dr. Victor Flambaum is a Professor of Physics and holds a Chair of Department of Physics Theoretical Physics. Ph.D., DSc. from the Institute of Nuclear Physics, Sydney, Australia Novosibirsk, Russia. He has about 200 publications in atomic, nuclear, v.fl[email protected] particle, solid state, statistical physics, and astrophysics including works on violation of fundamental symmetries (parity, time reversal), test of unification theories, temporal and spatial variation of fundamental constants from Big Bang to present, many-body theory and high-precision atomic calculations, as well as statistical theory of finite chaotic Fermi systems and enhancement of weak interactions, high-temperature superconductivity, and conductance quantization.

David R. Flower Chapter C.36

University of Durham Professor Flower teaches at the University of Durham (UK). He was awarded Department of Physics his Ph.D. by the University of London in 1969. After working at the Observatoire Durham, United Kingdom de Paris (Meudon, France) and at the ETH (Zuerich, Switzerland), he joined the david.fl[email protected] Physics Department of the University of Durham in 1978. He has been Professor of Physics since 1994. His research interests are in atomic and molecular physics related to astrophysics. He is currently preparing the second edition of his book on “Molecular Collisions in the Interstellar Medium”.

A. Lewis Ford Chapter D.50

Texas A&M University Dr. Ford’s research interests lie in theoretical atomic and molecular Department of Physics physics: inner-shell excitation, ionization, charge transfer, and College Station, TX, USA electronic properties of diatomic molecules. Professor Ford joined the [email protected] Texas A&M faculty in 1973. After receiving his B.A. degree from Rice University, he completed his Ph.D. at the University of Texas at Austin in 1972 and did post-doctoral work at Harvard. Professor Ford is a member of the American Physical Society, Division of Electron, Atomic,and Optical Physics. 1410 About the Authors

Jane L. Fox Chapter G.84

Wright State University Jane Fox received her Ph.D. from Harvard University in Chemical Department of Physics Physics and has held positions at the State University of New York at Dayton, OH, USA Stony Brook, and the Harvard/Smithsonian Astrophysical Observatory. [email protected] She has been elected a Fellow of the American Geophysical Union. Her research has focused on the chemistry, luminosity, heating of the Authors thermospheres/ionospheres of the planets, and their evolution.

Matthias Freyberger Chapter F.78 Universität Ulm Dr. Matthias Freyberger is extraordinary Professor at the Department of Quantum Abteilung für Quantenphysik Physics at the University of Ulm, Germany. His research interests are in quantum Ulm, Germany optics, atom optics, quantum estimation theory, and the foundations of quantum [email protected] mechanics.

Thomas F. Gallagher Chapter B.14 University of Virginia Thomas F. Gallagher received his Ph.D. in physics in 1971 from Harvard University Department of Physics and is now the Jesse W. Beams Professor of Physics at the University of Virginia. Charlottesville, VA, USA His research is focused on the use of Rydberg atoms to realize novel physical systems. [email protected]

Muriel Gargaud Chapter D.51

Observatoire Aquitain des Sciences de Muriel Gargaud is an astrophysicist at the “Observatoire Aquitain des Sciences de l’Univers l’Univers” in Bordeaux, France. She studied for 2O years the physico-chemistry of the Floirac, France interstellar medium, her current research is now astrobiology. Astrobiolgy is an [email protected] interdisciplinary research field (astronomy, geology, chemistry, biology) looking for the origins of life, its evolution and its development on Earth but also in and beyond the Solar System. She is the main scientific editor of “Lectures in Astrobiology” by Springer, Heidelberg 2005.

Alan Garscadden Chapter G.87

Airforce Research Laboratory Alan Garscadden received his B.Sc. and Ph.D. from Queen’s University, Area B Belfast, Northern Ireland. He is the chief Scientist, Propulsion Wright Patterson Air Force Base, OH, Directorate, Air Force Research Laboratory. Wright-Patterson AFB, USA Ohio and Edwards AFB, California. Alan also performs basic and [email protected] applied research in non-equilibrium plasmas and energized gas flows, lasers, mass spectroscopy measurements, and electron collision cross sections. He is a Fellow of the APS, IEEE, AIAA and of the UK Institute of Physics.

John Glass Chapter D.52

British Telecommunications John Glass earned his Ph.D. on Relativistic Ion-Atom Collisions from Solution Design The Queen’s University of Belfast in 1995. His Ph.D. focussed on Belfast, Northern Ireland, UK distorted wave approximations in electron capture, in particular, the first [email protected] fully symmetrical CDW solution via the Sommerfeld-Maue approximation. Dr. Glass now works in large-scale Business Support Systems, Solutions Design for British Telecommunications plc. About the Authors 1411

S. Pedro Goldman Chapter B.13 The University of Western Ontario Professor Pedro Goldman completed a Ph.D. in Relativistic Atomic Physics at the Department of Physics & Astronomy University of Windsor. His work in atomic physics includes pioneering work London, ON, Canada on relativistic variational basis sets, relativistic calculations for many-electron atoms [email protected] and diatomic molecules, accurate calculations for atoms in strong magnetic fields and accurate calculations of QED energy corrections and of the energy levels of Helium. Presently his research is directed to the optimization of the radiation therapy of tumours. He has as well received numerous teaching awards. Authors

Ian P. Grant Chapter B.22

University of Oxford Ian Grant is Emeritus Professor of Mathematical Physics, University of Oxford and Mathematical Institute a Fellow of the Royal Society. He graduated from Oxford with a degree in Oxford, UK Mathematics and obtained his D. Phil. in Theoretical Physics in 1954. His interest in [email protected] relativistic electronic structure of atoms arose whilst he was working for the UK Atomic Energy Authority at Aldermaston from 1957 to 1964 and the field has been a major component of his research ever since. He returned to Oxford to a research post in 1964 and was a full-time member of academic staff from 1969 until his retirement in 1998. He is the author of more than 220 research papers, many of them on relativistic quantum theory applied to atomic and molecular structure and processes.

William G. Harter Chapter C.32

University of Arkansas Professor Harter’s research centers on theory of spectroscopy and what Department of Physics it reveals about quantum phenomena and symmetry principles of Fayetteville, AR, USA structure and dynamics. Current study focuses on how wave mechanics [email protected] of light relates to matter waves and their relativistic symmetry ranging from intrinsic frames of floppy molecules to manifold dynamics of astrophysical objects. A strong educational effort is being developed to make modern theory more accessible. He is a Fellow of American Physical Society (DAMOP).

Carsten Henkel Chapter F.77 Universität Potsdam Carsten Henkel is Docteur en Sciences from the Université Paris-Sud Orsay. Institut für Physik He habilitated in 2004 at Potsdam University where he is currently a Privatdozent. Potsdam, Germany His research interests are in atom optics and nano optics. He is involved in several carsten.henkel European projects on physical implementations of quantum information processing. @quantum.physik.uni-potsdam.de

Eric Herbst Chapter C.37

The Ohio State University Dr. Eric Herbst is Distinguished University Professor of Physics, Astronomy, and Departments of Physics Chemistry at The Ohio State University. Herbst is a Fellow of both the American Columbus, OH, USA Physical Society and the Royal Society of Chemistry (UK). His specialty is the [email protected] chemistry of molecules in interstellar clouds, which are large accumulations of gas and dust particles in our Galaxy and others in which star and planetary formation occur.

Robert N. Hill Chapter A.9

Saint Paul, MN, USA Professor Robert Nyden Hill received his Ph.D. from Yale University in rnhill@fishnet.com 1962. In 1964, after postdoctoral fellowships at Princeton and Yale, he joined the faculty of the University of Delaware Physics Department. He retired in 1997, and moved to Saint Paul, Minnesota. He has published papers in relativistic dynamics, statistical mechanics, mathematical physics, and atomic and molecular physics. 1412 About the Authors

David L. Huestis Chapter C.33

SRI International David L. Huestis received his Ph.D. in Chemistry from the California Molecular Physics Laboratory Institute of Technology in 1973. He is a Fellow of the American Menlo Park, CA, USA Physical Society. His research activities include a wide range of [email protected] experimental and theoretical investigations of fundamental kinetic and optical processes involving atoms, small molecules, liquids, and solids. Authors Two major application areas have been chemical kinetics and optical physics of high-power visible and ultraviolet gas lasers and the optical emissions of terrestrial and planetary atmospheres.

Mitio Inokuti Chapter G.92 Argonne National Laboratory Dr. Mitio Inokuti earned his Ph.D. in Applied Physics from the University of Tokyo in Physics Division 1962. From 1973–1995 he was Senior Physicist at Argonne National Laboratory. He Argonne, IL, USA is a Fellow of the American Physical Society and a member of the Radiation Research [email protected] Society. Since 1985 he is a member of the International Commission on Radiation Units and Measurements, and since 1988 a member of the Editorial Board for Advances in Atomic, Molecular, and Optical Physics. He also is Associate Editor of the Journal of Applied Physics. His research interests focus on theoretical research in radiation physics and chemistry, and in atomic and molecular physics.

Juha Javanainen Chapters F.75, F.76

University of Connecticut Juha Javanainen is Professor of Physics at the University of Connecticut. Department of Physics Unit 3046 He has worked on a number of topics in theoretical quantum optics, and Storrs, CT, USA currently concentrates on quantum degenerate gases. [email protected]

Erik T. Jensen Chapter G.89

University of Northern British Columbia Erik Jensen is an Associate Professor of Physics at the University of Department of Physics Northern British Columbia (Canada). He obtained his Ph.D. in the Prince George, BC, Canada Surface Physics Group at Cambridge University in 1990 and did [email protected] post-Doctoral work with Prof. John Polanyi at the University of Toronto. His research interests are in low-energy electron and photon initiated dynamics for molecules at surfaces.

Brian R. Judd Chapters A.3, A.6 The Johns Hopkins University Brian Judd has had a life-long interest in applying group theory to the spectroscopic Department of Physics and Astronomy properties of the rare earths. He held appointments at Oxford, Chicago, Paris and Baltimore, MD, USA Berkeley before joining the Physics Department of the Johns Hopkins University in [email protected] 1966. He received the Spedding Award for Rare-Earth Research in 1988 and is an Honorary Fellow of Brasenose College, Oxford.

Alexander A. Kachanov Chapter C.43

Research and Development Alexander Kachanov received the M.Sc. degree in physics from Moscow Institute of Picarro, Inc. Physics and Technology in 1976, and the Ph.D. degree in physics from the Institute of Sunnyvale, CA, USA Spectroscopy of the Russian Academy of Sciences in 1987. In 2001 he joined Picarro, [email protected] Inc., where his research interests focus on ultra-sensitive gas detection and development of novel laser sources. About the Authors 1413

Savely G. Karshenboim Chapter B.30

D.I.Mendeleev Institute for Metrology Dr. Savely G.Karshenboim was graduated in 1983 from St. Petersburg (VNIIM) (then Leningrad) State University, Russia where he also received Quantum Metrology Department his Ph.D. in 1992 and habilitatatetd in 1999. He has been a member St. Petersburg, Russia of D.I. Mendeleev Institute for Metrology since 1983 and is at present [email protected] a head of Laboratory for Precision Physics and Metrology of simple atomic systems. Since 1994 until now he has enjoyed numerous visiting Authors opportunities at Max-Planck-Institut für Quantenoptik. He is a member of the CODATA task group on fundamental constants and SUNAMCO commission of IUPAP. SUNAMCO is a commission on Symbols, Units, Nomenclature, Atomic Masses and Fundamental Constants. Dr. Karshenboim’s scientific interests include precision physics of simple atoms, quantum electrodynamics (QED), determination of fundamental constants and search for their variations.

Kate P. Kirby Chapter G.85 Harvard-Smithsonian Center for Kate Kirby has a Ph.D. in Chemical Physics from the University of Chicago, and is Astrophysics currently director of the Institute for Theoretical Atomic, Molecular, and Optical Cambridge, MA, USA Physics. Her research interests center on theoretical studies of ultracold molecule [email protected] formation and atomic and molecular structure and processes which are of interest to astronomy and atmospheric physics. Such processes include: photoionization, photodissociation, radiative association, charge transfer, and line-broadening.

Sir Peter L. Knight Chapter F.81

Imperial College London Sir Peter Knight is Head of Physics at Imperial College. He is Chief Scientific Advisor Department of Physics Blackett Laboratory to the National Physical Laboratory and past President of the Optical Society of London, UK America. He is a Fellow of the Royal Society and was knighted in 2005. He researches [email protected] in strong field physics and quantum information and edits the Journal of Modern optics and contemporary physics.

Manfred O. Krause Chapter E.61

Oak Ridge National Laboratory Dr. Krause was a Senior Scientist at the Oak Ridge National Laboratory Oak Ridge, TN, USA working primarily in the field of photoelectron spectrometry of atoms [email protected] with the use of synchrotron radiation. He received his Dr. rer. nat. in physics at the Technische Universität and the Max Planck Institut für Metallforschung in Stuttgart in 1954. He joined the Oak Ridge National Laboratory in 1963 and retired in 1995. He is a Fellow of the American Physical Society, and was a Professeur d’Echange at the University of Paris in 1975 and an Alexander von Humboldt awardee at the University of Freiburg in 1976.

Paul G. Kwiat Chapter F.80 University of Illinois at Paul G. Kwiat is the Bardeen Chair in Physics, at the University of Illinois, in Urbana-Champaign Urbana-Champaign. A Fellow of the American Physical Society and the Optical Department of Physics Society of America, he studies the phenomena of entanglement, quantum Urbana, IL, USA interrogation, quantum erasure, and optical implementations of quantum information [email protected] protocols. He can’t resist a good swing dance. 1414 About the Authors

Maciej Lewenstein Chapter F.74

ICFO–Institut de Ciéncies Fotóniques Born in Warsaw Poland, Dr. Maciej Lewenstein worked for many years Barcelona, Spain in the Center for Theoretical Physics in Warsaw. He graduated from the [email protected] University of Essen, worked for several years at CEA, and the University of Hannover. Currently he leads the theoretical quantum optics group at ICFO, Barcelona, Spain. His interests include physics Authors of ultracold gases, quantum information, and the physics of matter in strong fields. He is a Fellow of APS.

James D. Louck Chapter A.2 Los Alamos National Laboratory James Louck is a Los Alamos National Laboratory Retired Fellow. He earned his Retired Laboratory Fellow Ph.D. in molecular physics from The Ohio State University in 1958, and is the Los Alamos, NM, USA co-author of three books. Except for the years 1960 - 1963 at Auburn University, his [email protected] career was in the Theoretical Division at Los Alamos developing symmetry methods for physical systems. His current research is in the inter-relations between symmetry and combinatorics.

Joseph H. Macek Chapter D.53

University of Tennessee and Oak Ridge Dr. Joseph Macek is a Distinguished Professor at the University of Tennessee and National Laboratory a Distinguished Scientist at Oak Ridge National Laboratory. His currrent research Department of Physics and Astronomy concentrates on thetheory of atomic collisions. He has been assigned Co-Chair of the Knoxville, TN, USA local committee for the annual meeting of the Division of Atomic and Molecular [email protected] Physics of the American Physical Society, Knoxville, TN 2006.

Mary L. Mandich Chapter C.39

Lucent Technologies Inc. Mary Mandich is a Technical Manager and Distinguished Member Bell Laboratories of Technical Staff at Bell Laboratories and currently leads research in Murray Hill, NJ, USA high speed backplanes and optical remoting for next generation [email protected] telecommunication networks. She obtained her Ph.D. degree in Physical Chemistry at Columbia University. She holds 6 U.S. Patents and has authored 2 book chapters and more than 55 scientific publications in chemistry, physics, and materials science.

Steven T. Manson Chapter D.53 Georgia State University Professor Manson is on the faculty at Georgia State University. He received the Ph.D. Department of Physics and Astronomy from Columbia University in 1966, and did a two-year post-doc at the NBS (now Atlanta, GA, USA NIST) working with Ugo Fano and John Cooper. He started as a faculty member at [email protected] Georgia State University in 1968 and has been Regents Professor since 1984. His research has been primarily in the area of theoretical studies of ionization of atoms and ions by charged particles and photons. He is a Fellow of the American Physical Society.

William C. Martin Chapter B.10

National Institute of Standards and Dr. Martin’s research has included the measurement and energy-level analysis of Technology atomic spectra. He has also published a number of critical compilations of atomic Atomic Physics Division spectroscopic data, including a large volume for the rare-earth elements. In his current Gaithersburg, MD, USA position as Scientist Emeritus at NIST, Dr. Martin is continuing work on [email protected] internet-accessible atomic spectra databases. About the Authors 1415

Jim F. McCann Chapter D.52

Queen’s University Belfast Jim McCann was a Ph.D. student of Prof. Derrick Crothers at Queen’s Dept. of Applied Mathematics and University, Belfast. He is currently a Reader in Theoretical Physics at Theoretical Physics Queen’s and works in the field of Quantum Optics and Quantum Belfast, Northern Ireland, UK Information Processing. [email protected] Authors

Ronald McCarroll Chapter D.51

Université Pierre et Marie Curie Ronald McCarroll is a Professor of Physics at the Université Pierre et Laboratoire de Chimie Physique Marie Curie in Paris. He obtained his Ph.D. degree in Theoretical Paris Cedex 05, France Physics at Queen’s University, Belfast. After a post-doctoral fellowship [email protected] at the National Physics Laboratory, Teddington and a Lectureship at Queen’s University, Belfast he was appointed as a Directeur de Recherche au CNRS at the Observatoire de Pari, Meudon. Later, he moved to the Université de Bordeaux I as Professor in Astrophysics and finally to Paris as Professor in Physics at the Univerité Pierre et Marie Curie. He has worked in the field atomic and molecular photodynamics, particularly in view of their application to astrophysics and the physics of fusion plasmas. He is the author of more then 130 papers in refereed journals and contributed more than 20 specialised reviews to books and other specialised publications.

Fiona McCausland Chapter D.52 Northern Ireland Civil Service Dr. Fiona McCausland gained her Ph.D. in Theoretical Physics in 1995 from the Department of Enterprise Trade and Queen’s University of Belfast. Following a year spent as a Post Doctoral Research Investment Assistant at the University, she joined the Northern Ireland Civil Service in September Belfast, Northern Ireland, UK 1996. She currently holds the position of Project Manager in the Department of fi[email protected] Enterprise, Trade and Investment.

William J. McConkey Chapter E.63

University of Windsor Dr. Bill McConkey is a physicist with an extensive background in the measurement Department of Physics of absolute cross section data for the atomic, molecular, and optical physics Windsor, ON, Canada community. His laboratory is recognised as a world leader in electron collisions [email protected] research. He has been awarded the Gold Medal of the Canadian Association of Physicists (1999) and the Allis Prize of the American Physical Society (2004) for his work.

Robert P. McEachran Chapter D.48

Australian National University Professor McEachran received his Ph.D. from the University of Western Atomic and Molecular Physics Ontario, Canada and then spent two years at the University College Laboratories Research School of Physical London (England) before joining York University in Toronto in 1964. Sciences and Engineering In 1997 he accepted an Adjunct Professorship at the Australian National Canberra, Australia [email protected] University. His current research interests are the theoretical treatment of electron/positron scattering from heavy atoms within a relativistic framework.

James H. McGuire Chapter D.57

Tulane University Dr. McGuire is Murchison Mallory Chair and department chair at Department of Physics Tulane University. He is a past Chair of the Division of Atomic, New Orleans, LA, USA Molecular and Optical Physics (DAMOP) of the American Physical [email protected] Society. His research interests are in electron correlation dynamics. entanglement, complexity and correlation, and quantum time. 1416 About the Authors

Dieter Meschede Chapter F.79 Rheinische Professor Dieter Meschede teaches at the Institute for Applied Physics in Bonn. After Friedrich-Wilhelms-Universität Bonn his studies in Hanover and Cologne and having been awarded his Dr. rer. nat in Munich Institut für Angewandte Physik in 1984, he first worked at Yale University. Then he became senior scientist at the MPI Bonn, Germany for Quantum Optics, Garching. He has been Professor of Physics since 1990, first in [email protected] Hanover, since 1994 in Bonn. Professor Meschede is author of “Optics, Light, and Laser”, some 90 refereed articles, and, since 2001, editor of the “Gerthsen”textbook. Authors

Pierre Meystre Chapter F.68

University of Arizona Pierre Meystre’s research ranges from laser theory to cavity QED and to the physics of Department of Physics quantum-degenerate atomic and molecular systems. With Murray Sargent, he Tucson, AZ, USA coauthored the textbook “Elements of Quantum Optics,”and he recently published the [email protected] monograph “Atom Optics”, both with Springer-erlag. He has been awarded the Senior Scientist Research Prize of the Humboldt Foundation and the R.W. Wood Prize of the Optical Society of America. He is currently a Regents Professor and the Head of the Physics Department at The University of Arizona.

Peter W. Milonni Chapter F.70

Los Alamos, NM, USA Peter Milonni is a Laboratory Fellow (retired) at Los Alamos National [email protected] Laboratory. His main interests are in theoretical physics, especially quantum optics and electrodynamics. He is an author of several books including Lasers (with J. H. Eberly), The Quantum Vacuum, and Fast Light, Slow Light, and Left-Handed Light. Previously he held positions with the U. S. Air Force, the Perkin-Elmer Corporation, and the University of Arkansas.

Peter J. Mohr Chapter B.28

National Institute of Standards and Dr. Peter Mohr received his Ph.D. from the University of California at Technology Berkeley in 1973 and spent some years at the Lawrence Berkeley Atomic Physics Division Laboratory (1973–1978), at Yale University (1978–1985), at the Gaithersburg, MD, USA National Science Foundation (1985–1987), and at the National Bureau [email protected] of Standards/ National Institute of Standards and Technology from 1987 until now. He is a Fellow of the American Physical Society, and received the Alexander von Humboldt Senior Research Award in 1995. He held the Chair of the CODATA Task Group on Fundamental Constants from 1999 to 2006 and was Chair of the Precision Measurement and Fundamental Constants Topical Group of the American Physical Society from 2000–2001.

John D. Morgan III Chapters B.20, G.90

University of Delaware Dr. Morgan is Associate Professor and obtained his B.S. from The George Washington Department of Physics and Astronomy University, his M.Sc. in Theoretical Chemistry from Oxford University, and his Ph.D. Newark, DE, USA in Chemistry from Berkeley. He has served on the editorial boards of the Journal of [email protected] Mathematical Physics and the International Journal of Quantum Chemistry. His wide-ranging interests include the application of sophisticated mathematical techniques to assist the accurate calculation of properties of atoms and molecules. About the Authors 1417

Michael S. Murillo Chapter G.86

Los Alamos National Laboratory Dr. Murillo received his Ph.D. in theoretical atomic and plasma physics Theoretical Division from Rice University. He then received a Director’s Postdoctoral Los Alamos, NM, USA Felloship at Los Alamos, where he has remained since. His current [email protected] research interests lie in the areas of dense and strongly coupled plasmas, including laser-produced plasmas, dusty plasmas, astrophysical plasmas, and ultracold plasmas. He applies both analytical and Authors molecular dynamics methods to these systems.

Evgueni E. Nikitin Chapter D.49

Technion-Israel Institute of Technology Professor, Nikitin Evgueni is a researcher, head of the research group, Department of Chemistry and Professor of Chemical Physics at the Institute of Chemical Physics, Haifa, Israel Moscow, since 1958. He is also Professor of Physical Chemistry, [email protected] Technion, Haifa, since 1991. He is a member of the Deutsche Akademie der Naturforscher Leopoldina, the European Academy of Arts, Sciences and Humanities, and the International Academy of Quantum Molecular Sciences. His research concentrates on the theory of inelastic and reactive scattering, theory of nonadiabatic processes, statistical theory of chemical reactions, and atom-molecule processes at low energies. He authored 15 books and about 300 papers. Research awards: Alexander von Humboldt Award, Gauss Professorship, and Barecha Fellowship

Robert F. O’Connell Chapter F.78 Louisiana State University Professor O’Connell earned his Ph.D. in 1962 from the University of Notre Dame, Department of Physics and Astronomy Indiana. For many years , in collaboration with G. W. Ford , he has been studying Baton Rouge, LA, USA dissipative and fluctuation phenomena in quantum mechanics and related applications. [email protected] In addition, he is using the generalized quantum Langevin equation to explore recent topical questions in non-equilibrium statistical mechanics (particularly claims that the fundamental laws of thermodynamics may be violated in the quantum regime).

Francesca O’Rourke Chapter D.52

Queen’s University Belfast Dr. O’Rourke obtained her Ph.D. in Ion-Atom Collisions from Queens University, Department of Applied Mathematics and Belfast, in 1991. She now lectures in Applied Mathematics and Theoretical Physics at Theoretical Physics Queens University, Belfast. Her current research interests include heavy particle Belfast, UK collisions in atomic and molecular physics and more recently mathematical modelling [email protected] in Biomedicine.

Ronald E. Olson Chapter D.58

University of Missouri-Rolla Ronald E. Olson, Curators’ Professor of Physics earned his Ph.D. from Physics Department Purdue University in 1967. He is a Fellow of the American Physics Rolla, MO, USA Society and a Fulbright Fellow to France. He was received the [email protected] Humboldt Senior Prize Award, the University of Missouri system-wide Presidential Award for Research and Creativity. His research interests concentrate on theory of elastic and inelastic total and differential scattering cross sections: atom–atom, ion–atom, and ion–ion. Studies of multiply charged ion–atom collisions, Rydberg atom collisions, negative ion detachment mechanisms, and Penning and associative ionization. 1418 About the Authors

Barbara A. Paldus Chapter C.43

Skymoon Ventures Dr. Barbara Paldus received her Ph.D. in electrical engineering from Palo Alto, CA, USA Stanford University. She is a partner at Skymoon Ventures, where she [email protected] works with early stage photonics companies. Previously, she was CTO at Picarro, which she founded in 1998. She has received numerous research awards, most recently the Adolph Lomb Prize (2001) by the Authors OSA for her work in cavity ring-down spectroscopy.

Josef Paldus Chapters A.4, A.5 University of Waterloo Josef Paldus, FRSC, is a Distinguished Professor Emeritus in the Department of Department of Applied Mathematics Applied Mathematics, Department of Chemistry, and Guelph-Waterloo Center for Waterloo, ON, Canada Graduate Work in Chemistry – Waterloo Campus, at the University of Waterloo, [email protected] Waterloo, ON Canada. He is also an Adjunct Professor in the Department of Chemistry of the University of Florida in Gainesville, FL, USA. He received his Ph.D. degree from the Czechoslovak Academy of Sciences and his RNDr. and Dr.Sc. degrees from the Faculty of Mathematics and Physics of the Charles University in Prague, Czech Republic. His research interests are in the methodology of quantum chemistry, the many-electron correlation problem, and the electronic structure of molecular systems in general. On these topics he published about 300 papers, reviews, and monograph chapters. He is a member of several professional societies and editorial boards, and received various awards and international fellowships, notably a Killam Fellowship, Institute for Advanced Study in Berlin Fellowship, Alexander von Humboldt Senior Scientist Award, and most recently a Gold Medal of the Charles University. He is also a Fellow of the Royal Society of Canada and of the Fields Institute for Research in Mathematical Sciences.

Ruth T. Pedlow Chapter D.52

Queen’s University Belfast Ruth Pedlow is working towards completion of her Ph.D. in heavy Department of Applied Mathematics particle collisions in atomic and molecular physics at Queens University and Theoretical Physics of Belfast. Belfast, UK [email protected]

David J. Pegg Chapter E.60

University of Tennessee Currently I am investigating the structure and dynamics of atomic and Department of Physics molecular negative ions by studying how they interact with photons and Knoxville, TN, USA electrons. The threshold behaviour and resonance structure in [email protected] detachment cross sections are used to measure correlation-sensitive parameters. Experiments on photo detachment involve the use of lasers or synchrotron radiation. Such measurements, for example, lead to information on the process of multiple electron detachment induced by the absorption of a single photon. Electron-impact detachment and dissociation processes are studied using a magnetic storage ring. These studies, for example, yield information on the production and decay of doubly negative charged molecular and cluster negative ions.

Ekkehard Peik Chapter B.30 Physikalisch-Technische Bundesanstalt Dr. Ekkehard Peik received his doctorate and the habilitation in physics at the Braunschweig, Germany University of Munich. His research interests are in the fields of laser-cooling and [email protected] trapping of atoms and ions, precision laser spectroscopy and the application to optical time and frequency metrology and tests of fundamental physics. He is now head of the group ‘Optical Clocks’ at PTB and also a lecturer at the University of Hannover. About the Authors 1419

Ronald Phaneuf Chapter E.64

University of Nevada Professor Phaneuf received a Ph.D. in atomic physics from the University of Windsor Department of Physics in 1973 and has since been engaged in experimental research on interactions of ions Reno, NV, USA with electrons, atoms, molecules and photons using merged-beams and crossed-beams [email protected] techniques. He was formerly at JILA and Oak Ridge National Laboratory. His current research emphasis is photon–ion interactions using synchrotron radiation. Authors

Eric H. Pinnington Chapter B.18

University of Alberta Eric Pinnington obtained his Ph.D. in Physics at Imperial College in Department of Physics 1962. Prior to joining the University of Alberta in 1965, he held an Edmonton, AB, Canada NRC postdoctoral fellowship at McMaster University in Hamilton, [email protected] Ontario, and an Alexander von Humboldt Fellowship at the Max Planck Institute for Astrophysics in Munich. He was elected Fellow of the American Physical Society in 1995. He became Professor Emeritus of Physics in 1997.

Richard C. Powell Chapter F.71 University of Arizona Powell was educated in physics at the United States Naval Academy and Arizona State Optical Sciences Center University. He has been a research scientist and professor at Air Force Cambridge Tuscon, AZ, USA Research Laboratories, Sandia National Laboratory, and Lawrence Livermore [email protected] National Laboratory, Oklahoma State University and the University of Arizona. He has authored two textbooks and over 260 scientific papers in laser spectroscopy and solid-state laser development. Powell is an elected Fellow of both the American Physical Society and the Optical Society of America and has served a President of OSA. He has been elected to the Russian Academy of Engineering Science.

John F. Reading Chapter D.50

Texas A&M University Professor Reading earned his Ph.D. from the University of Birmingham, UK, in 1964. Department of Physics His current research interests are in theoretical calculations of cross sections for College Station, TX, USA excitation and ionization following fast ion–atom collisions, the role of Pauli [email protected] correlation in inner-shell vacancy production, and the role of dynamic electronic correlation. The latter especially in comparision of proton and anti-proton-induced single and double ionization of helium. He was named The Distinguished Texas Scientist of 1995 by the Texas Academy of Sciences and is Editor of the proceedings of several conferences on ion–atom collisions.

Jonathan R. Sapirstein Chapters B.27, B.29

University of Notre Dame Dr. Sapirstein earned his Ph.D. from Stanford University in 1979. He Department of Physics did postdoctoral work at UCLA and Cornell, and is at the University of Notre Dame, IN, USA Notre Dame, Indiana, since 1984. Current research interest in parity [email protected] non-conservation in atoms, QED effects in highly charged many-electron ions, QED calculations in hydrogen, positronium, muonium, and helium. Dr. Sapirstein is a Fellow of the American Physical Society.

Stefan Scheel Chapter F.81

Imperial College London Stefan Scheel received his Ph.D. (Dr. rer. nat.) from the Blackett Laboratory Friedrich-Schiller-University Jena in 2001. He is an EPSRC Advanced London, UK Research Fellow in the Quantum Optics and Laser Science group in the [email protected] Department of Physics at Imperial College London. His main research areas include QED in dielectric materials, quantum information processing using linear optics, and decoherence processes in atom chip experiments. 1420 About the Authors

Axel Schenzle Chapter F.79 Ludwig-Maximilians-Universität Professor Schenzle has been working on various aspects of Theoretical Quantum Department für Physik Optics, the description of classical and quantummechanical noise in microscopic and München, Germany mesoscopic systems, Bose–Einstein-Condensation, Quantum Information Theory, [email protected] qunatum computing and decoherence. He has been Deputy Rector of the University of Munich and Dean for many years. Authors

Reinhard Schinke Chapter C.34

Max-Planck-Institut für Dynamik & Dr. Reinhard Schinke received his Ph.D. from the Physics department of the Selbstorganisation University of Kaiserslautern in 1976. His main area of research is molecular Göttingen, Germany dynamics, in particular energy transfer in atomic collisions, chemical reactions, and [email protected] photodissociation. He is author of the book Photodissociation Dynamics. In recent years his interest shifted to dynamical investigations of recombination processes with particular emphasis on the ozone isotope effect.

Wolfgang P. Schleich Chapter F.78

Universität Ulm Prof. Schleich studied physics and mathematics at the Abteilung für Quantenphysik Ludwig-Maximilians-Universität München where he obtained his Ulm, Germany Diplom, Doktor, and Habilitation. He worked at the University of New [email protected] Mexico (Albuquerque) and University of Texas (Austin) and the Max-Planck Institut für Quantenoptik in Garching. Since 1991 he has held a chair of theoretical physics at the Universität Ulm. He has more than 200 publications, is a Fellow of APS, IOP and OSA and an elected member of the Heidelberger Akademie der Wissenschaften and the Leopoldina, and has received numerous awards including the Leibniz Prize and the Max-Planck Prize.

Michael Schulz Chapter E.65 University of Missouri-Rolla Professor Dr. Michael Schulz received his Ph.D. in Physics from the University of Physics Department Heidelberg in 1987 to become a Teaching Assistant from 1981–1987. After positions Rolla, MO, USA at Oak Ridge National Laboratory and Kansas State University he joined the [email protected] University of Missouri-Rolla as Assistant Professor in 1990. Since 2002 he is Professor of Physics and since 2003 Director of the Laboratory for Atomic, Molecular, and Optical Research. His scientific concentrate on experimental atomic physics, dynamics of many-body problem, correlation effects, and three-dimensional imaging of atomic break-up processes. He is a Fellow of the American Physical Society and was Mercator Scholar 2004–2005.

Peter L. Smith Chapter C.44

Harvard University Peter L. Smith received his Ph.D. degree in Physics from Caltech in 1972 and, after Harvard-Smithsonian Center for a year of teaching, came to and stayed at the Harvard-Smithsonian Center for Astrophysics Astrophysics. He is involved in measurements of fundamental atomic and molecular Cambridge, MA, USA parameters at ultraviolet wavelengths for analysis of astronomical spectra, and design [email protected] and calibration of instruments for ultraviolet spectroscopic and/or radiometric measurements, especially of the Sun, from earth-orbiting satellites. About the Authors 1421

Anthony F. Starace Chapter B.24

The University of Nebraska Dr. Starace earned his Ph.D. from the University of Chicago in 1971 Department of Physics and Astronomy and is George Holmes University Professor of Physics at the University Lincoln, NE, USA of Nebraska since 2001. His primary research interests concern the [email protected] interaction of intense laser light with atoms, especially single and multiphoton detachment and ionization processes. He is a Fellow of the American Physical Society and the American Association for the Authors Advancement of Science, and is currently an Associate Editor of Reviews of Modern Physics.

Glenn Stark Chapter C.44

Wellesley College Professor Stark’s research interest is in the field of experimental Department of Physics molecular spectroscopy. His laboratory programs emphasize molecular Wellesley, MA, USA transitions of interest to the astrophysics and aeronomy communities, [email protected] primarily involving the measurement and interpretation of high-resolution absorption spectra of vacuum ultraviolet and extreme ultraviolet transitions. Related activities include Fourier transform spectroscopy of diatomic molecules, and laser spectroscopies of diatomics.

Allan Stauffer Chapter D.48 Department of Physics and Astronomy Allan Stauffer has published numerous papers in the field of electron and positron York University scattering from atoms and simple molecules. In collaboration with numerous Toronto, ON, Canada colleagues, he has been involved with extensive scattering calculations and developed [email protected] methods to carry out these investigations and has worked closely with groups involved in measuring these processes.

Aephraim M. Steinberg Chapter F.80

University of Toronto Aephraim Steinberg works on experimental quantum optics and laser cooling, with Department of Physics specific emphasis on foundational questions in quantum mechanics (esp. quantum Toronto, ON, Canada measurement) and on quantum information. His obssession is with tunneling times; [email protected] in 1994, he demonstrated (with Kwiat and Chiao) the superluminal tunneling of photons, and in 2005, he is starting an experiment to probe tunneling times for Bose-condensed atoms through optical barriers.

Stig Stenholm Chapter F.69

Royal Institute of Technology Stig Stenholm was Pprofessor of Laser Physics and Quantum Optics at Physics Department the Royal Institute of Technology, Stockholm. He studied Technical Stockholm, Sweden Physics at the Helsinki Institute of Technology and Mathematics at the [email protected] University of Helsinki. He worked at the Research Institute for Theoretical Physics in Helsinki until 1997, when moving to Stockholm. Theoretical research fields include spectroscopy, quantum optics, and informatics

Jack C. Straton Chapter D.57

Portland State University Jack Straton earned a doctorate in quantum theory from the University University Studies of Oregon and served as both a volunteer and professional diversity Portland, OR, USA trainer over the past 18 years. He is an Assistant Professor in Portland State University’s interdisciplinary University Studies program, where his teaching blends science, art, diversity, and social responsibility. His research ranges from Quantum Scattering Theory to Anti-racist Pedagogy. 1422 About the Authors

Carlos R. Stroud Jr. Chapter F.73

University of Rochester Professor Stroud is Professor of Optics, Professor of Physics and Director of the Institute of Optics Center for Quantum Information at the University of Rochester where he works in Rochester, NY, USA a variety of areas of experimental and theoretical quantum optics and atomic physics. [email protected] His group pioneered the area of Rydberg electron wave packet physics observing localization, decays, revivals and interferometry with a single electron. Authors

Barry N. Taylor Chapter B.28

National Institute of Standards and Barry N. Taylor received his Ph.D. in Physics from the University of Technology Pennsylvania in 1963. He remained at Penn as a faculty member until Atom Physics Division he joined RCA Laboratories in Princeton, NJ in 1966. He joined the Gaithersburg, MD, USA National Bureau of Standards (now NIST) in 1970 as a Section Chief in [email protected] the Electricity Division, becoming its Chief in 1974. In 1988 he became manager of the NIST Fundamental Constants Data Center, retiring from NIST and that position in 2001. Since then he has been a NIST Scientist Emeritus in the Data Center. Dr. Taylor has authored or co-authored over 100 publications, is a fellow of the APS and IEEE, and has received a number of awards. His current research focuses on the evaluation of data related to the fundamental constants and improving the International System of Units (SI).

Aaron Temkin Chapter B.25 NASA Goddard Space Flight Center Dr. Temkin is a research physicist (emeritus) at NASA/GSFC. He has specialized Laboratory for Solar and Space Physics (primarily) in scattering problems of electrons from atoms and molecules, and Greenbelt, MD, USA associated processes (autoionization, in particular). He received his Ph.D. degree from [email protected] the Massachusetts Institute of Technology in 1956, and has been at his present institution since 1960.

Sandor Trajmar Chapter E.63

California Institute of Technology Dr. Sandor Trajmar received his Ph.D. in physical chemistry from the University of Jet Propulsion Laboratory California at Berkeley, California,. He was Head of the Electron collision Physics Redwood City, USA Group, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, [email protected] California. He retired in January 1997.

Elmar Träbert Chapter B.18

Ruhr-Universität Bochum Professor Elmar Träbert obtained his doctorate and professorial title at Experimentalphysik III/NB3 Ruhr-Universität Bochum. He has extensive experience in time-resolved Bochum, Germany spectroscopy and atomic lifetime measurements mainly from working [email protected] with beam-foil spectroscopic techniques, a heavy-ion storage ring, as well as radio-frequency and electron beam ion traps in more than a dozen laboratories.

Turgay Uzer Chapter B.15

Georgia Institute of Technology Professor Turgay Uzer obtained his doctorate at Harvard and was School of Physics a postdoctoral fellow at Caltech. Currently he is Regents’ Professor in Atlanta, GA, USA the School of Physics, Georgia Institute of Technology. His research [email protected] interests include: Rydberg atoms and molecules, semiclassical theories, nonlinear dynamics/chaos, intramolecular energy transfer, and chemical reactivity. About the Authors 1423

Karl Vogel Chapter F.78 Universität Ulm Dr. Vogel received his PhD from the Universität Ulm in 1989. His research area is Abteilung für Quantenphysik theoretical quantum optics. In particular, he investigated how quantum states of the Ulm, Germany radiation field can be prepared and how they can be measured. [email protected] Authors Jon C. Weisheit Chapter G.86

Washington State University Jon Weisheit recently joined Washington State Universtity’s Intstitute for Shock Institute for Shock Physics Physics, where he holds appointments as Research Professor and Associate Director, Pullman, WA, USA and conducts research focused on understanding quantum phenomena in high energy [email protected] density matter. He is a Fellow of the American Physical Society, and is a frequent advisor in government agencies on issues pertaining both to basic science and to national defense programs. Her received his graduate degrees in space science and in physics from Rice University.

Wolfgang L. Wiese Chapter B.10

National Institute of Standards and Dr. Wolfgang Wiese is a physicist with extensive research background Technology in atomic spectroscopy and in the critical tabulation of atomic reference Gaithersburg, MD, USA data. He has worked at the National Institute of Standards and [email protected] Technology for more than 40 years and has led the Atomic Physics Division from 1978 to 2004. He has authored 6 data volumes on Atomic Transition Probabilities, 15 book chapters and about 225 shorter research papers.

Martin Wilkens Chapter F.77

Universität Potsdam Dr. Martin Wilkens received a Ph.D. In Physics from Essen University. Institut für Physik He spent his post-doctoral years in Warsaw, Tucson, and Konstanz and Potsdam, Germany has been appointed Professor for Theoretical Physics / Quantum Optics [email protected] at Potsdam University in 1997. His current research areas are Bose-Einstein condensation, degenerate quantum gases, and quantum information processing and communication. 1425

Detailed Contents

List of Tables ...... XLVII List of Abbreviations ...... LV

1 Units and Constants William E. Baylis, Gordon W. F. Drake ...... 1 1.1 Electromagnetic Units ...... 1 1.2 Atomic Units ...... 5

1.3 Mathematical Constants ...... 5 Cont. Detailed 1.3.1 Series Summation Formula ...... 5 References ...... 6

Part A Mathematical Methods

2 Angular Momentum Theory James D. Louck ...... 9 2.1 Orbital Angular Momentum ...... 12 2.1.1 Cartesian Representation ...... 12 2.1.2 Spherical Polar Coordinate Representation ...... 15 2.2 Abstract Angular Momentum ...... 16 2.3 Representation Functions ...... 18 2.3.1 Parametrizations of the Groups SU(2) and SO(3,R) ...... 18 2.3.2 Explicit Forms of Representation Functions ...... 19 2.3.3 Relations to Special Functions ...... 21 2.3.4 Orthogonality Properties ...... 21 2.3.5 Recurrence Relations ...... 22 2.3.6 Symmetry Relations ...... 23 2.4 Group and Lie Algebra Actions ...... 25 2.4.1 Matrix Group Actions ...... 25 2.4.2 Lie Algebra Actions ...... 26 2.4.3 Hilbert Spaces ...... 26 2.4.4 Relation to Angular Momentum Theory ...... 26 2.5 Differential Operator Realizations of Angular Momentum ...... 28 2.6 The Symmetric Rotor and Representation Functions ...... 29 2.7 Wigner–Clebsch–Gordan and 3-j Coefficients ...... 31 2.7.1 Kronecker Product Reduction ...... 32 2.7.2 Tensor Product Space Construction ...... 33 2.7.3 Explicit Forms of WCG-Coefficients ...... 33 2.7.4 Symmetries of WCG-Coefficients in 3-j Symbol Form ...... 35 2.7.5 Recurrence Relations ...... 36 2.7.6 Limiting Properties and Asymptotic Forms ...... 36 2.7.7 WCG-Coefficients as Discretized Representation Functions ... 37 1426 Detailed Contents

2.8 Tensor Operator Algebra ...... 37 2.8.1 Conceptual Framework ...... 37 2.8.2 Universal Enveloping Algebra of J ...... 38 2.8.3 Algebra of Irreducible Tensor Operators ...... 39 2.8.4 Wigner–Eckart Theorem ...... 39 2.8.5 Unit Tensor Operators or Wigner Operators ...... 40 2.9 Racah Coefficients ...... 43 2.9.1 Basic Relations Between WCG and Racah Coefficients ...... 43 2.9.2 Orthogonality and Explicit Form ...... 43 2.9.3 The Fundamental Identities Between Racah Coefficients ..... 44 2.9.4 Schwinger–Bargmann Generating Function and its Combinatorics ...... 44 ealdCont. Detailed 2.9.5 Symmetries of 6–j Coefficients ...... 45 2.9.6 Further Properties ...... 46 2.10 The 9–j Coefficients ...... 47 2.10.1 Hilbert Space and Tensor Operator Actions ...... 47 2.10.2 9–j Invariant Operators ...... 47 2.10.3 Basic Relations Between 9–j Coefficients and 6–j Coefficients ...... 48 2.10.4 Symmetry Relations for 9–j Coefficients and Reduction to 6–j Coefficients ...... 49 2.10.5 Explicit Algebraic Form of 9–j Coefficients ...... 49 2.10.6 Racah Operators ...... 49 2.10.7 Schwinger–Wu Generating Function and its Combinatorics . 51 2.11 Tensor Spherical Harmonics ...... 52 2.11.1 Spinor Spherical Harmonics as Matrix Functions ...... 53 2.11.2 Vector Spherical Harmonics as Matrix Functions ...... 53 2.11.3 Vector Solid Harmonics as Vector Functions ...... 53 2.12 Coupling and Recoupling Theory and 3n–j Coefficients ...... 54 2.12.1 Composite Angular Momentum Systems ...... 54 2.12.2 Binary Coupling Theory: Combinatorics ...... 56 2.12.3 Implementation of Binary Couplings ...... 57 2.12.4 Construction of all Transformation Coefficients in Binary Coupling Theory ...... 58 2.12.5 Unsolved Problems in Recoupling Theory ...... 59 2.13 Supplement on Combinatorial Foundations ...... 60 2.13.1 SU(2) Solid Harmonics ...... 60 2.13.2 Combinatorial Definition of Wigner–Clebsch–Gordan Coefficients ...... 61 2.13.3 Magic Square Realization of the Addition of Two Angular Momenta ...... 63 2.13.4 MacMahon’s and Schwinger’s Master Theorems ...... 64 2.13.5 The Pfaffian and Double Pfaffian ...... 65 2.13.6 Generating Functions for Coupled Wave Functions and Recoupling Coefficients ...... 66 2.14 Tables ...... 69 References ...... 72 Detailed Contents 1427

3 Group Theory for Atomic Shells Brian R. Judd ...... 75 3.1 Generators ...... 75 3.1.1 Group Elements ...... 75 3.1.2 Conditions on the Structure Constants ...... 76 3.1.3 Cartan–Weyl Form ...... 76 3.1.4 Atomic Operators as Generators ...... 76 3.2 Classification of Lie Algebras ...... 76 3.2.1 Introduction ...... 76 3.2.2 The Semisimple Lie Algebras ...... 76 3.3 Irreducible Representations ...... 77 3.3.1 Labels ...... 77 ealdCont. Detailed 3.3.2 Dimensions ...... 77 3.3.3 Casimir’s Operator ...... 77 3.4 Branching Rules ...... 78 3.4.1 Introduction ...... 78 3.4.2 U(n) ⊃ SU(n) ...... 78 3.4.3 Canonical Reductions ...... 79 3.4.4 Other Reductions ...... 79 3.5 Kronecker Products ...... 79 3.5.1 Outer Products of Tableaux ...... 79 3.5.2 Other Outer Products ...... 80 3.5.3 Plethysms ...... 80 3.6 Atomic States ...... 80 3.6.1 Shell Structure ...... 80 3.6.2 Automorphisms of SO(8) ...... 81 3.6.3 Hydrogen and Hydrogen-Like Atoms ...... 81 3.7 The Generalized Wigner–Eckart Theorem ...... 82 3.7.1 Operators ...... 82 3.7.2 The Theorem ...... 82 3.7.3 Calculation of the Isoscalar Factors ...... 82 3.7.4 Generalizations of Angular Momentum Theory ...... 83 3.8 Checks ...... 83 References ...... 84

4 Dynamical Groups Josef Paldus ...... 87 4.1 Noncompact Dynamical Groups ...... 87 4.1.1 Realizations of so(2,1) ...... 88 4.1.2 Hydrogenic Realization of so(4,2) ...... 88 4.2 Hamiltonian Transformation and Simple Applications ...... 90 4.2.1 N-Dimensional Isotropic Harmonic Oscillator ...... 90 4.2.2 N-Dimensional Hydrogenic Atom ...... 91 4.2.3 Perturbed Hydrogenic Systems ...... 91 4.3 Compact Dynamical Groups ...... 92 4.3.1 Unitary Group and Its Representations ...... 92 4.3.2 Orthogonal Group O(n) and Its Representations ...... 93 1428 Detailed Contents

4.3.3 Clifford Algebras and Spinor Representations ...... 94 4.3.4 Bosonic and Fermionic Realizations of U(n) ...... 94 4.3.5 Vibron Model ...... 95 4.3.6 Many-Electron Correlation Problem ...... 96 4.3.7 Clifford Algebra Unitary Group Approach ...... 97 4.3.8 Spin-Dependent Operators ...... 97 References ...... 98

5 Perturbation Theory Josef Paldus ...... 101 5.1 Matrix Perturbation Theory (PT) ...... 101 5.1.1 Basic Concepts ...... 101 ealdCont. Detailed 5.1.2 Level-Shift Operators ...... 102 5.1.3 General Formalism ...... 102 5.1.4 Nondegenerate Case ...... 103 5.2 Time-Independent Perturbation Theory ...... 103 5.2.1 General Formulation ...... 103 5.2.2 Brillouin–Wigner and Rayleigh–Schrödinger PT (RSPT) ...... 104 5.2.3 Bracketing Theorem and RSPT ...... 104 5.3 Fermionic Many-Body Perturbation Theory (MBPT) ...... 105 5.3.1 Time Independent Wick’s Theorem ...... 105 5.3.2 Normal Product Form of PT ...... 105 5.3.3 Møller–Plesset and Epstein–Nesbet PT ...... 106 5.3.4 Diagrammatic MBPT ...... 107 5.3.5 Vacuum and Wave Function Diagrams ...... 107 5.3.6 Hartree–Fock Diagrams ...... 108 5.3.7 Linked and Connected Cluster Theorems ...... 108 5.3.8 Coupled Cluster Theory ...... 109 5.4 Time-Dependent Perturbation Theory ...... 111 5.4.1 Evolution Operator PT Expansion ...... 111 5.4.2 Gell–Mann and Low Formula ...... 111 5.4.3 Potential Scattering and Quantum Dynamics ...... 111 5.4.4 Born Series ...... 112 5.4.5 Variation of Constants Method ...... 112 References ...... 113

6 Second Quantization Brian R. Judd ...... 115 6.1 Basic Properties ...... 115 6.1.1 Definitions ...... 115 6.1.2 Representation of States ...... 115 6.1.3 Representation of Operators ...... 116 6.2 Tensors ...... 116 6.2.1 Construction ...... 116 6.2.2 Coupled Forms ...... 116 6.2.3 Coefficients of Fractional Parentage ...... 117 Detailed Contents 1429

6.3 Quasispin ...... 117 6.3.1 Fermions ...... 117 6.3.2 Bosons ...... 118 6.3.3 Triple Tensors ...... 118 6.3.4 Conjugation ...... 118 6.3.5 Dependence on Electron Number ...... 119 6.3.6 The Half-filled Shell ...... 119 6.4 Complementarity ...... 119 6.4.1 Spin–Quasispin Interchange ...... 119 6.4.2 Matrix Elements ...... 119 6.5 Quasiparticles ...... 120 References ...... 121 ealdCont. Detailed

7 Density Matrices Klaus Bartschat ...... 123 7.1 Basic Formulae ...... 123 7.1.1 Pure States ...... 123 7.1.2 Mixed States ...... 124 7.1.3 Expectation Values ...... 124 7.1.4 The Liouville Equation ...... 124 7.1.5 Systems in Thermal Equilibrium ...... 125 7.1.6 Relaxation Processes ...... 125 7.2 Spin and Light Polarizations ...... 125 7.2.1 Spin-Polarized Electrons ...... 125 7.2.2 Light Polarization ...... 125 7.3 Atomic Collisions ...... 126 7.3.1 Scattering Amplitudes ...... 126 7.3.2 Reduced Density Matrices ...... 126 7.4 Irreducible Tensor Operators ...... 127 7.4.1 Definition ...... 127 7.4.2 Transformation Properties ...... 127 7.4.3 Symmetry Properties of State Multipoles ...... 128 7.4.4 Orientation and Alignment ...... 128 7.4.5 Coupled Systems ...... 129 7.5 Time Evolution of State Multipoles ...... 129 7.5.1 Perturbation Coefficients ...... 129 7.5.2 Quantum Beats ...... 129 7.5.3 Time Integration over Quantum Beats ...... 130 7.6 Examples ...... 130 7.6.1 Generalized STU-parameters ...... 130 7.6.2 Radiation from Excited States: Stokes Parameters ...... 131 7.7 Summary ...... 133 References ...... 133

8 Computational Techniques David R. Schultz, Michael R. Strayer ...... 135 8.1 Representation of Functions ...... 135 1430 Detailed Contents

8.1.1 Interpolation ...... 135 8.1.2 Fitting ...... 137 8.1.3 Fourier Analysis ...... 139 8.1.4 Approximating Integrals ...... 139 8.1.5 Approximating Derivatives ...... 140 8.2 Differential and Integral Equations ...... 141 8.2.1 Ordinary Differential Equations ...... 141 8.2.2 Differencing Algorithms for Partial Differential Equations .... 143 8.2.3 Variational Methods ...... 144 8.2.4 Finite Elements ...... 144 8.2.5 Integral Equations ...... 146 8.3 Computational Linear Algebra ...... 148 ealdCont. Detailed 8.4 Monte Carlo Methods ...... 149 8.4.1 Random Numbers ...... 149 8.4.2 Distributions of Random Numbers ...... 150 8.4.3 Monte Carlo Integration ...... 151 References ...... 151

9 Hydrogenic Wave Functions Robert N. Hill ...... 153 9.1 Schrödinger Equation ...... 153 9.1.1 Spherical Coordinates ...... 153 9.1.2 Parabolic Coordinates ...... 154 9.1.3 Momentum Space ...... 156 9.2 Dirac Equation ...... 157 9.3 The Coulomb Green’s Function ...... 159 9.3.1 The Green’s Function for the Schrödinger Equation ...... 159 9.3.2 The Green’s Function for the Dirac Equation ...... 161 9.4 Special Functions ...... 162 9.4.1 Confluent Hypergeometric Functions ...... 162 9.4.2 Laguerre Polynomials ...... 166 9.4.3 Gegenbauer Polynomials ...... 169 9.4.4 Legendre Functions ...... 169 References ...... 170

Part B Atoms

10 Atomic Spectroscopy William C. Martin, Wolfgang L. Wiese ...... 175 10.1 Frequency, Wavenumber, Wavelength ...... 176 10.2 Atomic States, Shells, and Configurations ...... 176 10.3 Hydrogen and Hydrogen-Like Ions ...... 176 10.4 Alkalis and Alkali-Like Spectra ...... 177 10.5 Helium and Helium-Like Ions; LS Coupling ...... 177 10.6 Hierarchy of Atomic Structure in LS Coupling ...... 177 10.7 Allowed Terms or Levels for Equivalent Electrons ...... 178 Detailed Contents 1431

10.7.1 LS Coupling ...... 178 10.7.2 jj Coupling ...... 178 10.8 Notations for Different Coupling Schemes ...... 179 10.8.1 LS Coupling (Russell–Saunders Coupling) ...... 179 10.8.2 jj Coupling of Equivalent Electrons ...... 180 10.8.3 J1j or J1J2 Coupling ...... 180 10.8.4 J1l or J1L2 Coupling (J1K Coupling) ...... 180 10.8.5 LS1 Coupling (LK Coupling) ...... 181 10.8.6 Coupling Schemes and Term Symbols ...... 181 10.9 Eigenvector Composition of Levels ...... 181 10.10 Ground Levels and Ionization Energies for the Neutral Atoms ...... 182 10.11 Zeeman Effect ...... 183 ealdCont. Detailed 10.12 Term Series, Quantum Defects, and Spectral-Line Series ...... 184 10.13 Sequences ...... 185 10.13.1 Isoelectronic Sequence ...... 185 10.13.2 Isoionic, Isonuclear, and Homologous Sequences ...... 185 10.14 Spectral Wavelength Ranges, Dispersion of Air ...... 185 10.15 Wavelength (Frequency) Standards ...... 186 10.16 Spectral Lines: Selection Rules, Intensities, Transition Probabilities, f Values, and Line Strengths ...... 186 10.16.1 Emission Intensities (Transition Probabilities) ...... 186 10.16.2 Absorption f Values ...... 186 10.16.3 Line Strengths ...... 186 10.16.4 Relationships Between A, f,andS ...... 187 10.16.5 Relationships Between Line and Multiplet Values ...... 192 10.16.6 Relative Strengths for Lines of Multiplets in LS Coupling ... 193 10.17 Atomic Lifetimes ...... 194 10.18 Regularities and Scaling ...... 194 10.18.1 Transitions in Hydrogenic (One-Electron) Species ...... 194 10.18.2 Systematic Trends and Regularities in Atoms and Ions with Two or More Electrons ...... 194 10.19 Spectral Line Shapes, Widths, and Shifts ...... 195 10.19.1 Doppler Broadening ...... 195 10.19.2 Pressure Broadening ...... 195 10.20 Spectral Continuum Radiation ...... 196 10.20.1 Hydrogenic Species ...... 196 10.20.2 Many-Electron Systems ...... 196 10.21 Sources of Spectroscopic Data ...... 197 References ...... 197

11 High Precision Calculations for Helium Gordon W. F. Drake...... 199 11.1 The Three-Body Schrödinger Equation ...... 199 11.1.1 Formal Mathematical Properties ...... 200 11.2 Computational Methods ...... 200 11.2.1 Variational Methods ...... 200 11.2.2 Construction of Basis Sets ...... 201 1432 Detailed Contents

11.2.3 Calculation of Matrix Elements ...... 202 11.2.4 Other Computational Methods ...... 205 11.3 Variational Eigenvalues ...... 205 11.3.1 Expectation Values of Operators and Sum Rules ...... 205 11.4 Total Energies ...... 208 11.4.1 Quantum Defect Extrapolations ...... 211 11.4.2 Asymptotic Expansions ...... 213 11.5 Radiative Transitions ...... 215 11.5.1 Basic Formulation ...... 215 11.5.2 Oscillator Strength Table ...... 216 11.6 Future Perspectives ...... 218 References ...... 218 ealdCont. Detailed

12 Atomic Multipoles William E. Baylis ...... 221 12.1 Polarization and Multipoles ...... 222 12.2 The Density Matrix in Liouville Space ...... 222 12.3 Diagonal Representation: State Populations ...... 224 12.4 Interaction with Light ...... 224 12.5 Extensions ...... 225 References ...... 226

13 Atoms in Strong Fields S. Pedro Goldman, Mark M. Cassar ...... 227 13.1 Electron in a Uniform Magnetic Field ...... 227 13.1.1 Nonrelativistic Theory ...... 227 13.1.2 Relativistic Theory ...... 228 13.2 Atoms in Uniform Magnetic Fields ...... 228 13.2.1 Anomalous Zeeman Effect ...... 228 13.2.2 Normal Zeeman Effect ...... 229 13.2.3 Paschen–Back Effect ...... 229 13.3 Atoms in Very Strong Magnetic Fields ...... 230 13.4 Atoms in Electric Fields ...... 231 13.4.1 Stark Ionization ...... 231 13.4.2 Linear Stark Effect ...... 231 13.4.3 Quadratic Stark Effect ...... 232 13.4.4 Other Stark Corrections ...... 232 13.5 Recent Developments ...... 233 References ...... 234

14 Rydberg Atoms Thomas F. Gallagher ...... 235 14.1 Wave Functions and Quantum Defect Theory ...... 235 14.2 Optical Excitation and Radiative Lifetimes ...... 237 14.3 Electric Fields ...... 238 14.4 Magnetic Fields ...... 241 14.5 Microwave Fields ...... 242 Detailed Contents 1433

14.6 Collisions ...... 243 14.7 Autoionizing Rydberg States ...... 244 References ...... 245

15 Rydberg Atoms in Strong Static Fields Thomas Bartsch, Turgay Uzer ...... 247 15.1 Scaled-Energy Spectroscopy ...... 248 15.2 Closed-Orbit Theory ...... 248 15.3 Classical and Quantum Chaos ...... 249 15.3.1 Magnetic Field ...... 249 15.3.2 Parallel Electric and Magnetic Fields ...... 250 15.3.3 Crossed Electric and Magnetic Fields ...... 250 ealdCont. Detailed 15.4 Nuclear-Mass Effects ...... 251 References ...... 251

16 Hyperfine Structure Guy T. Emery ...... 253 16.1 Splittings and Intensities ...... 254 16.1.1 Angular Momentum Coupling ...... 254 16.1.2 Energy Splittings ...... 254 16.1.3 Intensities ...... 255 16.2 Isotope Shifts ...... 256 16.2.1 Normal Mass Shift ...... 256 16.2.2 Specific Mass Shift ...... 256 16.2.3 Field Shift ...... 256 16.2.4 Separation of Mass Shift and Field Shift ...... 257 16.3 Hyperfine Structure ...... 258 16.3.1 Electric Multipoles ...... 258 16.3.2 Magnetic Multipoles ...... 258 16.3.3 Hyperfine Anomalies ...... 259 References ...... 259

17 Precision Oscillator Strength and Lifetime Measurements Lorenzo J. Curtis ...... 261 17.1 Oscillator Strengths ...... 262 17.1.1 Absorption and Dispersion Measurements ...... 262 17.1.2 Emission Measurements ...... 263 17.1.3 Combined Absorption, Emission and Lifetime Measurements ...... 263 17.1.4 Branching Ratios in Highly Ionized Atoms ...... 264 17.2 Lifetimes ...... 264 17.2.1 The Hanle Effect ...... 265 17.2.2 Time-Resolved Decay Measurements ...... 265 17.2.3 Other Methods ...... 267 17.2.4 Multiplexed Detection ...... 267 References ...... 268 1434 Detailed Contents

18 Spectroscopy of Ions Using Fast Beams and Ion Traps Eric H. Pinnington, Elmar Träbert ...... 269 18.1 Spectroscopy Using Fast Ion Beams ...... 269 18.1.1 Beam–Foil Spectroscopy ...... 269 18.1.2 Beam-Gas Spectroscopy ...... 270 18.1.3 Beam-Laser Spectroscopy ...... 271 18.1.4 Other Techniques of Ion-Beam Spectroscopy ...... 272 18.2 Spectroscopy Using Ion Traps ...... 272 18.2.1 Electron Beam Ion Traps ...... 273 18.2.2 Heavy-Ion Storage Rings ...... 275 References ...... 277 ealdCont. Detailed 19 Line Shapes and Radiation Transfer Alan Gallagher...... 279 19.1 Collisional Line Shapes ...... 279 19.1.1 Voigt Line Shape ...... 279 19.1.2 Interaction Potentials ...... 280 19.1.3 Classical Oscillator Approximation ...... 280 19.1.4 Impact Approximation ...... 281 19.1.5 Examples: Line Core ...... 282 19.1.6 ∆ and γc Characteristics ...... 284 19.1.7 Quasistatic Approximation ...... 284 19.1.8 Satellites ...... 285 19.1.9 Bound States and Other Quantum Effects ...... 286 19.1.10 Einstein A and B Coefficients ...... 286 19.2 Radiation Trapping ...... 287 19.2.1 Holstein–Biberman Theory ...... 287 19.2.2 Additional Factors ...... 289 19.2.3 Measurements ...... 290 References ...... 292

20 Thomas–Fermi and Other Density-Functional Theories John D. Morgan III...... 295 20.1 Thomas–Fermi Theoryand Its Extensions ...... 296 20.1.1 Thomas–Fermi Theory ...... 296 20.1.2 Thomas–Fermi–von Weizsäcker Theory ...... 298 20.1.3 Thomas–Fermi–Dirac Theory ...... 299 20.1.4 Thomas–Fermi–von Weizsäcker–Dirac Theory ...... 299 20.1.5 Thomas–Fermi Theory with Different Spin Densities ...... 300 20.2 Nonrelativistic Energies of Heavy Atoms ...... 300 20.3 General Density Functional Theory ...... 301 20.3.1 The Hohenberg–Kohn Theorem for the One-Electron Density ...... 301 20.3.2 The Kohn–Sham Method for Including Exchange and Correlation Corrections ...... 302 20.3.3 Density Functional Theory for Excited States ...... 303 Detailed Contents 1435

20.3.4 Relativistic and Quantum Field Theoretic Density Functional Theory ...... 303 20.4 Recent Developments ...... 303 References ...... 304

21 Atomic Structure: Multiconfiguration Hartree–Fock Theories Charlotte F. Fischer ...... 307 21.1 Hamiltonians: Schrödinger and Breit–Pauli ...... 307 21.2 Wave Functions: LS and LSJ Coupling ...... 308 21.3 Variational Principle ...... 309 21.4 Hartree–Fock Theory ...... 309 21.4.1 Diagonal Energy Parameters and Koopmans’ Theorem 311

...... Cont. Detailed 21.4.2 The Fixed-Core Hartree–Fock Approximation ...... 311 21.4.3 Brillouin’s Theorem ...... 311 21.4.4 Properties of Hartree–Fock Functions ...... 312 21.5 Multiconfiguration Hartree–Fock Theory ...... 313 21.5.1 Z-Dependent Theory ...... 313 21.5.2 The MCHF Approximation ...... 314 21.5.3 Systematic Methods ...... 315 21.5.4 Excited States ...... 316 21.5.5 Autoionizing States ...... 316 21.6 Configuration Interaction Methods ...... 316 21.7 Atomic Properties ...... 318 21.7.1 Isotope Effects ...... 318 21.7.2 Hyperfine Effects ...... 319 21.7.3 Metastable States and Lifetimes ...... 320 21.7.4 Transition Probabilities ...... 321 21.7.5 Electron Affinities ...... 321 21.8 Summary ...... 322 References ...... 322

22 Relativistic Atomic Structure Ian P. Grant ...... 325 22.1 Mathematical Preliminaries ...... 326 22.1.1 Relativistic Notation: Minkowski Space-Time ...... 326 22.1.2 Lorentz Transformations ...... 326 22.1.3 Classification of Lorentz Transformations ...... 326 22.1.4 Contravariant and Covariant Vectors ...... 327 22.1.5 Poincaré Transformations ...... 327 22.2 Dirac’s Equation ...... 328 22.2.1 Characterization of Dirac States ...... 328 22.2.2 The Charge-Current 4-Vector ...... 328 22.3 QED: Relativistic Atomic and Molecular Structure ...... 329 22.3.1 The QED Equations of Motion ...... 329 22.3.2 The Quantized Electron–Positron Field ...... 329 22.3.3 Quantized Electromagnetic Field ...... 330 22.3.4 QED Perturbation Theory ...... 331 1436 Detailed Contents

22.3.5 Propagators ...... 333 22.3.6 Effective Interaction of Electrons ...... 333 22.4 Many-Body Theory For Atoms ...... 334 22.4.1 Effective Hamiltonians ...... 335 22.4.2 Nonrelativistic Limit: Breit–Pauli Hamiltonian ...... 335 22.4.3 Perturbation Theory: Nondegenerate Case ...... 335 22.4.4 Perturbation Theory: Open-Shell Case ...... 336 22.4.5 Perturbation Theory: Algorithms ...... 337 22.5 Spherical Symmetry ...... 337 22.5.1 Eigenstates of Angular Momentum ...... 337 22.5.2 Eigenstates of Dirac Hamiltonian in Spherical Coordinates .. 338 22.5.3 Radial Amplitudes ...... 340 ealdCont. Detailed 22.5.4 Square Integrable Solutions ...... 341 22.5.5 Hydrogenic Solutions ...... 342 22.5.6 The Free Electron Problem in Spherical Coordinates ...... 343 22.6 Numerical Approximation of Central Field Dirac Equations ...... 344 22.6.1 Finite Differences ...... 344 22.6.2 Expansion Methods ...... 345 22.6.3 Catalogue of Basis Sets for Atomic Calculations ...... 347 22.7 Many-Body Calculations ...... 350 22.7.1 Atomic States ...... 350 22.7.2 Slater Determinants ...... 350 22.7.3 Configurational States ...... 350 22.7.4 CSF Expansion ...... 350 22.7.5 Matrix Element Construction ...... 350 22.7.6 Dirac–Hartree–Fock and Other Theories ...... 351 22.7.7 Radiative Corrections ...... 353 22.7.8 Radiative Processes ...... 353 22.8 Recent Developments ...... 354 22.8.1 Technical Advances ...... 354 22.8.2 Software for Relativistic Atomic Structure and Properties ... 354 References ...... 355

23 Many-Body Theory of Atomic Structure and Processes Miron Ya. Amusia...... 359 23.1 Diagrammatic Technique ...... 360 23.1.1 Basic Elements ...... 360 23.1.2 Construction Principles for Diagrams ...... 360 23.1.3 Correspondence Rules ...... 362 23.1.4 Higher-Order Corrections and Summation of Sequences .... 363 23.2 Calculation of Atomic Properties ...... 365 23.2.1 Electron Correlations in Ground State Properties ...... 365 23.2.2 Characteristics of One-Particle States ...... 366 23.2.3 Electron Scattering ...... 367 23.2.4 Two-Electron and Two-Vacancy States ...... 369 23.2.5 Electron–Vacancy States ...... 370 Detailed Contents 1437

23.2.6 Photoionization in RPAE and Beyond ...... 371 23.2.7 Photon Emission and Bremsstrahlung ...... 374 23.3 Concluding Remarks ...... 375 References ...... 376

24 Photoionization of Atoms Anthony F. Starace ...... 379 24.1 General Considerations ...... 379 24.1.1 The Interaction Hamiltonian ...... 379 24.1.2 Alternative Forms for the Transition Matrix Element ...... 380 24.1.3 Selection Rules for Electric Dipole Transitions ...... 381 24.1.4 Boundary Conditions on the Final State Wave Function ..... 381 ealdCont. Detailed 24.1.5 Photoionization Cross Sections ...... 382 24.2 An Independent Electron Model ...... 382 24.2.1 Central Potential Model ...... 382 24.2.2 High Energy Behavior ...... 383 24.2.3 Near Threshold Behavior ...... 383 24.3 Particle–Hole Interaction Effects ...... 384 24.3.1 Intrachannel Interactions ...... 384 24.3.2 Virtual Double Excitations ...... 384 24.3.3 Interchannel Interactions ...... 385 24.3.4 Photoionization of Ar ...... 385 24.4 Theoretical Methods for Photoionization ...... 386 24.4.1 Calculational Methods ...... 386 24.4.2 Other Interaction Effects ...... 387 24.5 Recent Developments ...... 387 24.6 Future Directions ...... 388 References ...... 388

25 Autoionization Aaron Temkin, Anand K. Bhatia ...... 391 25.1 Introduction ...... 391 25.1.1 Auger Effect ...... 391 25.1.2 Autoionization, Autodetachment, and Radiative Decay ..... 391 25.1.3 Formation, Scattering, and Resonances ...... 391 25.2 The Projection Operator Formalism ...... 392 25.2.1 The Optical Potential ...... 392 25.2.2 Expansion of Vop:TheQHQ Problem ...... 392 25.3 Forms of P and Q ...... 393 25.3.1 The Feshbach Form ...... 393 25.3.2 Reduction for the N=1Target...... 394 25.3.3 Alternative Projection and Projection-Like Operators ...... 394 25.4 Width, Shift, and Shape Parameter ...... 394 25.4.1 Width and Shift ...... 394 25.4.2 Shape Parameter ...... 395 25.4.3 Relation to Breit–Wigner Parameters ...... 396 1438 Detailed Contents

25.5 Other Calculational Methods ...... 396 25.5.1 Complex Rotation Method ...... 396 25.5.2 Pseudopotential Method ...... 397 25.6 Related Topics ...... 398 References ...... 399

26 Green’s Functions of Field Theory Gordon Feldman, Thomas Fulton ...... 401 26.1 The Two-Point Green’s Function ...... 402 26.2 The Four-Point Green’s Function ...... 405 26.3 Radiative Transitions ...... 406 26.4 Radiative Corrections ...... 408 ealdCont. Detailed References ...... 411

27 Quantum Electrodynamics Jonathan R. Sapirstein ...... 413 27.1 Covariant Perturbation Theory ...... 413 27.2 Renormalization Theory and Gauge Choices ...... 414 27.3 Tests of QED in Lepton Scattering ...... 416 27.4 Electron and Muon g Factors ...... 416 27.5 Recoil Corrections ...... 418 27.6 Fine Structure ...... 420 27.7 Hyperfine Structure ...... 421 27.7.1 Muonium Hyperfine Splitting ...... 421 27.7.2 Hydrogen Hyperfine Splitting ...... 422 27.8 Orthopositronium Decay Rate ...... 422 27.9 Precision Tests of QED in Neutral Helium ...... 423 27.10 QED in Highly Charged One-Electron Ions ...... 424 27.11 QED in Highly Charged Many-Electron Ions ...... 425 References ...... 427

28 Tests of Fundamental Physics Peter J. Mohr, Barry N. Taylor ...... 429 28.1 Electron g-Factor Anomaly ...... 429 28.2 Electron g-Factor in 12C5+ and 16O7+ ...... 432 28.3 Hydrogen and Deuterium Atoms ...... 437 28.3.1 Dirac Eigenvalue ...... 437 28.3.2 Relativistic Recoil ...... 438 28.3.3 Nuclear Polarization ...... 439 28.3.4 Self Energy ...... 439 28.3.5 Vacuum Polarization ...... 440 28.3.6 Two-Photon Corrections ...... 441 28.3.7 Three-Photon Corrections ...... 442 28.3.8 Finite Nuclear Size ...... 443 28.3.9 Nuclear-Size Correction to Self Energy and Vacuum Polarization ...... 443 Detailed Contents 1439

28.3.10 Radiative-Recoil Corrections ...... 444 28.3.11 Nucleus Self Energy ...... 444 28.3.12 Total Energy and Uncertainty ...... 444 28.3.13 Transition Frequencies Between Levels with n = 2 ...... 445 References ...... 445

29 Parity Nonconserving Effects in Atoms Jonathan R. Sapirstein ...... 449 29.1 The Standard Model ...... 450 29.2 PNC in Cesium ...... 451 29.3 Many-Body Perturbation Theory ...... 451

29.4 PNC Calculations ...... 452 Cont. Detailed 29.5 Recent Developments ...... 453 29.6 Comparison with Experiment ...... 453 References ...... 454

30 Atomic Clocks and Constraints on Variations of Fundamental Constants Savely G. Karshenboim, Victor Flambaum, Ekkehard Peik ...... 455 30.1 Atomic Clocks and Frequency Standards ...... 456 30.1.1 Caesium Atomic Fountain ...... 456 30.1.2 Single-Ion Trap ...... 457 30.1.3 Laser-Cooled Neutral Atoms ...... 457 30.1.4 Two-Photon Transitionsand Doppler-Free Spectroscopy .... 458 30.1.5 Optical Frequency Measurements ...... 458 30.1.6 Limitations on Frequency Variations ...... 458 30.2 Atomic Spectra and their Dependence on the Fundamental Constants ...... 459 30.2.1 The Spectrum of Hydrogenand Nonrelativistic Atoms ...... 459 30.2.2 Hyperfine Structureand the Schmidt Model ...... 459 30.2.3 Atomic Spectra: Relativistic Corrections ...... 460 30.3 Laboratory Constraints on Time the Variations of the Fundamental Constants ...... 460 30.3.1 Constraints from Absolute Optical Measurements ...... 460 30.3.2 Constraints from Microwave Clocks ...... 461 30.3.3 Model-Dependent Constraints ...... 461 30.4 Summary ...... 462 References ...... 462

Part C Molecules

31 Molecular Structure David R. Yarkony ...... 467 31.1 Concepts ...... 468 31.1.1 Nonadiabatic Ansatz: Born–Oppenheimer Approximation .. 468 1440 Detailed Contents

31.1.2 Born–Oppenheimer Potential Energy Surfaces and Their Topology ...... 469 31.1.3 Classification of Interstate Couplings: Adiabatic and Diabatic Bases ...... 469 31.1.4 Surfaces of Intersection of Potential Energy Surfaces ...... 470 31.2 Characterization of Potential Energy Surfaces ...... 470 31.2.1 The Self-Consistent Field (SCF) Method ...... 471 31.2.2 Electron Correlation: Wave Function Based Methods ...... 472 31.2.3 Electron Correlation: Density Functional Theory ...... 475 31.2.4 Weakly Interacting Systems ...... 476 31.3 Intersurface Interactions: Perturbations ...... 476 31.3.1 Derivative Couplings ...... 476 ealdCont. Detailed 31.3.2 Breit–Pauli Interactions ...... 477 31.3.3 Surfaces of Intersection ...... 479 31.4 Nuclear Motion ...... 480 31.4.1 General Considerations ...... 480 31.4.2 Rotational-Vibrational Structure ...... 481 31.4.3 Coupling of Electronic and Rotational Angular Momentum in Weakly Interacting ...... 482 31.4.4 Reaction Path ...... 483 31.5 Reaction Mechanisms: A Spin-Forbidden Chemical Reaction ...... 484 31.6 Recent Developments ...... 486 References ...... 486

32 Molecular Symmetry and Dynamics William G. Harter ...... 491 32.1 Dynamics and Spectra of Molecular Rotors ...... 491 32.1.1 Rigid Rotors ...... 492 32.1.2 Molecular States Inside and Out ...... 492 32.1.3 Rigid Asymmetric Rotor Eigensolutions and Dynamics ...... 493 32.2 Rotational Energy Surfaces and Semiclassical Rotational Dynamics ...... 494 32.3 Symmetry of Molecular Rotors ...... 498 32.3.1 Asymmetric Rotor Symmetry Analysis ...... 498 32.4 Tetrahedral-Octahedral Rotational Dynamics and Spectra ...... 499 32.4.1 Semirigid Octahedral Rotors and Centrifugal Tensor Hamiltonians ...... 499 32.4.2 Octahedral and Tetrahedral Rotational Energy Surfaces ..... 500 32.4.3 Octahedral and Tetrahedral Rotational Fine Structure ...... 500 32.4.4 Octahedral Superfine Structure ...... 502 32.5 High Resolution Rovibrational Structure ...... 503 32.5.1 Tetrahedral Nuclear Hyperfine Structure ...... 505 32.5.2 Superhyperfine Structure and Spontaneous Symmetry Breaking ...... 505 32.5.3 Extreme Molecular Symmetry Effects ...... 506 32.6 Composite Rotors and Multiple RES ...... 507 32.6.1 3D-Rotor and 2D-Oscillator Analogy ...... 509 Detailed Contents 1441

32.6.2 Gyro-Rotors and 2D-Local Mode Analogy ...... 510 32.6.3 Multiple Gyro-Rotor RES and Eigensurfaces ...... 511 References ...... 512

33 Radiative Transition Probabilities David L. Huestis...... 515 33.1 Overview ...... 515 33.1.1 Intensity versus Line-Position Spectroscopy ...... 515 33.2 Molecular Wave Functions in the Rotating Frame ...... 516 33.2.1 Symmetries of the Exact Wave Function ...... 516 33.2.2 Rotation Matrices ...... 517 33.2.3 Transformation of Ordinary Objects into the Rotating Frame 517 ealdCont. Detailed 33.3 The Energy–Intensity Model ...... 518 33.3.1 States, Levels, and Components ...... 518 33.3.2 The Basis Set and Matrix Hamiltonian ...... 518 33.3.3 Fitting Experimental Energies ...... 520 33.3.4 The Transition Moment Matrix ...... 520 33.3.5 Fitting Experimental Intensities ...... 520 33.4 Selection Rules ...... 521 33.4.1 Symmetry Types ...... 521 33.4.2 Rotational Branches and Parity ...... 521 33.4.3 Nuclear Spin, Spatial Symmetry, and Statistics ...... 522 33.4.4 Electron Orbital and Spin Angular Momenta ...... 523 33.5 Absorption Cross Sections and Radiative Lifetimes ...... 524 33.5.1 Radiation Relations ...... 524 33.5.2 Transition Moments ...... 524 33.6 Vibrational Band Strengths ...... 525 33.6.1 Franck–Condon Factors ...... 525 33.6.2 Vibrational Transitions ...... 526 33.7 Rotational Branch Strengths ...... 526 33.7.1 Branch Structure and Transition Type ...... 526 33.7.2 Hönl–London Factors ...... 527 33.7.3 Sum Rules ...... 528 33.7.4 Hund’s Cases ...... 528 33.7.5 Symmetric Tops ...... 530 33.7.6 Asymmetric Tops ...... 530 33.8 Forbidden Transitions ...... 530 33.8.1 Spin-Changing Transitions ...... 530 33.8.2 Orbitally-Forbidden Transitions ...... 531 33.9 Recent Developments ...... 531 References ...... 532

34 Molecular Photodissociation Abigail J. Dobbyn, David H. Mordaunt, Reinhard Schinke ...... 535 34.1 Observables ...... 537 34.1.1 Scalar Properties ...... 537 34.1.2 Vector Correlations ...... 537 1442 Detailed Contents

34.2 Experimental Techniques ...... 539 34.3 Theoretical Techniques ...... 540 34.4 Concepts in Dissociation ...... 541 34.4.1 Direct Dissociation ...... 541 34.4.2 Vibrational Predissociation ...... 542 34.4.3 Electronic Predissociation ...... 542 34.5 Recent Developments ...... 543 34.6 Summary ...... 544 References ...... 545

35 Time-Resolved Molecular Dynamics Volker Engel 547 ealdCont. Detailed ...... 35.1 Pump–Probe Experiments ...... 548 35.2 Theoretical Description ...... 548 35.3 Applications ...... 550 35.3.1 Internal Vibrational Dynamics of Diatomic Molecules in the Gas Phase ...... 550 35.3.2 Elementary Gas-Phase Chemical Reactions ...... 550 35.3.3 Molecular Dynamics in Liquid and Solid Surroundings ...... 551 35.4 Recent Developments ...... 551 35.4.1 Faster Dynamics ...... 551 35.4.2 X-Ray Pulses ...... 551 35.4.3 Time-Resolved Diffraction ...... 551 35.4.4 Dynamics and Control ...... 552 References ...... 552

36 Nonreactive Scattering David R. Flower ...... 555 36.1 Definitions ...... 555 36.2 Semiclassical Method ...... 556 36.3 Quantal Method ...... 556 36.4 Symmetries and Conservation Laws ...... 557 36.5 Coordinate Systems ...... 557 36.6 Scattering Equations ...... 558 36.7 Matrix Elements ...... 558 36.7.1 Centrifugal Potential ...... 558 36.7.2 Interaction Potential ...... 559 References ...... 560

37 Gas Phase Reactions Eric Herbst ...... 561 37.1 Normal Bimolecular Reactions ...... 563 37.1.1 Capture Theories ...... 563 37.1.2 Phase Space Theories ...... 565 37.1.3 Short-Range Barriers ...... 566 37.1.4 Complexes Followed by Barriers ...... 568 37.1.5 The Role of Tunneling ...... 569 Detailed Contents 1443

37.2 Association Reactions ...... 570 37.2.1 Radiative Stabilization ...... 570 37.2.2 Complex Formation and Dissociation ...... 571 37.2.3 Competition with Exoergic Channels ...... 572 37.3 Concluding Remarks ...... 572 References ...... 573

38 Gas Phase Ionic Reactions Nigel G. Adams ...... 575 38.1 Overview ...... 575 38.2 Reaction Energetics ...... 576 38.3 Chemical Kinetics ...... 578 ealdCont. Detailed 38.4 Reaction Processes ...... 578 38.4.1 Binary Ion–Neutral Reactions ...... 579 38.4.2 Ternary Ion–Molecule Reactions ...... 581 38.5 Electron Attachment ...... 582 38.6 Recombination ...... 583 38.6.1 Electron–Ion Recombination ...... 583 38.6.2 Ion–Ion Recombination (Mutual Neutralization) ...... 584 References ...... 585

39 Clusters Mary L. Mandich ...... 589 39.1 Metal Clusters ...... 590 39.1.1 Geometric Structures ...... 590 39.1.2 Electronic and Magnetic Properties ...... 590 39.1.3 Chemical Properties ...... 592 39.1.4 Stable Metal Cluster Molecules and Metallocarbohedrenes .. 593 39.2 Carbon Clusters ...... 593 39.2.1 Small Carbon Clusters ...... 594 39.2.2 Fullerenes ...... 594 39.2.3 Giant Carbon Clusters: Tubes, Capsules, Onions, Russian Dolls, Papier Mâché...... 595 39.3 Ionic Clusters ...... 596 39.3.1 Geometric Structures ...... 596 39.3.2 Electronic and Chemical Properties ...... 596 39.4 Semiconductor Clusters ...... 597 39.4.1 Silicon and Germanium Clusters ...... 597 39.4.2 Group III–V and Group II–VI Semiconductor Clusters ...... 598 39.5 Noble Gas Clusters ...... 599 39.5.1 Geometric Structures ...... 599 39.5.2 Electronic Properties ...... 600 39.5.3 Doped Noble Gas Clusters ...... 600 39.5.4 Helium Clusters ...... 601 39.6 Molecular Clusters ...... 602 39.6.1 Geometric Structures and Phase Dynamics ...... 602 1444 Detailed Contents

39.6.2 Electronic Properties: Charge Solvation ...... 602 39.7 Recent Developments ...... 603 References ...... 604

40 Infrared Spectroscopy Henry Buijs ...... 607 40.1 Intensities of Infrared Radiation ...... 607 40.2 Sources for IR Absorption Spectroscopy ...... 608 40.3 Source, Spectrometer, Sample and Detector Relationship ...... 608 40.4 Simplified Principle of FTIR Spectroscopy ...... 608 40.4.1 Interferogram Generation:The Michelson Interferometer ... 609 40.4.2 Description of Wavefront Interference with Time Delay ..... 609 ealdCont. Detailed 40.4.3 The Operation of Spectrum Determination ...... 610 40.5 Optical Aspects of FTIR Technology ...... 611 40.6 The Scanning Michelson Interferometer ...... 612 40.7 Recent Developments ...... 613 40.8 Conclusion ...... 613 References ...... 613

41 Laser Spectroscopy in the Submillimeter and Far-Infrared Regions Kenneth M. Evenson†,JohnM.Brown...... 615 41.1 Experimental Techniques using Coherent SM-FIR Radiation ...... 616 41.1.1 Tunable FIR Spectroscopy with CO2 Laser Difference Generation in a MIM Diode ...... 617 41.1.2 Laser Magnetic Resonance ...... 618 41.1.3 TuFIR and LMR Detectors ...... 619 41.2 Submillimeter and FIR Astronomy ...... 620 41.3 Upper Atmospheric Studies ...... 620 References ...... 621

42 Spectroscopic Techniques: Lasers Paul Engelking ...... 623 42.1 Laser Basics ...... 623 42.1.1 Stimulated Emission ...... 623 42.1.2 Laser Configurations ...... 623 42.1.3 Gain ...... 623 42.1.4 Laser Light ...... 624 42.2 Laser Designs ...... 625 42.2.1 Cavities ...... 625 42.2.2 Pumping ...... 626 42.3 Interaction of Laser Light with Matter ...... 628 42.3.1 Linear Absorption ...... 628 42.3.2 Multiphoton Absorption ...... 628 42.3.3 Level Shifts ...... 629 42.3.4 Hole Burning ...... 629 42.3.5 Nonlinear Optics ...... 629 Detailed Contents 1445

42.3.6 Raman Scattering ...... 630 42.4 Recent Developments ...... 630 References ...... 631

43 Spectroscopic Techniques: Cavity-Enhanced Methods Barbara A. Paldus, Alexander A. Kachanov ...... 633 43.1 Limitations of Traditional Absorption Spectrometers ...... 633 43.2 Cavity Ring-Down Spectroscopy ...... 634 43.2.1 Pulsed Cavity Ring-Down Spectroscopy ...... 634 43.2.2 Continuous-Wave Cavity Ring-Down Spectroscopy (CW-CRDS) ...... 635 43.3 Cavity Enhanced Spectroscopy ...... 636 ealdCont. Detailed 43.3.1 Cavity Enhanced Transmission Spectroscopy (CETS) ...... 637 43.3.2 Locked Cavity Enhanced Transmission Spectroscopy (L-CETS) 638 43.4 Extensions to Solids and Liquids ...... 639 References ...... 640

44 Spectroscopic Techniques: Ultraviolet Glenn Stark, Peter L. Smith ...... 641 44.1 Light Sources ...... 642 44.1.1 Synchrotron Radiation ...... 642 44.1.2 Laser-Produced Plasmas ...... 643 44.1.3 Arcs, Sparks, and Discharges ...... 644 44.1.4 Supercontinuum Radiation ...... 644 44.2 VUV Lasers ...... 645 44.3 Spectrometers ...... 647 44.3.1 Grating Spectrometers ...... 647 44.3.2 Fourier Transform Spectrometers ...... 648 44.4 Detectors ...... 648 44.5 Optical Materials ...... 651 References ...... 652

Part D Scattering Theory

45 Elastic Scattering: Classical, Quantal, and Semiclassical M. Raymond Flannery...... 659 45.1 Classical Scattering Formulae ...... 659 45.1.1 Deflection Functions ...... 660 45.1.2 Elastic Scattering Cross Section ...... 661 45.1.3 Center-of-Mass to Laboratory Coordinate Conversion ...... 662 45.1.4 Glory and Rainbow Scattering ...... 662 45.1.5 Orbiting and Spiraling Collisions ...... 662 45.1.6 Quantities Derived from Classical Scattering ...... 663 45.1.7 Collision Action ...... 663 45.2 Quantal Scattering Formulae ...... 664 45.2.1 Basic Formulae ...... 664 1446 Detailed Contents

45.2.2 Identical Particles: Symmetry Oscillations ...... 666 45.2.3 Partial Wave Expansion ...... 667 45.2.4 Scattering Length and Effective Range ...... 668 45.2.5 Logarithmic Derivatives ...... 670 45.2.6 Coulomb Scattering ...... 671 45.2.7 Resonance Scattering ...... 671 45.2.8 Integral Equation for Phase Shift ...... 673 45.2.9 Variable Phase Method ...... 673 45.2.10 General Amplitudes ...... 674 45.3 Semiclassical Scattering Formulae ...... 675 45.3.1 Scattering Amplitude: Exact Poisson Sum Representation ... 675 45.3.2 Semiclassical Procedure ...... 675 ealdCont. Detailed 45.3.3 Semiclassical Amplitudes: Integral Representation ...... 676 45.3.4 Semiclassical Amplitudes and Cross Sections ...... 677 45.3.5 Diffraction and Glory Amplitudes ...... 679 45.3.6 Small-Angle (Diffraction) Scattering ...... 680 45.3.7 Small-Angle (Glory) Scattering ...... 681 45.3.8 Oscillations in Elastic Scattering ...... 683 45.4 Elastic Scattering in Reactive Systems ...... 683 45.4.1 Quantal Elastic, Absorption and Total Cross Sections ...... 683 45.5 Results for Model Potentials ...... 684 45.5.1 Born Amplitudes and Cross Sections for Model Potentials ... 689 References ...... 689

46 Orientation and Alignment in Atomic and Molecular Collisions Nils Andersen ...... 693 46.1 Collisions Involving Unpolarized Beams ...... 694 46.1.1 The Fully Coherent Case ...... 694 46.1.2 The Incoherent Case with Conservation of Atomic Reflection Symmetry ...... 697 46.1.3 The Incoherent Case without Conservation of Atomic Reflection Symmetry ...... 697 46.2 Collisions Involving Spin-Polarized Beams ...... 699 46.2.1 The Fully Coherent Case ...... 699 46.2.2 The Incoherent Case with Conservation of Atomic Reflection Symmetry ...... 699 46.2.3 The Incoherent Case without Conservation of Atomic Reflection Symmetry ...... 700 46.3 Example ...... 702 46.3.1 The First Born Approximation ...... 702 46.4 Recent Developments ...... 703 46.4.1 S → D Excitation ...... 703 46.4.2 P → P Excitation ...... 703 46.4.3 Relativistic Effects in S → P Excitation ...... 703 46.5 Summary ...... 703 References ...... 703 Detailed Contents 1447

47 Electron–Atom, Electron–Ion, and Electron–Molecule Collisions Philip Burke ...... 705 47.1 Electron–Atom and Electron–Ion Collisions ...... 705 47.1.1 Low-Energy Elastic Scattering and Excitation ...... 705 47.1.2 Relativistic Effects for Heavy Atoms and Ions ...... 708 47.1.3 Multichannel Resonance Theory ...... 710 47.1.4 Multichannel Quantum Defect Theory ...... 711 47.1.5 Solution of the Coupled Integrodifferential Equations ...... 712 47.1.6 Intermediate and High Energy Elastic Scattering and Excitation ...... 714 47.1.7 Ionization ...... 717 47.2 Electron–Molecule Collisions ...... 720 ealdCont. Detailed 47.2.1 Laboratory Frame Representation ...... 720 47.2.2 Molecular Frame Representation ...... 721 47.2.3 Inclusion of the Nuclear Motion ...... 722 47.2.4 Electron Collisions with Polyatomic Molecules ...... 723 47.3 Electron–Atom Collisions in a Laser Field ...... 723 47.3.1 Potential Scattering ...... 724 47.3.2 Scattering by Complex Atoms and Ions ...... 725 References ...... 727

48 Positron Collisions Robert P. McEachran, Allan Stauffer ...... 731 48.1 Scattering Channels ...... 731 48.1.1 Postronium Formation ...... 731 48.1.2 Annihilation ...... 732 48.2 Theoretical Methods ...... 733 48.3 Particular Applications ...... 735 48.3.1 Atomic Hydrogen ...... 735 48.3.2 Noble Gases ...... 735 48.3.3 Other Atoms ...... 736 48.3.4 Molecular Hydrogen ...... 737 48.3.5 Other Molecules ...... 737 48.4 Binding of Positrons to Atoms ...... 737 48.5 Reviews ...... 738 References ...... 738

49 Adiabatic and Diabatic Collision Processes at Low Energies Evgueni E. Nikitin ...... 741 49.1 Basic Definitions ...... 741 49.1.1 Slow Quasiclassical Collisions ...... 741 49.1.2 Adiabatic and Diabatic Electronic States ...... 742 49.1.3 Nonadiabatic Transitions: The Massey Parameter ...... 742 49.2 Two-State Approximation ...... 743 49.2.1 Relation Between Adiabatic and Diabatic Basis Functions .. 743 49.2.2 Coupled Equations and Transition Probabilities in the Common Trajectory Approximation ...... 744 1448 Detailed Contents

49.2.3 Selection Rules for Nonadiabatic Coupling ...... 745 49.3 Single-Passage Transition Probabilities: Analytical Models ...... 746 49.3.1 Crossing and Narrow Avoided Crossing of Potential Energy Curves: The Landau–Zener Model in the Common Trajectory Approximation ...... 746 49.3.2 Arbitrary Avoided Crossing and Diverging Potential Energy Curves: The Nikitin Model in the Common Trajectory Approximation ...... 747 49.3.3 Beyond the Common Trajectory Approximation ...... 748 49.4 Double-Passage Transition Probabilities and Cross Sections ...... 749 49.4.1 Mean Transition Probability and the Stückelberg Phase ..... 749 49.4.2 Approximate Formulae for the Transition Probabilities ...... 750 ealdCont. Detailed 49.4.3 Integral Cross Sections for a Double-Passage Transition Probability ...... 751 49.5 Multiple-Passage Transition Probabilities ...... 751 49.5.1 Multiple Passage in Atomic Collisions ...... 751 49.5.2 Multiple Passage in Molecular Collisions ...... 751 References ...... 752

50 Ion–Atom and Atom–Atom Collisions A. Lewis Ford, John F. Reading ...... 753 50.1 Treatment of Heavy Particle Motion ...... 754 50.2 Independent-Particle Models Versus Many-Electron Treatments ...... 755 50.3 Analytical Approximations Versus Numerical Calculations ...... 756 50.3.1 Single-Centered Expansion ...... 757 50.3.2 Two-Centered Expansion ...... 758 50.3.3 One-and-a-Half Centered Expansion ...... 758 50.4 Description of the Ionization Continuum ...... 758 References ...... 759

51 Ion–Atom Charge Transfer Reactions at Low Energies Muriel Gargaud, Ronald McCarroll ...... 761 51.1 Molecular Structure Calculations ...... 762 51.1.1 Ab Initio Methods ...... 762 51.1.2 Model Potential Methods ...... 763 51.1.3 Empirical Estimates ...... 764 51.2 Dynamics of the Collision ...... 765 51.3 Radial and Rotational Coupling Matrix Elements ...... 766 51.4 Total Electron Capture Cross Sections ...... 767 51.5 Landau–Zener Approximation ...... 769 51.6 Differential Cross Sections ...... 769 51.7 Orientation Effects ...... 770 51.8 New Developments ...... 772 References ...... 772 Detailed Contents 1449

52 Continuum Distorted Wave and Wannier Methods Derrick Crothers, Fiona McCausland, John Glass, Jim F. McCann, Francesca O’Rourke, Ruth T. Pedlow ...... 775 52.1 Continuum Distorted Wave Method ...... 775 52.1.1 Perturbation Theory ...... 775 52.1.2 Relativistic Continuum-Distorted Waves ...... 778 52.1.3 Variational CDW ...... 778 52.1.4 Ionization ...... 779 52.2 Wannier Method ...... 781 52.2.1 The Wannier Threshold Law ...... 781 52.2.2 Peterkop’s Semiclassical Theory ...... 782 52.2.3 The Quantal Semiclassical Approximation ...... 783 ealdCont. Detailed References ...... 786

53 Ionization in High Energy Ion–Atom Collisions Joseph H. Macek, Steven T. Manson ...... 789 53.1 Born Approximation ...... 789 53.2 Prominent Features ...... 792 53.2.1 Target Electrons ...... 792 53.2.2 Projectile Electrons ...... 796 53.3 Recent Developments ...... 796 References ...... 796

54 Electron–Ion and Ion–Ion Recombination M. Raymond Flannery...... 799 54.1 Recombination Processes ...... 800 54.1.1 Electron–Ion Recombination ...... 800 54.1.2 Positive–Ion Negative–Ion Recombination ...... 800 54.1.3 Balances ...... 800 54.2 Collisional-Radiative Recombination ...... 801 54.2.1 Saha and Boltzmann Distributions ...... 801 54.2.2 Quasi-Steady State Distributions ...... 802 54.2.3 Ionization and Recombination Coefficients ...... 802 54.2.4 Working Rate Formulae ...... 802 54.3 Macroscopic Methods ...... 803 54.3.1 Resonant Capture-Stabilization Model: Dissociative and Dielectronic Recombination ...... 803 54.3.2 Reactive Sphere Model: Three-Body Electron–Ion and Ion–Ion Recombination ...... 804 54.3.3 Working Formulae for Three-Body Collisional Recombination at Low Density ...... 805 54.3.4 Recombination Influenced by Diffusional Drift at High Gas Densities ...... 806 54.4 Dissociative Recombination ...... 807 54.4.1 Curve-Crossing Mechanisms ...... 807 54.4.2 Quantal Cross Section ...... 808 54.4.3 Noncrossing Mechanism ...... 810 1450 Detailed Contents

54.5 Mutual Neutralization ...... 810 54.5.1 Landau–Zener Probability for Single Crossing at RX ...... 811 54.5.2 Cross Section and Rate Coefficient for Mutual Neutralization 811 54.6 One-Way Microscopic Equilibrium Current, Flux, and Pair-Distributions ...... 811 54.7 Microscopic Methods for Termolecular Ion–Ion Recombination ...... 812 54.7.1 Time Dependent Method: Low Gas Density ...... 813 54.7.2 Time Independent Methods: Low Gas Density ...... 814 54.7.3 Recombination at Higher Gas Densities ...... 815 54.7.4 Master Equations ...... 816 54.7.5 Recombination Rate ...... 816 ealdCont. Detailed 54.8 Radiative Recombination ...... 817 54.8.1 Detailed Balance and Recombination-Ionization Cross Sections ...... 817 54.8.2 Kramers Cross Sections, Rates, Electron Energy-Loss Rates and Radiated Power for Hydrogenic Systems ...... 818 54.8.3 Basic Formulae for Quantal Cross Sections ...... 819 54.8.4 Bound-Free Oscillator Strengths ...... 822 54.8.5 Radiative Recombination Rate ...... 822 54.8.6 Gaunt Factor, Cross Sections and Rates for Hydrogenic Systems ...... 823 54.8.7 Exact Universal Rate Scaling Law and Results for Hydrogenic Systems ...... 823 54.9 Useful Quantities ...... 824 References ...... 824

55 Dielectronic Recombination Michael S. Pindzola, Donald C. Griffin, Nigel R. Badnell ...... 829 55.1 Theoretical Formulation ...... 830 55.2 Comparisons with Experiment ...... 831 55.2.1 Low-Z Ions ...... 831 55.2.2 High-Z Ions and Relativistic Effects ...... 831 55.3 Radiative-Dielectronic Recombination Interference ...... 832 55.4 Dielectronic Recombinationin Plasmas ...... 833 References ...... 833

56 Rydberg Collisions: Binary Encounter, Born and Impulse Approximations Edmund J. Mansky ...... 835 56.1 Rydberg Collision Processes ...... 836 56.2 General Properties of Rydberg States ...... 836 56.2.1 Dipole Moments ...... 836 56.2.2 Radial Integrals ...... 836 56.2.3 Line Strengths ...... 837 56.2.4 Form Factors ...... 838 56.2.5 Impact Broadening ...... 838 Detailed Contents 1451

56.3 Correspondence Principles ...... 839 56.3.1 Bohr–Sommerfeld Quantization ...... 839 56.3.2 Bohr Correspondence Principle ...... 839 56.3.3 Heisenberg Correspondence Principle ...... 839 56.3.4 Strong Coupling Correspondence Principle ...... 840 56.3.5 Equivalent Oscillator Theorem ...... 840 56.4 Distribution Functions ...... 840 56.4.1 Spatial Distributions ...... 840 56.4.2 Momentum Distributions ...... 840 56.5 Classical Theory ...... 841 56.6 Working Formulae for Rydberg Collisions ...... 842 56.6.1 Inelastic n,-Changing Transitions ...... 842 ealdCont. Detailed 56.6.2 Inelastic n → n Transitions ...... 843 56.6.3 Quasi-Elastic -Mixing Transitions ...... 844 56.6.4 Elastic n  → n  Transitions ...... 844 56.6.5 Fine Structure n  J → n  J Transitions ...... 844 56.7 Impulse Approximation ...... 845 56.7.1 Quantal Impulse Approximation ...... 845 56.7.2 Classical Impulse Approximation ...... 849 56.7.3 Semiquantal Impulse Approximation ...... 851 56.8 Binary Encounter Approximation ...... 852 56.8.1 Differential Cross Sections ...... 852 56.8.2 Integral Cross Sections ...... 853 56.8.3 Classical Ionization Cross Section ...... 855 56.8.4 Classical Charge Transfer Cross Section ...... 855 56.9 Born Approximation ...... 856 56.9.1 Form Factors ...... 856 56.9.2 Hydrogenic Form Factors ...... 856 56.9.3 Excitation Cross Sections ...... 858 56.9.4 Ionization Cross Sections ...... 859 56.9.5 Capture Cross Sections ...... 859 References ...... 860

57 Mass Transfer at High Energies: Thomas Peak James H. McGuire, Jack C. Straton, Takeshi Ishihara ...... 863 57.1 The Classical Thomas Process ...... 863 57.2 Quantum Description ...... 864 57.2.1 Uncertainty Effects ...... 864 57.2.2 Conservation of Overall Energy and Momentum ...... 864 57.2.3 Conservation of Intermediate Energy ...... 865 57.2.4 Example: Proton–Helium Scattering ...... 865 57.3 Off-Energy-Shell Effects ...... 866 57.4 Dispersion Relations ...... 866 57.5 Destructive Interference of Amplitudes ...... 867 57.6 Recent Developments ...... 867 References ...... 868 1452 Detailed Contents

58 Classical Trajectory and Monte Carlo Techniques Ronald E. Olson ...... 869 58.1 Theoretical Background ...... 869 58.1.1 Hydrogenic Targets ...... 869 58.1.2 Nonhydrogenic One-Electron Models ...... 870 58.1.3 Multiply-Charged Projectiles and Many-Electron Targets ... 870 58.2 Region of Validity ...... 871 58.3 Applications ...... 871 58.3.1 Hydrogenic Atom Targets ...... 871 58.3.2 Pseudo One-Electron Targets ...... 872 58.3.3 State-Selective Electron Capture ...... 872 58.3.4 Exotic Projectiles ...... 873 ealdCont. Detailed 58.3.5 Heavy Particle Dynamics ...... 873 58.4 Conclusions ...... 874 References ...... 874

59 Collisional Broadening of Spectral Lines Gillian Peach ...... 875 59.1 Impact Approximation ...... 875 59.2 Isolated Lines ...... 876 59.2.1 Semiclassical Theory ...... 876 59.2.2 Simple Formulae ...... 877 59.2.3 Perturbation Theory ...... 878 59.2.4 Broadening by Charged Particles ...... 879 59.2.5 Empirical Formulae ...... 879 59.3 Overlapping Lines ...... 880 59.3.1 Transitions in Hydrogen and Hydrogenic Ions ...... 880 59.3.2 Infrared and Radio Lines ...... 882 59.4 Quantum-Mechanical Theory ...... 882 59.4.1 Impact Approximation ...... 882 59.4.2 Broadening by Electrons ...... 883 59.4.3 Broadening by Atoms ...... 884 59.5 One-Perturber Approximation ...... 885 59.5.1 General Approach and Utility ...... 885 59.5.2 Broadening by Electrons ...... 885 59.5.3 Broadening by Atoms ...... 886 59.6 Unified Theories and Conclusions ...... 888 References ...... 888

Part E Scattering Experiments

60 Photodetachment David J. Pegg ...... 891 60.1 Negative Ions ...... 891 60.2 Photodetachment ...... 892 60.2.1 Threshold Behavior ...... 892 Detailed Contents 1453

60.2.2 Resonance Structure ...... 892 60.2.3 Higher Order Processes ...... 893 60.3 Experimental Procedures ...... 893 60.3.1 Production of Negative Ions ...... 893 60.3.2 Interacting Beams ...... 893 60.3.3 Light Sources ...... 894 60.3.4 Detection Schemes ...... 895 60.4 Results ...... 895 60.4.1 Threshold Measurements ...... 895 60.4.2 Resonance Parameters ...... 896 60.4.3 Lifetimes of Metastable Negative Ions ...... 897 60.4.4 Multielectron Detachment ...... 898 ealdCont. Detailed References ...... 898

61 Photon–Atom Interactions: Low Energy Denise Caldwell, Manfred O. Krause ...... 901 61.1 Theoretical Concepts ...... 901 61.1.1 Differential Analysis ...... 901 61.1.2 Electron Correlation Effects ...... 904 61.2 Experimental Methods ...... 907 61.2.1 Synchrotron Radiation Source ...... 907 61.2.2 Photoelectron Spectrometry ...... 908 61.2.3 Resolution and Natural Width ...... 910 61.3 Additional Considerations ...... 911 References ...... 912

62 Photon–Atom Interactions: Intermediate Energies Bernd Crasemann ...... 915 62.1 Overview ...... 915 62.1.1 Photon-Atom Processes ...... 915 62.2 Elastic Photon-Atom Scattering ...... 916 62.2.1 Rayleigh Scattering ...... 916 62.2.2 Nuclear Scattering ...... 917 62.3 Inelastic Photon-Atom Interactions ...... 918 62.3.1 Photoionization ...... 918 62.3.2 Compton Scattering ...... 919 62.4 Atomic Response to Inelastic Photon-Atom Interactions ...... 919 62.4.1 Auger Transitions ...... 919 62.4.2 X-Ray Emission ...... 921 62.4.3 Widths and Fluorescence Yields ...... 921 62.4.4 Multi-Electron Excitations ...... 921 62.4.5 Momentum Spectroscopy ...... 922 62.4.6 Ultrashort Light Pulses ...... 922 62.4.7 Nondipolar Interactions ...... 923 62.5 Threshold Phenomena ...... 923 62.5.1 Raman Processes ...... 924 62.5.2 Post-Collision Interaction ...... 925 References ...... 925 1454 Detailed Contents

63 Electron–Atom and Electron–Molecule Collisions Sandor Trajmar, William J. McConkey, Isik Kanik ...... 929 63.1 Basic Concepts ...... 929 63.1.1 Electron Impact Processes ...... 929 63.1.2 Definition of Cross Sections ...... 929 63.1.3 Scattering Measurements ...... 930 63.2 Collision Processes ...... 933 63.2.1 Total Scattering Cross Sections ...... 933 63.2.2 Elastic Scattering Cross Sections ...... 933 63.2.3 Momentum Transfer Cross Sections ...... 933 63.2.4 Excitation Cross Sections ...... 933 63.2.5 Dissociation Cross Sections ...... 935 ealdCont. Detailed 63.2.6 Ionization Cross Sections ...... 935 63.3 Coincidence and Superelastic Measurements ...... 936 63.4 Experiments with Polarized Electrons ...... 938 63.5 Electron Collisions with Excited Species ...... 939 63.6 Electron Collisions in Traps ...... 939 63.7 Future Developments ...... 940 References ...... 940

64 Ion–Atom Scattering Experiments: Low Energy Ronald Phaneuf ...... 943 64.1 Low Energy Ion–Atom Collision Processes ...... 943 64.2 Experimental Methods for Total Cross Section Measurements ...... 945 64.2.1 Gas Target Beam Attenuation Method ...... 945 64.2.2 Gas Target Product Growth Method ...... 945 64.2.3 Crossed Ion and Thermal Beams Method ...... 945 64.2.4 Fast Merged Beams Method ...... 946 64.2.5 Trapped Ion Method ...... 946 64.2.6 Swarm Method ...... 947 64.3 Methods for State and Angular Selective Measurements ...... 947 64.3.1 Photon Emission Spectroscopy ...... 947 64.3.2 Translational Energy Spectroscopy ...... 947 64.3.3 Electron Emission Spectroscopy ...... 948 64.3.4 Angular Differential Measurements ...... 948 64.3.5 Recoil Ion Momentum Spectroscopy ...... 948 References ...... 948

65 Ion–Atom Collisions – High Energy Lew Cocke, Michael Schulz ...... 951 65.1 Basic One-Electron Processes ...... 951 65.1.1 Perturbative Processes ...... 951 65.1.2 Nonperturbative Processes ...... 955 65.2 Multi-Electron Processes ...... 957 65.3 Electron Spectra in Ion–Atom Collisions ...... 959 65.3.1 General Characteristics ...... 959 65.3.2 High Resolution Measurements ...... 960 Detailed Contents 1455

65.4 Quasi-Free Electron Processes in Ion–Atom Collisions ...... 961 65.4.1 Radiative Electron Capture ...... 961 65.4.2 Resonant Transfer and Excitation ...... 961 65.4.3 Excitation and Ionization ...... 961 65.5 Some Exotic Processes ...... 962 65.5.1 Molecular Orbital X-Rays ...... 962 65.5.2 Positron Production from Atomic Processes ...... 962 References ...... 963

66 Reactive Scattering Arthur G. Suits, Yuan T. Lee ...... 967

66.1 Experimental Methods ...... 967 Cont. Detailed 66.1.1 Molecular Beam Sources ...... 967 66.1.2 Reagent Preparation ...... 968 66.1.3 Detection of Neutral Products ...... 969 66.1.4 A Typical Signal Calculation ...... 971 66.2 Experimental Configurations ...... 971 66.2.1 Crossed-Beam Rotatable Detector ...... 971 66.2.2 Doppler Techniques ...... 973 66.2.3 Product Imaging ...... 973 66.2.4 Laboratory to Center-of-Mass Transformation ...... 975 66.3 Elastic and Inelastic Scattering ...... 976 66.3.1 The Differential Cross Section ...... 976 66.3.2 Rotationally Inelastic Scattering ...... 977 66.3.3 Vibrationally Inelastic Scattering ...... 977 66.3.4 Electronically Inelastic Scattering ...... 978 66.4 Reactive Scattering ...... 978 66.4.1 Harpoon and Stripping Reactions ...... 978 66.4.2 Rebound Reactions ...... 979 66.4.3 Long-lived Complexes ...... 979 66.5 Recent Developments ...... 980 References ...... 980

67 Ion–Molecule Reactions James M. Farrar ...... 983 67.1 Instrumentation ...... 985 67.2 Kinematic Analysis ...... 985 67.3 Scattering Cross Sections ...... 987 67.3.1 State-to-State Differential Cross Sections ...... 987 67.3.2 Velocity–Angle Differential Cross Sections ...... 988 67.3.3 Total Cross Sections with State-Selected Reactants ...... 989 67.3.4 Product–State Resolved Total Cross Sections ...... 989 67.3.5 State-to-State Total Cross Sections ...... 990 67.3.6 Energy Dependent Total Cross Sections ...... 990 67.4 New Directions: Complexity and Imaging ...... 991 References ...... 992 1456 Detailed Contents

Part F Quantum Optics

68 Light–Matter Interaction Pierre Meystre ...... 997 68.1 Multipole Expansion ...... 997 68.1.1 Electric Dipole (E1) Interaction ...... 998 68.1.2 Electric Quadrupole (E2) Interaction ...... 998 68.1.3 Magnetic Dipole (M1) Interaction ...... 999 68.2 Lorentz Atom ...... 999 68.2.1 Complex Notation ...... 999 68.2.2 Index of Refraction ...... 999 68.2.3 Beer’s Law ...... 1000 ealdCont. Detailed 68.2.4 Slowly-Varying Envelope Approximation ...... 1000 68.3 Two-Level Atoms ...... 1000 68.3.1 Hamiltonian ...... 1001 68.3.2 Rotating Wave Approximation ...... 1001 68.3.3 Rabi Frequency ...... 1001 68.3.4 Dressed States ...... 1002 68.3.5 Optical Bloch Equations ...... 1003 68.4 Relaxation Mechanisms ...... 1003 68.4.1 Relaxation Toward Unobserved Levels ...... 1003 68.4.2 Relaxation Toward Levels of Interest ...... 1004 68.4.3 Optical Bloch Equations with Decay ...... 1004 68.4.4 Density Matrix Equations ...... 1004 68.5 Rate Equation Approximation ...... 1005 68.5.1 Steady State ...... 1005 68.5.2 Saturation ...... 1005 68.5.3 Einstein A and B Coefficients ...... 1005 68.6 Light Scattering ...... 1006 68.6.1 Rayleigh Scattering ...... 1006 68.6.2 Thomson Scattering ...... 1006 68.6.3 Resonant Scattering ...... 1006 References ...... 1007

69 Absorption and Gain Spectra Stig Stenholm ...... 1009 69.1 Index of Refraction ...... 1009 69.2 Density Matrix Treatment of the Two-Level Atom ...... 1010 69.3 Line Broadening ...... 1011 69.4 The Rate Equation Limit ...... 1013 69.5 Two-Level Doppler-Free Spectroscopy ...... 1015 69.6 Three-Level Spectroscopy ...... 1016 69.7 Special Effects in Three-Level Systems ...... 1018 69.8 Summary of the Literature ...... 1020 References ...... 1020 Detailed Contents 1457

70 Laser Principles Peter W. Milonni ...... 1023 70.1 Gain, Threshold, and Matter–Field Coupling ...... 1023 70.2 Continuous Wave, Single-Mode Operation ...... 1025 70.3 Laser Resonators ...... 1028 70.4 Photon Statistics ...... 1030 70.5 Multi-Mode and Pulsed Operation ...... 1031 70.6 Instabilities and Chaos ...... 1033 70.7 Recent Developments ...... 1033 References ...... 1034

71 Types of Lasers ealdCont. Detailed Richard C. Powell ...... 1035 71.1 Gas Lasers ...... 1036 71.1.1 Neutral Atom Lasers ...... 1036 71.1.2 Ion Lasers ...... 1036 71.1.3 Metal Vapor Lasers ...... 1037 71.1.4 Molecular Lasers ...... 1037 71.1.5 Excimer Lasers ...... 1038 71.1.6 Nonlinear Mixing ...... 1038 71.1.7 Chemical Lasers ...... 1039 71.2 Solid State Lasers ...... 1039 71.2.1 Transition Metal Ion Lasers ...... 1040 71.2.2 Rare Earth Ion Lasers ...... 1040 71.2.3 ColorCenterLasers...... 1042 71.2.4 New Types of Solid State Laser Systems ...... 1043 71.2.5 Frequency Shifters ...... 1043 71.3 Semiconductor Lasers ...... 1043 71.4 Liquid Lasers ...... 1044 71.4.1 Organic Dye Lasers ...... 1044 71.4.2 Rare Earth Chelate Lasers ...... 1045 71.4.3 Inorganic Rare Earth Liquid Lasers ...... 1045 71.5 Other Types of Lasers ...... 1045 71.5.1 X-Ray and Extreme UV Lasers ...... 1045 71.5.2 Nuclear Pumped Lasers ...... 1046 71.5.3 Free Electron Lasers ...... 1046 71.6 Recent Developments ...... 1046 References ...... 1048

72 Nonlinear Optics Alexander L. Gaeta, Robert W. Boyd ...... 1051 72.1 Nonlinear Susceptibility ...... 1051 72.1.1 Tensor Properties ...... 1052 72.1.2 Nonlinear Refractive Index ...... 1052 72.1.3 Quantum Mechanical Expression for χ(n) ...... 1052 72.1.4 The Hyperpolarizability ...... 1053 1458 Detailed Contents

72.2 Wave Equation in Nonlinear Optics ...... 1054 72.2.1 Coupled-Amplitude Equations ...... 1054 72.2.2 Phase Matching ...... 1054 72.2.3 Manley–Rowe Relations ...... 1055 72.2.4 Pulse Propagation ...... 1055 72.3 Second-Order Processes ...... 1056 72.3.1 Sum Frequency Generation ...... 1056 72.3.2 Second Harmonic Generation ...... 1056 72.3.3 Difference Frequency Generation ...... 1056 72.3.4 Parametric Amplification and Oscillation ...... 1056 72.3.5 Focused Beams ...... 1056 72.4 Third-Order Processes ...... 1057 ealdCont. Detailed 72.4.1 Third-Harmonic Generation ...... 1057 72.4.2 Self-Phase and Cross-Phase Modulation ...... 1057 72.4.3 Four-Wave Mixing ...... 1058 72.4.4 Self-Focusing and Self-Trapping ...... 1058 72.4.5 Saturable Absorption ...... 1058 72.4.6 Two-Photon Absorption ...... 1058 72.4.7 Nonlinear Ellipse Rotation ...... 1059 72.5 Stimulated Light Scattering ...... 1059 72.5.1 Stimulated Raman Scattering ...... 1059 72.5.2 Stimulated Brillouin Scattering ...... 1060 72.6 Other Nonlinear Optical Processes ...... 1061 72.6.1 High-Order Harmonic Generation ...... 1061 72.6.2 Electro-Optic Effect ...... 1061 72.6.3 Photorefractive Effect ...... 1061 72.6.4 Ultrafast and Intense-Field Nonlinear Optics ...... 1062 References ...... 1062

73 Coherent Transients Joseph H. Eberly, Carlos R. Stroud Jr...... 1065 73.1 Optical Bloch Equations ...... 1065 73.2 Numerical Estimates of Parameters ...... 1066 73.3 Homogeneous Relaxation ...... 1066 73.3.1 Rabi Oscillations ...... 1067 73.3.2 Bloch Vector and Bloch Sphere ...... 1067 73.3.3 Pi Pulses and Pulse Area ...... 1067 73.3.4 Adiabatic Following ...... 1068 73.4 Inhomogeneous Relaxation ...... 1068 73.4.1 Free Induction Decay ...... 1068 73.4.2 Photon Echoes ...... 1069 73.5 Resonant Pulse Propagation ...... 1069 73.5.1 Maxwell–Bloch Equations ...... 1069 73.5.2 Index of Refraction and Beers Law ...... 1070 73.5.3 The Area Theorem and Self-Induced Transparency ...... 1070 73.6 Multi-Level Generalizations ...... 1071 73.6.1 Rydberg Packets and Intrinsic Relaxation ...... 1071 Detailed Contents 1459

73.6.2 Multiphoton Resonance and Two-Photon Bloch Equations ...... 1072 73.6.3 Pump–Probe Resonance and Dark States ...... 1073 73.6.4 Three-Level Transparency ...... 1074 73.7 Disentanglement and “Sudden Death” of Coherent Transients ...... 1074 References ...... 1076

74 Multiphoton and Strong-Field Processes Kenneth C. Kulander, Maciej Lewenstein ...... 1077 74.1 Weak Field Multiphoton Processes ...... 1078 74.1.1 Perturbation Theory ...... 1078 74.1.2 Resonant Enhanced Multiphoton Ionization ...... 1078 ealdCont. Detailed 74.1.3 Multi-Electron Effects ...... 1079 74.1.4 Autoionization ...... 1079 74.1.5 Coherence and Statistics ...... 1079 74.1.6 Effects of Field Fluctuations ...... 1079 74.1.7 Excitation with Multiple Laser Fields ...... 1080 74.2 Strong-Field Multiphoton Processes ...... 1080 74.2.1 Nonperturbative Multiphoton Ionization ...... 1081 74.2.2 Tunneling Ionization ...... 1081 74.2.3 Multiple Ionization ...... 1081 74.2.4 Above Threshold Ionization ...... 1081 74.2.5 High Harmonic Generation ...... 1082 74.2.6 Stabilization of Atoms in Intense Laser Fields ...... 1083 74.2.7 Molecules in Intense Laser Fields ...... 1084 74.2.8 Microwave Ionization of Rydberg Atoms ...... 1084 74.3 Strong-Field Calculational Techniques ...... 1086 74.3.1 Floquet Theory ...... 1086 74.3.2 Direct Integration of the TDSE ...... 1086 74.3.3 Volkov States ...... 1086 74.3.4 Strong Field Approximations ...... 1087 74.3.5 Phase Space Averaging Method ...... 1087 References ...... 1088

75 Cooling and Trapping Juha Javanainen ...... 1091 75.1 Notation ...... 1091 75.2 Control of Atomic Motion by Light ...... 1092 75.2.1 General Theory ...... 1092 75.2.2 Two-State Atoms ...... 1094 75.2.3 Multistate Atoms ...... 1097 75.3 Magnetic Trap for Atoms ...... 1099 75.4 Trapping and Cooling of Charged Particles ...... 1099 75.4.1 Paul Trap ...... 1099 75.4.2 Penning Trap ...... 1101 75.4.3 Collective Effects in Ion Clouds ...... 1102 1460 Detailed Contents

75.5 Applications of Cooling and Trapping ...... 1103 75.5.1 Neutral Atoms ...... 1103 75.5.2 Trapped Particles ...... 1104 References ...... 1105

76 Quantum Degenerate Gases Juha Javanainen ...... 1107 76.1 Elements of Quantum Field Theory ...... 1107 76.1.1 Bosons ...... 1108 76.1.2 Fermions ...... 1109 76.1.3 Bosons versus Fermions ...... 1109 76.2 Basic Properties of Degenerate Gases 1110

ealdCont. Detailed ...... 76.2.1 Bosons ...... 1110 76.2.2 Meaning of Macroscopic Wave Function ...... 1114 76.2.3 Fermions ...... 1115 76.3 Experimental ...... 1115 76.3.1 Preparing a BEC ...... 1115 76.3.2 Preparing a Degenerate Fermi Gas ...... 1117 76.3.3 Monitoring Degenerate Gases ...... 1117 76.4 BEC Superfluid ...... 1117 76.4.1 Vortices ...... 1117 76.4.2 Superfluidity ...... 1118 76.5 Current Active Topics ...... 1119 76.5.1 Atom–Molecule Systems ...... 1119 76.5.2 Optical Lattice with a BEC ...... 1121 References ...... 1123

77 De Broglie Optics Carsten Henkel, Martin Wilkens ...... 1125 77.1 Overview ...... 1125 77.2 Hamiltonian of de Broglie Optics ...... 1126 77.2.1 Gravitation and Rotation ...... 1127 77.2.2 Charged Particles ...... 1127 77.2.3 Neutrons ...... 1127 77.2.4 Spins ...... 1127 77.2.5 Atoms ...... 1127 77.3 Principles of de Broglie Optics ...... 1129 77.3.1 Light Optics Analogy ...... 1129 77.3.2 WKB Approximation ...... 1130 77.3.3 Phase and Group Velocity ...... 1130 77.3.4 Paraxial Approximation ...... 1130 77.3.5 Raman–Nath Approximation ...... 1131 77.4 Refraction and Reflection ...... 1131 77.4.1 Atomic Mirrors ...... 1131 77.4.2 Atomic Cavities ...... 1132 77.4.3 Atomic Lenses ...... 1132 77.4.4 Atomic Waveguides ...... 1132 Detailed Contents 1461

77.5 Diffraction ...... 1133 77.5.1 Fraunhofer Diffraction ...... 1133 77.5.2 Fresnel Diffraction ...... 1133 77.5.3 Near-Resonant Kapitza–Dirac Effect ...... 1133 77.5.4 Atom Beam Splitters ...... 1134 77.6 Interference ...... 1135 77.6.1 Interference Phase Shift ...... 1135 77.6.2 Internal State Interferometry ...... 1136 77.6.3 Manipulation of Cavity Fields by Atom Interferometry ...... 1137 77.7 Coherence of Scalar Matter Waves ...... 1137 77.7.1 Atomic Sources ...... 1137 77.7.2 Atom Decoherence ...... 1138 ealdCont. Detailed References ...... 1139

78 Quantized Field Effects Matthias Freyberger, Karl Vogel, Wolfgang P. Schleich, Robert F. O’Connell 1141 78.1 Field Quantization ...... 1142 78.2 Field States ...... 1142 78.2.1 Number States ...... 1143 78.2.2 Coherent States ...... 1143 78.2.3 Squeezed States ...... 1144 78.2.4 Phase States ...... 1145 78.3 Quantum Coherence Theory ...... 1146 78.3.1 Correlation Functions ...... 1146 78.3.2 Photon Correlations ...... 1146 78.3.3 Photon Bunching and Antibunching ...... 1147 78.4 Photodetection Theory ...... 1147 78.4.1 Homodyne and Heterodyne Detection ...... 1147 78.5 Quasi-Probability Distributions ...... 1148 78.5.1 s-Ordered Operators ...... 1148 78.5.2 The P Function ...... 1149 78.5.3 The Wigner Function ...... 1149 78.5.4 The Q Function ...... 1151 78.5.5 Relations Between Quasi-Probabilities ...... 1151 78.6 Reservoir Theory ...... 1151 78.6.1 Thermal Reservoir ...... 1152 78.6.2 Squeezed Reservoir ...... 1152 78.7 Master Equation ...... 1152 78.7.1 Damped Harmonic Oscillator ...... 1153 78.7.2 Damped Two-Level Atom ...... 1153 78.8 Solution of the Master Equation ...... 1154 78.8.1 Damped Harmonic Oscillator ...... 1154 78.8.2 Damped Two-Level Atom ...... 1155 78.9 Quantum Regression Hypothesis ...... 1156 78.9.1 Two-Time Correlation Functions and Master Equation ...... 1156 78.9.2 Two-Time Correlation Functions and Expectation Values .... 1156 1462 Detailed Contents

78.10 Quantum Noise Operators ...... 1157 78.10.1 Quantum Langevin Equations ...... 1157 78.10.2 Stochastic Differential Equations ...... 1158 78.11 Quantum Monte Carlo Formalism ...... 1159 78.12 Spontaneous Emission in Free Space ...... 1159 78.13 Resonance Fluorescence ...... 1160 78.13.1 Equations of Motion ...... 1160 78.13.2 Intensity of Emitted Light ...... 1160 78.13.3 Spectrum of the Fluorescence Light ...... 1161 78.13.4 Photon Correlations ...... 1161 78.14 Recent Developments ...... 1162 78.14.1 Literature ...... 1162 ealdCont. Detailed 78.14.2 Field States ...... 1162 78.14.3 Reservoir Theory ...... 1162 References ...... 1163

79 Entangled Atoms and Fields: Cavity QED Dieter Meschede, Axel Schenzle ...... 1167 79.1 Atoms and Fields ...... 1167 79.1.1 Atoms ...... 1167 79.1.2 Electromagnetic Fields ...... 1168 79.2 Weak Coupling in Cavity QED ...... 1169 79.2.1 Radiating Atoms in Waveguides ...... 1169 79.2.2 Trapped Radiating Atoms and Their Mirror Images ...... 1170 79.2.3 Radiating Atoms in Resonators ...... 1170 79.2.4 Radiative Shifts and Forces ...... 1171 79.2.5 Experiments on Weak Coupling ...... 1172 79.2.6 Cavity QED and Dielectrics ...... 1173 79.3 Strong Coupling in Cavity QED ...... 1173 79.4 Strong Coupling in Experiments ...... 1174 79.4.1 Rydberg Atoms and Microwave Cavities ...... 1174 79.4.2 Strong Coupling in Open Optical Cavities ...... 1174 79.5 Microscopic Masers and Lasers ...... 1175 79.5.1 The Jaynes–Cummings Model ...... 1175 79.5.2 Fock States, Coherent States and Thermal States ...... 1175 79.5.3 Vacuum Splitting ...... 1177 79.6 Micromasers ...... 1178 79.6.1 Maser Threshold ...... 1178 79.6.2 Nonclassical Features of the Field ...... 1179 79.6.3 Trapping States ...... 1179 79.6.4 Atom Counting Statistics ...... 1180 79.7 Quantum Theory of Measurement ...... 1180 79.8 Applications of Cavity QED ...... 1181 79.8.1 Detecting and Trapping Atoms through Strong Coupling .... 1181 79.8.2 Generation of Entanglement ...... 1181 79.8.3 Single Photon Sources ...... 1182 References ...... 1182 Detailed Contents 1463

80 Quantum Optical Tests of the Foundations of Physics Aephraim M. Steinberg, Paul G. Kwiat, Raymond Y. Chiao ...... 1185 80.1 The Photon Hypothesis ...... 1186 80.2 Quantum Properties of Light ...... 1186 80.2.1 Vacuum Fluctuations: Cavity QED ...... 1186 80.2.2 The Down-Conversion Two-Photon Light Source ...... 1187 80.2.3 Squeezed States of Light ...... 1187 80.3 Nonclassical Interference ...... 1188 80.3.1 Single-Photon and Matter–Wave Interference ...... 1188 80.3.2 “Nonlocal” Interference Effects and Energy–Time Uncertainty ...... 1189 80.3.3 Two-Photon Interference ...... 1190 ealdCont. Detailed 80.4 Complementarity and Coherence ...... 1191 80.4.1 Wave–Particle Duality ...... 1191 80.4.2 Quantum Eraser ...... 1191 80.4.3 Vacuum-Induced Coherence ...... 1192 80.4.4 Suppression of Spontaneous Down-Conversion ...... 1192 80.5 Measurements in Quantum Mechanics ...... 1193 80.5.1 Quantum (Anti-)Zeno Effect ...... 1193 80.5.2 Quantum Nondemolition ...... 1193 80.5.3 Quantum Interrogation ...... 1194 80.5.4 Weak and “Protected” Measurements ...... 1195 80.6 The EPR Paradox and Bell’s Inequalities ...... 1195 80.6.1 Generalities ...... 1195 80.6.2 Polarization-Based Tests ...... 1196 80.6.3 Nonpolarization Tests ...... 1196 80.6.4 Bell Inequality Loopholes ...... 1198 80.6.5 Nonlocality Without Inequalities ...... 1199 80.7 Quantum Information ...... 1200 80.7.1 Information Content of a Quantum: (No) Cloning ...... 1200 80.7.2 Super-Dense Coding ...... 1200 80.7.3 Teleportation ...... 1200 80.7.4 Quantum Cryptography ...... 1201 80.7.5 Issues in Causality ...... 1202 80.8 The Single-Photon Tunneling Time ...... 1202 80.8.1 An Application of EPR Correlations to Time Measurements .. 1202 80.8.2 Superluminal Tunneling Times ...... 1203 80.8.3 Tunneling Delay in a Multilayer Dielectric Mirror ...... 1203 80.8.4 Interpretation of the Tunneling Time ...... 1204 80.8.5 Other Fast and Slow Light Schemes ...... 1205 80.9 Gravity and Quantum Optics ...... 1206 References ...... 1207

81 Quantum Information Peter L. Knight, Stefan Scheel ...... 1215 81.1 Quantifying Information ...... 1216 81.1.1 Separability Criterion ...... 1216 81.1.2 Entanglement Measures ...... 1217 1464 Detailed Contents

81.2 Simple Quantum Protocols ...... 1218 81.2.1 Quantum Key Distribution ...... 1219 81.2.2 Quantum Teleportation ...... 1219 81.2.3 Dense Coding ...... 1220 81.3 Unitary Transformations ...... 1221 81.3.1 Single-Qubit Operations ...... 1221 81.3.2 Two-Qubit Operations ...... 1221 81.3.3 Multi-Qubit Gates and Networks ...... 1222 81.4 Quantum Algorithms ...... 1222 81.4.1 Deutsch–Jozsa Algorithm ...... 1222 81.4.2 Grover’s Search Algorithm ...... 1223 81.5 Error Correction ...... 1223 ealdCont. Detailed 81.6 The DiVincenzo Checklist ...... 1224 81.6.1 Qubit Characterization, Scalability ...... 1224 81.6.2 Initialization ...... 1224 81.6.3 Long Decoherence Times ...... 1224 81.6.4 Universal Set of Quantum Gates ...... 1225 81.6.5 Qubit-Specific Measurement ...... 1225 81.7 Physical Implementations ...... 1225 81.7.1 Linear Optics ...... 1225 81.7.2 Trapped Ions ...... 1226 81.7.3 Cavity QED ...... 1226 81.7.4 Optical Lattices, Mott Insulator ...... 1227 81.8 Outlook ...... 1227 References ...... 1228

Part G Applications

82 Applications of Atomic and Molecular Physics to Astrophysics Alexander Dalgarno, Stephen Lepp ...... 1235 82.1 Photoionized Gas ...... 1235 82.2 Collisionally Ionized Gas ...... 1237 82.3 Diffuse Molecular Clouds ...... 1238 82.4 Dark Molecular Clouds ...... 1239 82.5 Circumstellar Shells and Stellar Atmospheres ...... 1241 82.6 Supernova Ejecta ...... 1242 82.7 Shocked Gas ...... 1243 82.8 The Early Universe ...... 1244 82.9 Recent Developments ...... 1244 82.10 Other Reading ...... 1245 References ...... 1245

83 Comets Paul D. Feldman ...... 1247 83.1 Observations ...... 1247 83.2 Excitation Mechanisms ...... 1250 Detailed Contents 1465

83.2.1 Basic Phenomenology ...... 1250 83.2.2 Fluorescence Equilibrium ...... 1250 83.2.3 Swings and Greenstein Effects ...... 1251 83.2.4 Bowen Fluorescence ...... 1252 83.2.5 Electron Impact Excitation ...... 1253 83.2.6 Prompt Emission ...... 1253 83.2.7 OH Level Inversion ...... 1254 83.3 Cometary Models ...... 1254 83.3.1 Photolytic Processes ...... 1254 83.3.2 Density Models ...... 1255 83.3.3 Radiative Transfer Effects ...... 1256 83.4 Summary ...... 1256 ealdCont. Detailed References ...... 1257

84 Aeronomy Jane L. Fox ...... 1259 84.1 Basic Structure of Atmospheres ...... 1259 84.1.1 Introduction ...... 1259 84.1.2 Atmospheric Regions ...... 1260 84.2 Density Distributions of Neutral Species ...... 1264 84.2.1 The Continuity Equation ...... 1264 84.2.2 Diffusion Coefficients ...... 1265 84.3 Interaction of Solar Radiation with the Atmosphere ...... 1265 84.3.1 Introduction ...... 1265 84.3.2 The Interaction of Solar Photons with Atmospheric Gases ... 1266 84.3.3 Interaction of Energetic Electrons with Atmospheric Gases . 1268 84.4 Ionospheres ...... 1271 84.4.1 Ionospheric Regions ...... 1271 84.4.2 Sources of Ionization ...... 1271 84.4.3 Nightside Ionospheres ...... 1277 84.4.4 Ionospheric Density Profiles ...... 1277 84.4.5 Ion Diffusion ...... 1279 84.5 Neutral, Ion and Electron Temperatures ...... 1281 84.6 Luminosity ...... 1284 84.7 Planetary Escape ...... 1287 References ...... 1290

85 Applications of Atomic and Molecular Physics to Global Change Kate P. Kirby, Kelly Chance ...... 1293 85.1 Overview ...... 1293 85.1.1 Global Change Issues ...... 1293 85.1.2 Structure of the Earth’s Atmosphere ...... 1293 85.2 Atmospheric Models and Data Needs ...... 1294 85.2.1 Modeling the Thermosphere and Ionosphere ...... 1294 85.2.2 Heating and Cooling Processes ...... 1295 85.2.3 Atomic and Molecular Data Needs ...... 1295 1466 Detailed Contents

85.3 Tropospheric Warming/Upper Atmosphere Cooling ...... 1295 85.3.1 Incoming and Outgoing Energy Fluxes ...... 1295 85.3.2 Tropospheric “Global” Warming ...... 1296 85.3.3 Upper Atmosphere Cooling ...... 1297 85.4 Stratospheric Ozone ...... 1298 85.4.1 Production and Destruction ...... 1298 85.4.2 The Antarctic Ozone Hole ...... 1299 85.4.3 Arctic Ozone Loss ...... 1300 85.4.4 Global Ozone Depletion ...... 1300 85.5 Atmospheric Measurements ...... 1300 References ...... 1301 ealdCont. Detailed 86 Atoms in Dense Plasmas Jon C. Weisheit, Michael S. Murillo ...... 1303 86.1 The Dense Plasma Environment ...... 1305 86.1.1 Plasma Parameters ...... 1305 86.1.2 Quasi-Static Fields in Plasmas ...... 1305 86.1.3 Coulomb Logarithms and Collision Frequencies ...... 1307 86.2 Atomic Models and Ionization Balance ...... 1308 86.2.1 Dilute Plasma Models ...... 1308 86.2.2 Dense Plasma “Chemical” Models ...... 1309 86.2.3 Dense Plasma “Physical” Models ...... 1310 86.3 Elementary Processes ...... 1311 86.3.1 Radiative Transitions and Opacity ...... 1311 86.3.2 Collisional Transitions ...... 1312 86.4 Simulations ...... 1313 86.4.1 Monte Carlo ...... 1313 86.4.2 Molecular Dynamics ...... 1313 86.4.3 The Deuterium EOS Problem ...... 1315 References ...... 1316

87 Conduction of Electricity in Gases Alan Garscadden ...... 1319 87.1 Electron Scattering and Transport Phenomena ...... 1320 87.1.1 Electron Scattering Experiments ...... 1320 87.1.2 Electron Transport Phenomena ...... 1321 87.1.3 The Boltzmann Equation ...... 1321 87.1.4 Electron-Atom Elastic Collisions ...... 1322 87.1.5 The Electron Drift Current ...... 1322 87.1.6 Cross Sections Derived from Swarm Data ...... 1326 87.2 Glow Discharge Phenomena ...... 1327 87.2.1 Cold Cathode Discharges ...... 1327 87.2.2 Hot Cathode Discharges ...... 1327 87.3 Atomic and Molecular Processes ...... 1328 87.3.1 Ionization ...... 1328 87.3.2 Electron Attachment ...... 1329 87.3.3 Recombination ...... 1330 Detailed Contents 1467

87.4 Electrical Discharge in Gases: Applications ...... 1330 87.4.1 High Frequency Breakdown ...... 1331 87.4.2 Parallel Plate Reactors and RF Discharges ...... 1331 87.5 Conclusions ...... 1333 References ...... 1333

88 Applications to Combustion David R. Crosley ...... 1335 88.1 Combustion Chemistry ...... 1336 88.2 Laser Combustion Diagnostics ...... 1337 88.2.1 Coherent Anti-Stokes Raman Scattering ...... 1338 88.2.2 Laser-Induced Fluorescence ...... 1339 ealdCont. Detailed 88.2.3 Degenerate Four-Wave Mixing ...... 1341 88.3 Recent Developments ...... 1342 References ...... 1342

89 Surface Physics Erik T. Jensen ...... 1343 89.1 Low Energy Electrons and Surface Science ...... 1343 89.2 Electron–Atom Interactions ...... 1344 89.2.1 Elastic Scattering: Low Energy Electron Diffraction (LEED) .... 1344 89.2.2 Inelastic Scattering: Electron Energy Loss Spectroscopy ...... 1345 89.2.3 Auger Electron Spectroscopy ...... 1345 89.3 Photon–Atom Interactions ...... 1346 89.3.1 Ultraviolet Photoelectron Spectroscopy (UPS) ...... 1346 89.3.2 Inverse Photoemission Spectroscopy (IPES) ...... 1347 89.3.3 X-Ray Photoelectron Spectroscopy (XPS) ...... 1348 89.3.4 X-Ray Absorption Methods ...... 1348 89.4 Atom–Surface Interactions ...... 1351 89.4.1 Physisorption ...... 1351 89.4.2 Chemisorption ...... 1352 89.5 Recent Developments ...... 1352 References ...... 1353

90 Interface with Nuclear Physics John D. Morgan III, James S. Cohen ...... 1355 90.1 Nuclear Size Effects in Atoms ...... 1356 90.1.1 Nuclear Size Effects on Nonrelativistic Energies ...... 1356 90.1.2 Nuclear Size Effects on Relativistic Energies ...... 1357 90.1.3 Nuclear Size Effects on QED Corrections ...... 1358 90.2 Electronic Structure Effects in Nuclear Physics ...... 1358 90.2.1 Electronic Effects on Closely Spaced Nuclear Energy Levels .. 1358 90.2.2 Electronic Effects on Tritium Beta Decay ...... 1358 90.2.3 Electronic Screening of Low Energy Nuclear Reactions ...... 1359 90.2.4 Atomic and Molecular Effects in Relativistic Ion–Atom Collisions ...... 1359 1468 Detailed Contents

90.3 Muon-Catalyzed Fusion ...... 1359 90.3.1 The Catalysis Cycle ...... 1361 90.3.2 Muon Atomic Capture ...... 1362 90.3.3 Muonic Atom Deexcitation and Transfer ...... 1363 90.3.4 Muonic Molecule Formation ...... 1364 90.3.5 Fusion ...... 1366 90.3.6 Sticking and Stripping ...... 1367 90.3.7 Prospectus ...... 1369 References ...... 1369

91 Charged-Particle–Matter Interactions Hans Bichsel ...... 1373 ealdCont. Detailed 91.1 Experimental Aspects ...... 1374 91.1.1 Energy Loss Experiments and Radiation Detectors ...... 1374 91.1.2 Inelastic Scattering Events ...... 1375 91.2 Theory of Cross Sections ...... 1376 91.2.1 Rutherford Cross Section ...... 1376 91.2.2 Binary Encounter Approximation ...... 1376 91.2.3 Bethe Model of Cross Section ...... 1377 91.2.4 Fermi Virtual Photon Method ...... 1377 91.3 Moments of the Cross Section ...... 1378 91.3.1 Total Collision Cross Section M0 ...... 1378 91.3.2 Stopping Power M1 ...... 1379 91.3.3 Second Moment M2 ...... 1380 91.4 Energy Loss Straggling ...... 1381 91.4.1 Straggling Parameters ...... 1381 91.4.2 Analytic Methods for Calculating Energy Loss Straggling Function ...... 1382 91.4.3 Particle identification (PID) ...... 1384 91.5 Multiple Scattering and Nuclear Reactions ...... 1384 91.6 Monte Carlo Calculations ...... 1384 91.7 Detector Conversion Factors ...... 1385 References ...... 1385

92 Radiation Physics Mitio Inokuti ...... 1389 92.1 General Overview ...... 1389 92.2 Radiation Absorption and its Consequences ...... 1390 92.2.1 Two Classes of Problems of Radiation Physics ...... 1390 92.2.2 Photons ...... 1391 92.2.3 Charged Particles ...... 1391 92.2.4 Neutrons ...... 1391 92.3 Electron Transport and Degradation ...... 1392 92.3.1 The Dominant Role of Electrons ...... 1392 92.3.2 Degradation Spectra and Yields of Products ...... 1392 92.3.3 Quantities Expressing the Yields of Products ...... 1394 Detailed Contents 1469

92.3.4 Track Structures ...... 1395 92.3.5 Condensed Matter Effects ...... 1396 92.4 Connections with Related Fields of Research ...... 1397 92.4.1 Astrophysics and Space Physics ...... 1397 92.4.2 Material Science ...... 1397 92.5 Supplement ...... 1397 References ...... 1398

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

Subject Index

3+ AlH potential energy 763 SiF4 spectrum – optical 262 Al3+ + H → Al2+ + H+ 762 – spin- 1 basis states for 506 – oscillator strength 261, 628 + + → + + ( ) 2 Ar N2 Ar N2 988, 989 U n solid harmonics 64 absorptive lineshape 1009 BHe3+ potential energy 764 Z + 1rule 920 abstraction, atom 580 B3+ + He → B2+ + He+ 762 π and 2π pulse 1067, 1068 accidental resonance 750 CCH + H2 −→ C2H2 + H 569 O symmetry ACT theory 566 CF4 spectrum 504 – character table 500 active set of orbitals 315 – rovibrational 503 – correlations with Cn 503 Adams–Bashforth formula 142 ( 2Π) + ( 1Σ +) ( ) CH X N2 X g reaction O 4 symmetry, of hydrogen 156 Adams–Moulton formula 142 484 O(1D ) 968 addition of angular momentum CO2 spectrum, rovibrational 505 O(n) representation theory 93 – magic squares 63 + + C + H2O →[COH] + H 988 β-decay ADDS 973 187 187 C2 symmetry, character table 498 – Re → Os 1358 adiabatic C3 1247 – general theory 1358 – approximation 742, 1128 C6H6 spectrum, rotational 499 – tritium 1358 energy-modified 723 + + −→ + + C2H2 H2 C2H3 H 569 jj coupling 180 in atom optics 1129 ujc Index Subject C60 spectrum, rotational 499 – allowed J values for 178 – capture theory 563, 1363 D2 symmetry 3– j coefficients 31 – correction 469 – character table 498 – explicit forms 33 – elimination 1005, 1073, 1093 – correlation with C2 499 – limiting properties and asymptotic – following 1068, 1099 F + D2 scattering 975, 979 forms 37 – Hamiltonian 742 H + H2 reaction 569 – recurrence relations 36 – ionization 1362 H + NO2 → OH + NO 973 – special cases 69 –lapserate 1261 H2 559, 560 – symmetries 35 – nuclei approximation 722, 723 – Monte Carlo method for 870 – tabulation of 70 – passage, of Rydberg atoms 240 H2CO 560 6– j coefficients, tabulation of 71 –PES 742 H2O 560 9– j coefficients 47 – potential 564 + H2 charge transfer 990 – algebraic form 49 charge transfer 943 + + → + + H2 H2 H2 H2 990 – definition 48 two-state system 810 + + → + + H2 He HeH H 989 – Hilbert space vibrational 535 He2 diatomic molecule 601 tensor operator actions 47 – representation 761 NH3 559 – reduction to 6– j coefficients 49 – state 280, 469, 762 + + −→ + + NH3 H2 NH4 H 569 – relations to 3– j coefficients 48 electronic 742 NO in combustion 1337 – relations to 6– j coefficients 48 vibronic 752 + 3 + N ( P ) + D2 → ND + D 990 – symmetry relations 49 – switching 111 + 3 + N ( P ) + H2 → NH + H 991 9– j, invariant operators 47 – transition 979 1 O( D ) + H2 scattering 979 adjoint action 101 OH (hydroxyl) radical A adsorption 1352 – in combustion 1337 Aharonov–Bohm effect 1136 OH level inversion 1254 ABCD law 1029 Aharonov–Casher effect 1127, OH2+ potential energy 762, 763 Abel transform 974 1136 O− + HF → F− + OH 986 ablation, laser 969 alignment 222, 693 O2+ + H → O+ + H+ 762 above threshold ionization (ATI) – angle 126 O5+ dielectronic recombination 1081 – atomic 936 830 – in circular polarization 1082 – density matrix formalism 128 SF6 spectrum, rotational 499 – peak shifting 1082 – in molecular beams 969 SO(3, R) and SU(2) solid harmonics – resonance substructure 1082 – in photoionization 903 61 absorption see also multiphoton alkali atom STU-parameter transitions 1000 – electron scattering by 368 – definition 130 – coefficient 262, 286, 524, 1000 – laser cooling parameters 1092 – generalized 130, 132 – discrete 186 – molecular beams 968 1472 Subject Index

– Rydberg states of 240 astrophysical factor 1359, 1366 – hydrogenic 153 – scattering by 872, 978 astrophysical plasma 1303 – many-body perturbation theory alkali metal clusters 590 astrophysics 1235, 1397 105, 359 alkali-like spectra 177 asymmetric hybrid model 777 – notation and nomenclature 176, ambipolar diffusion 1325 asymmetric top 493, 519, 560 177, 179 amplifying medium 1014 – Hamiltonian 507 – relativistic 329 Anderson localization 1085 – transition moments for 530 – Thomas–Fermi theory 295 Anger function 837 asymmetry parameter 382, 387 atomic units 3 angular correlation 937 asymptotic expansion 168 – physical quantities in (table) 5 – density matrix formalism 128 – method, for atomic energies 213 atomic waveguide 1132 angular distribution 935, 976 atmosphere atom–surface interactions 1351, – by Doppler spectroscopy 973 – effective thickness of 1260 1352 angular momentum – far-infrared and submillimeter attachment – abstract 16 spectroscopy of 620 – dissociative 576, 836 – cone (diagram) 502 – heating efficiency 1281 theory 722 – coupling scheme 177, 309, 920 – heating rates of 1282 – electron 576 – coupling schemes 313 – ion and electron temperature – electronic 1330 – differential operator realizations of profiles 1283 attosecond pulses 551, 1033 28 – luminosity of 1284 Auger emission 936 – orbital 12 – planetary escape mechanisms Auger process 391, 904, 959 cartesian representation 12 1287 – calculation of width 367 ujc Index Subject spherical polar coordinates 15 – pressure and density variations in – decay of deep vacancies 374 – transfer 126 1259 – post collision interactions 374 – transfer formalism 903 – temperature distribution model – resonant 905 anharmonic pumping 1329 1281 Auger satellites anisotropy parameter 903 – temperature structure 1293 – near-threshold 924 annihilation operator 76, 94, 105, atom Auger transition 919, 920 115, 118, 1108, 1109, 1142 – abstraction 580 – classification 920 anomalous dispersion 262, 1014 –chip 1116 – diagram lines 921 anomalous magnetic moment 227 – counting statistics 1180 –energy 920 – effects in helium 208 – decoherence 1138 – satellites 921 – measurement of 1105 – diffraction 1133 auroral activity 1266 antenna patterns 1171 – optics 1125 autocorrelation function 541 anticommutator 1109 – optics, nonlinear 1126 autodetachment 391, 583 antiproton scattering 756, 873 atomic beam 1132 autoionization 320, 391, 579, 904, anti-Zeno effect 1193 – beam splitters 1134 936 apparent excitation cross section atomic cascade – electron capture 943 934 – source of nonclassical light 1186 – formation of states 391 Appell function 166 atomic clocks 456 –H−(1S ) resonance calculation 395 Araki–Lieb inequality 1217 atomic fountain 456 –He−(1s2s22S ) autodetachment arbitrarily normalized decay curve atomic frame 694 state 393 (ANDC) method 267 atomic lens 1132, 1133 – in multiphoton processes 1079 arc 644 –thick 1132 – MCHF variational method for – Ar mini-arc 644 –thin 1132 316 argon atomic mirror 1131 – minimax method for 316 – photoionization of 385 – evanescent wave mirror 1131 – of Rydberg atoms 244 aromaticity rule 594 – magnetic mirror 1132 – of two-electron systems 398 Arrhenius rate law 563 atomic state function 350 – other applications of 399 association rate 813 atomic structure – saddle-point method for 316 associative detachment 576, 580, – eigenvector composition 181 – scattering resonances 391 983 – eigenvector purity 181 –sumrule 393 associative ionization 836 – ground level tabulation 182 automorphism 81 astronomy 1397 – ground state 182 avalanche pumping 1041 –comets 1248 – Hartree–Fock theory 308 avoided crossing 233, 743, 762 – submillimeter and far-infrared – helium 199 – narrow 746 620 – hierarchy of 177, 178 Axonometric plot 988 Subject Index 1473

B Beer’s length 1070 Bloch equations Bell inequality 1195 – optical 1066 Baker–Campell–Hausdorff identity – detection loophole 1198 – two-photon 1073 38 – effect of local reference frame Bloch operator 712 balance, microscopic 1198 Bloch sphere 1067 – coronal 800 – energy–time entanglement Bloch term, stopping power 1379 – improper 800 1197 Bloch vector 1003, 1067 – proper 800 – locality/timing loophole 1198 – adiabatic inversion 1068 – radiative 800 – loopholes 1198 – orbits of (diagram) 1067 Barkas term, stopping power 1379 – momentum entanglement 1196 – spreading of (diagram) 1069 basis functions – nonpolarization-based tests of Bloch–Siegert level shift 1001 – adiabatic and diabatic 743 1196 blocking temperature 592 – Hylleraas 204 – tested with ions 1198 body-fixed – molecular orbital 476, 518 Bell states 1220 – coordinates 30, 517, 519, 538, – radial scattering 712 Bell-state measurement 1220 557, 771 – Slater 317 Bennett hole 1012, 1016 – frame 742 – spline 317 Bernoulli number 102 Boersch effect 1126 – Sturmian 154, 759 Berry phase 480, 1129 Bogoliubov theory 1112 BB84-protocol 1219 – quantum nature 1189 Bohm–de Broglie deterministic BBK theory 781 Bethe integral 790 quantum mechanics 1205 beam Bethe logarithm 409 Bohr correspondence principle 839 – attenuation method 945 – asymptotic expansion for 209 Bohr formula 236 Index Subject –effusive 1138 – electric field effect 233 Bohr magneton 999 – splitters 1134 – two-electron 208 Bohr–Sommerfeld quantization 839 – supersonic 1138 Bethe model bolometer 969 beam–foil spectroscopy 266, 269 – cross section 1377 Boltzmann average momentum 824 – lifetime measurement 266 – mean excitation energy 1380 Boltzmann distribution BEC 1107 – stopping power 1379 – definition 802 – atom–molecule conversion 1119 Bethe ridge 792 Boltzmann equation 1321 – Bogoliubov theory 1112 Bethe theory for energy loss 1377 bond rupture 550 – critical density 1109 Bethe–Born approximation 794 Born approximation 716, 789, 856, – critical temperature 1109, 1115 – normalization to 934 1362 – dynamical instability 1112 Bethe–Salpeter equation 405 – capture cross section 859 – excitations 1112 betweenness condition 93 – dispersion relation 866 – fragmented 1114 Bhabha scattering 416 – elastic cross section 674 – free gas 1109 Biedenharn–Elliott identity 44, 50 – excitation cross section 858 – gas parameter 1113 Big Bang model 1244 – for alignment in scattering 702 – interference 1115 binary coupling theory – for charge transfer 777 – Josephson effect 1121 – combinatorics 56 – for heavy particle scattering 756, – mean-field theory 1110 – intermediate angular momenta 757 – noncondensate fraction 1113 57 – for ion–atom collisions 789 – optical lattice 1121 – types of coupling 57 – for line strength Sn 838 – orders of magnitude 1117 binary encounter approximation – ionization cross section 859 – persistent current 1118 (BEA) 757, 852, 1376 –planewave(PWBA) 757 – phase diffusion 1122 – double ionization 855 –testof 873 – phase dispersion 1122 binary encounter peak 794 – Thomas process 863 – quantization of circulation 1118 binary peak 953 Born sequence 112 – speed of sound 1112 binary reactions 578 Born series 112, 147, 716 – superfluid 1118 – ion–molecule 580 Born–Huang ansatz 468 – superfluidity 1117 – ion–neutral 579 Born–Markov approximation 1152 – trapped gas 1115 – temperature dependence 581 Born–Oppenheimer approximation –vortex 1117 bipartite quantum state 1216 468, 525, 536, 556, 721, 1129, BEC interference 1189 blackbody decay rate 238 1367 BEC-BCS crossover 1120 blackbody radiation 238, 524, 1006 – Born–Huang ansatz 468 Beer’s law 1000, 1070 Blatt–Jackson formula 668 – breakdown of 469 – atmospheric application of 1267 bleaching 1005 – in scattering theory 721 1474 Subject Index

Bose exclusion principle 507 B-spline 411 central potential model 88, 335 Bose–Einstein condensate 1107 buckminsterfullerene 593 –SO(4) symmetry of 82 Bose–Einstein condensation 1104, bunching, photon 1186 – for photoionization 383 1227 Burshtein–Mollow spectrum 1003 centrifugal barrier 563, 682, 1363 Bose–Einstein statistics 1108 – effect on adiabatic capture 1363 – two-photon interference 1190 C – effect on multiphoton ionization Bose–Hubbard Hamiltonian 1227 1082 Bose–Hubbard model 1122 cage effect 551 – effect on Rydberg states 236 Bose-symmetric molecule 507 caloric curve 600 centrifugal coupling tensor 500 boson 76, 94, 115, 1108 canonical reduction 79 centrifugal potential 558 – commutation relations 115 capture cusp, continuum electron channel – commutators 1108 794 – capture 762 – field operator 1108 capture theory 565 – Coster–Kronig 921 – operator 20 – Born approximation for 859 – coupled channels method 757 bosonic realization of U(4) 95 carbon chemistry, in molecular clouds – decay 261, 320, 921 bottleneck method 1239 – exoergic 570, 580 – for ion–dipole reactions 565 carbon clusters 593 – inelastic, projection operator – for recombination processes Cartan–Weyl form 76 393 815 cascade 934 – photoionization 381, 902 bow ties 263 Casimir effect 1186 – reaction 484, 572, 580 Bowen fluorescence 1237 Casimir forces 209 – scattering 706 ujc Index Subject –incomets 1252 – retarded limit 1172 channel function 706 bracketing theorem 104 Casimir operator 76, 78, 79, 83 channeling Bragg reflection 1134 –ofSO(3) and SO(2) 88 – in de Broglie optics 1132 Bragg regime 1134 catalysis, muon 1360 chaos 1033 Bragg rule, for Bethe logarithms causality – classical 249 1380 – superluminal group delays 1203 – in Rydberg atoms 1085 Bragg scattering conditions, optical – Wigner condition for scattering – intermanifold 249 1060 668 – intermittency route 1033 branching fraction 194, 261 caustics, in WKB approximation – intramanifold 250 branching ratio 1130 – Lorenz model for 1033 – in highly ionized atoms 264 cavitiy QED – period doubling route 1033 – radiative 264 – applications of 1181 – quantum 249 branching rule, group 78, 79 cavity bandwidth 1027 chaotic laser 1033 Breit interaction, relativistic 334, cavity dumping 1030 – spatial pattern formation 1033 352 cavity effects 238 Chapman layer 1277 Breit–Pauli interaction 307, 335, – excitation probability diagram Chapman production profile 1280 478, 709 1168 Chapman–Enskog formula 666 – in MCHF calculations 316 cavity fields characteristic conversion length Breit–Wigner line shape 396 – manipulation of 1137 1056 Bremsstrahlung 374 cavity limit, bad and good 1170, characteristic energy – in dense plasmas 1312 1171 – electron 1324 Brewster window 1027 cavity QED 1167, 1186, 1226 charge exchange 579, 943 Brillouin frequency shift 1060 – dielectrics 1173 – excitation 939 Brillouin gain coefficient 1060 – resonator types for 1171 – reaction 761 Brillouin linewidth 1060 – strong coupling 1173 charge solvation 602 Brillouin scattering – weak coupling 1169 charge transfer 579, 580, 753, 775, – stimulated 1060 cavity ring-down spectroscopy 943, 1294 anti-Stokes field 1060 1342 – double 753 Stokes field 1060 cavity, atomic 1132 – measurement of 989, 990 Brillouin susceptibility 1060 – Fabry–Perot resonator 1132 – recombination 1236 Brillouin’s theorem 311, 351 – gravito-optical 1132 – resonant 667, 1280 – generalized 316 – trampoline 1132 – symmetrical 581 broadband light source 1014 center of mass motion – with core rearrangement 761 Brueckner approximation 408 – quasiseparation in magnetic field charge-coupled device 650 Brueckner equation 404 251 charge–current 4-vector 329 Subject Index 1475 charged-particle–matter interactions – classical models 592 coherent transients 1065 1373 – copper 591 – multilevel generalizations 1071 charmonium 92 – doped 600, 601 coincidence Chebyshev interpolation 137 – electronic properties of 590, 596, – electron–photon 127, 131 chemical kinetics 578, 1336 600, 602 coincidence fringes chemical potential 1111 – electronic spectra of 591, 592 – in a Franson interferometer 1197, chemical reaction – elliptical distortions 591 1198 – gas phase 561, 576 – expansion 109 coincidence measurements 936 – ionic 576 – geometric structures 590, 592, cold atom collisions 1103 chemiluminescent reactions 1285 596, 599, 602 cold-target recoil-ion momentum chemisorption 592, 597, 1352 –giant 595 spectroscopy (COLTRIMS) 922 chemistry – helium 601 collective effects, in ion traps 1102 –ofclusters 592, 596 – ionic 596 collective excitation 592, 1375 – of combustion 1336 – ionization potentials 600 colliding pulse laser 1031 chirped pulse amplification 1031 – magnetic moment of 592 collision chirping 1031 – magnetic properties of 590 – action 664 chi-square curve fitting 138 – mercury 592 – complex 979, 988 chlorine, in upper atmosphere – metal 590 – delay time 664 1299 – molecular 602 – density matrix representation 696 Christoffel–Darboux formula 167 – noble gas 599 – dynamics chronological operator 111 – noble metal 590 and antimatter 873 classical electron radius 999, 1006 – operator 109 – frame 694 Index Subject classical oscillator approximation – phase change in 600, 602 – frequency 1270 280 – phase dynamics 602 in dense plasmas 1307 classical over-barrier model – quantum calculations for 590 – in laser field 940 – charge transfer 943 – reaction rates in 592 –integral 1322 classical scaling 1085 – semiconductor 597 – number 968 classical scattering theory 659, 841, – silicon and germanium 597 – orientation and alignment in 693 976 – spectroscopy of 590, 598, 600, – processes 933 – charge transfer 856 601 – strength 707 – electron removal cross section – states 1226 Gailitis average 712 842 – transition to bulk 590 – strong and weak 1004 – impulse approximation 849 – wetting 601 – theory see also scattering theory – ionization 855 CODATA 1 705 – Thomas process 863 coherence collisional association 576 classical trajectory Monte Carlo – and statistics 1079 collisional broadening (CTMC) method 869, 1362 – atomic 1001 – of Raman linewidths 1338 – nCTMC 870 – first-order field 1146 collisional narrowing 1013 classical trapping resonance 1085 – in three-level processes 1017 collisionally ionized gas 1237 classical-quantal coupling 1362 – induced by the vacuum 1192 collisional-radiative equilibrium Clebsch–Gordan coefficient 82, 558 – nth order 1146 1309 Clebsch–Gordan series 31 –ofmatterwaves 1137 combustion 1335 Clifford algebra 94, 97 – off-diagonal 1024 – models of 1336 Clifford numbers 94 – parameter 937 – nonturbulent flow 1336 cloning photons 1200 – quantum 1146 – pollutant emissions 1337 close-coupling method 706 – two-photon 1073 – turbulent flow 1336 – for heavy particle scattering 757 coherence length 1055 combustion chemistry 1336 closed shell 393, 401, 403, 407, – spatial 1138 – intermediates 1339 408, 411 – wave function collapse 1189 combustion diagnostics, laser 1337 closed-orbit theory 248 coherence time comets 576, 1247 cluster 589 –thermal 1138 – atomic and molecular processes in – adsorbate binding energy 593 coherent anti-Stokes Raman 1250 – alkali metal 590 scattering 630, 1338 – composite FOS spectrum of – binding energy of 591 coherent excitation 129, 694, 699 103P/Hartley 2 1249 – carbon 593 coherent state 1030, 1143, 1154, – density models 1255 – chemistry of 592, 596, 598 1176 – dust tail 1247 1476 Subject Index

– excitation mechanisms 1250 conical intersection 480, 486 – dissipative force 1094 – g-factor as a function of – points of 486 – Doppler 1095, 1100 heliocentric velocity 1252 conjugation operator 118 – Doppler limit 1092 – models 1254 connected cluster theorem 108 – evaporative 1099, 1116 –Oi energy level diagram 1253 connected diagram 108, 109 – frequency standards 1104 – observational data 1247 constant ionic state mode 910 – induced diffusion 1096 – phenomenology 1250 constant kinetic energy mode 910 – induced orientation 1097–1099 – photodissociation in 1254 continuity equation 329 – ion chaos 1102 – photoionization in 1254 – and recombination 806 – ion crystal 1102 – photolytic processes in 1254 – atmospheric 1264 – ion phase transitions 1102 –plasmatail 1247 continuous slowing down – magnetron motion 1102 – radiative transfer effects 1256 approximation (CSDA) 1270, – many ions 1102 – solar flux and fluorescence 1383, 1392 – optical molasses 1095 efficiency 1252 continuum distorted wave (CDW) – parameters, laser 1092 common trajectory approximation 757, 775 – polarization gradient 1097 743 – amplitude 777 – quantum theory 1094, 1097, 1098 complementarity 119 – and Monte Carlo techniques – Raman 1105 complementarity principle 1191 871 – recoil limit 1092 – quantum eraser 1191 – ionization theory 779 – resistive 1102 complete active space 315 – perturbation series 777 – semiclassical theory 1093, 1097, – perturbation theory 475 – projectile 777 1098 ujc Index Subject – reduced form 316 – second-order 777 – sideband 1100, 1102 – wave function 474 –target 777 – Sisyphus 1097 complete scattering experiment – variational 778 effect 1097, 1098 938 – wave function 777 – sympathetic 1103 completely positive map 1221 continuum lowering – temperature of trapped particle complex – plasma-induced 1309 1094, 1095, 1098, 1101, 1103 – collisional stabilization of 562 continuum radiation, atomic 196, – transverse diffusion 1095 – of atomic states 315 608, 642, 904, 1080 – velocity capture range 1094, – probabilities in quantum theory continuum radiation, stellar 1241 1095, 1098 1205 continuum wave function 155, 320, cooling, of stratosphere 1297 – radiative stabilization of 570 706 Cooper minimum 384 – rotation 396, 397 – Dirac equation 161, 330 coordinate systems, scattering 694 – rotation method 396 – normalization of 668, 790, 821 copper – scattering 979 – variational 713, 778 –clusters 591 complexity continuum-distorted wave (CDW) – photoeffect 916 – ion–molecule reactions 991 – relativistic 778 core composite rotor 507 – theory – excited states 392 Compton scattering 919 magnetically quantized 780 – penetration 177 concurrence 1075 contraction of operators 105 – scattering 249 condensation reaction 983 contravariant 4-vectors 327 Coriolis coupling 491, 559, 745, conditional probabilities in quantum controlled-NOT gate 1221 1127 theory 1205 controlled-phase gate 1221 coronal equilibrium 1309 Condon oscillations 286 convergence acceleration 169 correlation conducting sphere 591 convergent close coupling (CCC) – angular 128, 937 configuration interaction 107, 308 method 715 analysis of 696 – expansion 473 conversion factors 4 –CODATA 1 – in photoionization 922 cooling – dynamic 474, 763 – limited 96 – axial motion 1102 decay curve analysis 267 – method – cold collisions 1103 – internal or static 474 contracted 475 – critical velocity 1094, 1095, 1098 – of symmetry types 499 configuration state function 308, – cyclotron motion 1102 –Pauli 755 350, 471 – damping coefficient 1094, 1095, – photon 1031, 1146, 1186 confluent hypergeometric function 1097, 1099, 1101 – polarization 937 162 –diffusion 1093, 1095–1097 – valence 316 confocal parameter 1029 – diffusive heating 1095 – vector, in photodissociation 538 Subject Index 1477 correlation energy 106, 313 coupling crossed beam imaging apparatus – definition of 313 – electronic and rotational 482 992 – diagrammatic expression for 365 coupling schemes crossed beam imaging technique – Thomas–Fermi Z−1/3 expansion for – term symbols 179 991 300 coupling strength crossing distance 979 correlation function – atom–molecule 1120 Crothers semiclassical approximation – master equation 1156 coupling, atomic 785 26+ – photon 1146 – J1 j or J1 J2 180 Cu dielectronic recombination – quantum regression hypothesis – J1l or J1 L2 (J1 K) 180 832 1156 – LS (Russell–Saunders) 177 cubic graphs, classes of 60 – scattering 706 – LS1 (LK) 181 cubic splines 136 – two-time 1156 – jj 178 cuboid crystal 596 correlation potential 706 covariance matrix 1217 curve crossing 535, 807, 810, 978 – exchange 476 covariant 4-vectors 327 – matrix elements of AlH3+ 768 – Lee, Yang, Parr expression for covariant perturbation theory 413 curve fitting 137 302 CPT invariance 429, 430 – chi-square 138 correspondence principles creation operator 76, 94, 105, 115, – least squares 137 – Bohr 839 118, 1108, 1142 cusp conditions, Kato 200 – Bohr–Sommerfeld quantization critical angle cylindrical mirror analyzer 910 839 – for total reflection 1131 – equivalent oscillator theorem 840 critical density 1109 D – Heisenberg 839 critical laser intensity 1081 Index Subject – in Rydberg collisions 839 critical temperature 1109 damped harmonic oscillator 1153, – strong-coupling 840 critical velocity 1118 1154, 1157 cosmic rays 1238 cross section 659, 706, 882 damped two-level atom 1154, 1155 Coster–Kronig transition 920 – Bethe model of 1377 – in squeezed bath 1154 – super 920 – classical 659, 841, 977 damping rate Coulomb – collision strength 930 – longitudinal 1066 – boundary conditions 776, 779 – density matrix formalism for 131, – transverse 1066 – coupling parameter 1305 695 dark state 1018, 1073 – explosion 1084 – differential 661, 664, 665, 706, Darwin term 308, 709 – function 155 716, 717, 770, 930, 976, 984 dayglow 1284 – gauge 379 binary encounter approximation – spectra of selected planets 1287 –law 1 852 – terrestial spectrum 1286 – logarithms 1307 for Coulomb scattering 819 De Broglie optics 1125 – phase shift 821 – double differential 717, 791 – gravitation 1127 – repulsion 1360 – elastic scattering 661 – Hamiltonian 1126 – scattering 671, 819 – for multipolar relaxation 223 – rotation 1127 modified, effective range formula – frame transformation 517, 792, De Broglie wavelength 824 669 975, 985 –thermal 1138 – trajectory 754 – Galilean invariant 790 Debye length 1305 – wave, asymptotic form 790 –integral 661, 718, 751, 930 Debye shielding 1325 Coulomb–Born approximation – moment transfer 661 decay 1362 – moments of 661, 708, 814, 1378, – free induction 1068 Coulomb–Stark potential 239, 240 1380 – purely radiative 1005 counter-intuitive pulse sequencing – momentum transfer 930, 1320, decay rate 1073 1326 – inelastic collisions 1004 counting statistics 1186 – Rutherford 155, 671, 794, 819, – spontaneous 215, 1004 coupled cluster (CC) 109 1376 decoherence 1162, 1223 – approximation 401 – selection rules 932 decoherence times 1224 – calculations 353 – total scattering 707, 839, 933 decoherence-free subspace 1224 – expansion 109, 337 – transport 665 deflection function 976 – method 109, 472 – triple differential 717, 783 – formulae 660 coupled-channels method 757 crossed beam 971 deflection parameter 643 coupled-channels optical (CCO) – for ion–molecule reactions 988 degeneracy groups (algebras) 87 method 716 – ion-laser 265 degenerate Fermi gas 1109 1478 Subject Index

degenerate four-wave mixing 1341 – spectroscopic 969, 970 different-orbitals-for-different-spins delay time, collisional 664 – surface ionization 969 (DODS) 110 delayed choice, in quantum – vacuum photodiode 649 diffraction 1133 measurement 1191 detector conversion factors 1385 –atom 1133 Delbrück scattering 917 detuning 1001, 1010, 1024, 1058, – electron 1133 delta function 1066, 1081, 1091, 1128, 1175 – Fraunhofer limit 1133 – electric field effect on matrix – two-photon 1073 – Fresnel regime 1133 elements 233 deuterium 437 – Laue geometry 1134 delta rays 959 – equation of state 1315 – limit 1133 Demeur’s formula, electron energy deuteron charge radius 443 –neutron 1133 shift 416 Deutsch–Jozsa algorithm 1222 – small-angle 679 dense coding 1220 diabatic – superluminal group delays 1203 density functional theory 97, 98, – electronic state 742 diffusion 302, 475 – Hamiltonian 742 – coefficient 806, 1265, 1323 – locality 303 – matrix elements 767 – cross section see momentum density matrix 123, 221 – passage, of Rydberg atoms 240 transfer cross section 708 – diagonal representation 222 –PES 742 – free 1323 – equation of motion 1010 – potential – induced 1096 – for polarized beams 699 for mutual neutralization 810 diffusion method – for relaxation processes 125 – state 469, 1134, 1362 – for recombination processes 814 – for thermal equilibrium 125 diagrammatic technique 109, 359 diffusional-drift ujc Index Subject – from Stokes vector 696 diatomic molecules – in recombination processes 806 –full 126 – binding with noble gases 482 dipole – reduced 126 – dissociative electron–ion – approximation 999 – reduced spin 131 recombination 583 – coupling, of atoms and fields – two-level atom 1004, 1010, 1023, – electron scattering by 721 1169 1025 – noncrossing rule 470 – critical strength 1362 density of states – nonrigid 95 –force 1096 – classical 841 – one-electron 92 –moment 110, 998 – photon 215 – radiative transitions in 520 – potential 575 density operator 123 – rigid 95 – response function 1396 – irreducible components 127 – symmetric top structure 492 – scattering 686, 1345 – reduced 1152, 1159 – Thomas–Fermi ‘no binding’ result dipole approximation 902 – time evolution 124 295 dipole force 1094 depolarization 130 – vibrational structure 480 Dirac energy levels 438 – in Rydberg atom collisions 836 Dicke narrowing 1013 Dirac equation 328 – postcollisional 697 dielectric – angular distributions 339 depth-dose curve 1383 – cavity QED in 1173 – behavior near the origin 340 derivative coupling 476 – constant 3 – continuity equation 329 derivative, numerical approximation dielectronic recombination 800, – Coulomb Green’s function 161 of 140 829, 961, 1236, 1330 – eigenvectors 338 desorption 1352 –Au76+ 832 – finite nuclear models 341 detachment 983 – cross section 821 – free electron 343 detailed balance 623, 817, 822, –Cu26+ 832 – hydrogenic 91, 157 1006 – data generation 829 dynamical effects 342 detailed balancing 939 –inplasmas 833 – hydrogenic solutions detector 648 –O5+ 830 radial moments 342 – charge-coupled device 650 difference frequency generation – in scattering theory 709 – far-infrared 619 1056 – magnetic field 228 – ionization chamber 650 differencing algorithms 143 – nonrelativistic limit 341 – microchannel plate 649 differential cross section 908, 930 – point nucleus 341 – neutral particles 969 differential equations – radial density distributions 339 – nonoptical 969 – numerical methods 141 – spherical symmetry 337 – photographic plate 649 ordinary 141 jj-coupling subshells 339 – photomultiplier tube 649 – power series solution 146 eigenstates 338 – silicon photodiode 650 differential reactivity method 990 – square integrable solutions 341 Subject Index 1479

Dirac gamma matrices 328 dosimetry 1389 – for heavy particle scattering 755, Dirac–Hartree–Fock method 351, double excitation 906 778 1358 double ionization 780, 904, 906, Einstein A and B coefficients 237, Dirac–Pauli matrices 94 922 261, 286, 1005, 1023 direct dynamics 544 – binary encounter approximation for – molecular 524 direct excitation cross section 934 855 Einstein–Podolsky–Rosen (EPR) direction cosine matrix elements 22 – by antiprotons 756 paradox 1195 discharge – in heavy particle scattering 755 elastic scattering 661, 705, 933, 976 – cold cathode 1327 double Pfaffians – Born approximation 674 –flash 644 – skew symmetric matrices 65 – cross section 368, 661 –H2,D2 644 double-well potential 1121 – distorted wave approximation 674 – hot cathode 1328 doubly excited states 392 – effective range formulae 668 – noble gas 644 down conversion – in reactive systems 683 – positive column 1327 – energy–time correlations 1189 – intermediate and high energy 714 –rf 1331 – nonclassical features 1145 – low energy 705 discretization of the continuum 758 – polarization entanglement 1196 – of electrons 705 disentanglement 1074 – spontaneous 1187 thermal energy loss function dispersion – suppression of spontaneous 1192 1270 – anomalous 1014 dressed atom – oscillatory structure effects 683 – normal 1014 –two-level 1002 – small-angle 680, 681 – optical 262 dressed state 1002, 1161 electric dipole interaction 216, 380, – quantum mechanical cancellation – in electron scattering 724 998 Index Subject 1202 drift velocity 1323 – finite nuclear mass effect 216 dispersion relation 1129 – definition 1321 – length, velocity and acceleration – for Thomas scattering 866 dynamical algebras 87 forms 380 dispersive behaviour 1010 dynamical group – molecular 520 dispersive phase 1136 – noncompact 87 – motional correction 1127 displacement operator 1143 dynamical symmetry 492, 523 – two-level atom 1001 dissociation 562, 576 dynamical tunneling 494 electric dipole moment 216, 836, – electron impact 935 Dyson equation 112, 401, 403, 406, 998 – probabilities 804 408 – molecular 526 – spontaneous 562 Dyson orbital 368 electric dipole phase 1136 dissociative attachment 576, 722 electric dipole transition 187, 321, – in Rydberg atom collisions 836 E 380 dissociative ionization 1269 – finite nuclear mass effect 216 dissociative recombination 576, e–2e measurement 936 – helium results 216, 217 800, 807, 1239, 1274, 1277, 1294, Eagle mount 647 – hydrogenic matrix elements 836 1330 Earnshaw theorem 1099 – molecular 520, 526 – in the atmosphere 1295 Eckart coordinates 761, 765 – selection rules 381 – of diatomic ions 807 ECPSSR 757 – Stokes parameters for 131 – polyatomic 566 effective Hamiltonian 110 electric field distinct row table 96 effective range, in elastic scattering – atoms in 231, 247 distorted wave approximation 716 668 – hydrogenic wave functions in – for dielectronic recombination effective thickness of the atmosphere 232 833 1260 – operator 1142 – for elastic scattering 674 effusive beam 1138 electric multipole 258, 997 distorted wave Born approximation eigenpolarization 1054 electric polarization 999 – strong potential 793, 795 eikonal electric quadrupole transition 187, distribution functions –Bornseries 716, 726 192 – use of in Rydberg collisions 840 – criterion 776 electromagnetic field 1168 Doppler broadening 1012, 1103 – distorted state 779 – quantized 331 Doppler cooling 1095, 1100 – in de Broglie optics 1130 electromagnetic interaction 413 Doppler spectroscopy 973 – phase 673 electromagnetic units 1 Doppler-free resonance 1018 eikonal method electron Doppler-free spectroscopy 458, – for forward reactive scattering – magnetic moment 429 1015 684 – relative atomic mass 437 1480 Subject Index

electron affinity 321, 1330 – collisions with excited species – swapping 1201, 1220 –ofclusters 591, 598 939 – witness 1217 electron attachment 578, 582 – diagrammatic perturbation theory enthalpy change 576 electron beam ion traps 273 361 entropy electron capture 932, 955 – excitation cross sections 934 – change 576, 577 – Born approximation for 859 –inalaserfield 723, 726 – entanglement 1218 – cross section 764, 767, 770 electron–electron interaction – reduction 1181 – from hydrogen 944 operators – Shannon’s information 233 – impact parameter dependence 768 –Breit 334 Epstein–Nesbet perturbation theory –intheAl3+/Hsystem 767 – Coulomb 334 106 – influence of rotational coupling – Feynman 334 equation of continuity 1117 768 – Gaunt 334 equation of state – Monte Carlo method for 869, 870 electron–ion collisions 705 –deuterium 1315 – orientation effects 770 electron–ion recombination 575, –plasmas 1304 – state-selective 872 583 equation-of-motion method 110 – Thomas double-scattering 777 – working formulae 802 equilibrium constant 577 electron collisions electron–molecule collisions equitorial airglow, spectrum of – with trapped atoms 939 – inelastic 978 Jupiter 1289 electron configuration 176 – theory 720 equivalent electrons 176 electron correlation 96, 106 electron–photon coincidence equivalent oscillator theorem 840 – density functional theory 475 – geometry of 132 Euler angles 559 ujc Index Subject – Green’s function techniques for – measurement 936 Euler’s method 142 401 electron–photon excitation, Euler’s theorem 594 – in heavy particle scattering 756 simultaneous 724 evanescent light 1131 – many-body perturbation theory of electron–positron field 329 evanescent matter wave 1131 353, 365 electro-optic effect 1061 evaporative cooling 1099, 1116 – photoionization effects 379, 902, – linear 1061, 1062 evolution operator 111 922 – quadratic 1061 exchange asymmetry 938 – relativistic 353 emission intensity 186 exchange potential 706, 707 – wave function methods for 472 endohedral complexes 595 – gradient corrected 302 electron diffraction 1133, 1344 energy conversion factors 4 – local 722 electron energy loss 1270, 1343, energy disposal in elementary exchange reaction 1375, 1378, 1379, 1391 reactions 975 – Monte Carlo method for 869, 870 – degradation spectra and yields energy loss 931, 1374 exchange-correlation potential 302 1392 – cross section 1375, 1376 – validity tests 302 – electron transport 1392 – electron 1270 excitation in Fermi gas 1115 – spectroscopy 1345 – spectrum 931, 954 exclusive process 755 – spectrum in molecular hydrogen – straggling 1381 exohedral complexes 595 1393 – total cross section 1378 exosphere, terrestial 1261 electron impact processes 929, 1328 energy transfer extended X-ray absorption fine electron optics 1125 – cross section 841 structure (EXAFS) 1376 electron scattering – in combustion reactions 1336 extinction coefficient 1070 – by complex atoms 725 energy–intensity model, of molecular – by ions 725 transition strengths 518 F electron self-energy 353 entangled atoms and photons electron shell 176 1181 f value 186, 187, 194 electron shelving 1104 entangled states 1137, 1189, 1195 Fabry–Perot etalon 1027 electron transfer 943 entanglement 1216 Fabry–Perot resonator 625, 1132 electron transition moment, – apparatus to demonstrate 1197 factoring algorithm 1223 molecular 526 – energy–time 1197 factorization lemma 109 electron translation factor 776 – for quantum cryptography 1201 Fano factor 1394 electron transport – generation of 1181 Fano profile 904 – and degradation 1392 –momentum 1197 Fano, Ugo 1397 – in a molecular substance 1394 – of formation 1218 Fano–Lichten model 955 electron–atom collisions 705, 929 – orbital angular momentum 1197 Faraday dark space 1327 – benchmark measurements 934 – polarization 1196 Faraday effect 1016 Subject Index 1481 far-infrared (FIR) spectroscopy 615 fine structure – power series expansion for 856 – detectors 619 – atomic 177 – representation as microcanonical – instrumental resolution 618 – depolarization effects of 697 distribution 838 – spectrometer (diagram) 616 – Hamiltonian 307 – semiclassical limit 838 – tunable sources 617 – hydrogen 444 fountain, atomic 1104 fault tolerant computing 1223 – of helium 218 Fourier analysis 139 feedback 1023 – rotational 497, 500, 504 Fourier transform (FT) feedback control 552 – transition rates, in Rydberg – discrete 139 Felgett advantage, in Fourier collisions 844 –fast 139 transform spectroscopy 610 fine structure constant, from g − 2 – mass spectrometry 935 femtosecond laser pulses 644, measurement 432 – spectroscopy (FTS) 263, 608, 615 1031, 1035, 1045, 1080 fine structure effect 939 alignment techniques 612 Fermi – on electron scattering 939 spectrum generation 610 – contact term 319 – on low temperature reactions 565 four-wave mixing 1058 –energy 1109 fine structure transitions – optical phase conjugation 1058 –gas 1109 – cross sections for – sidemode squeezing 1145 degenerate 1109 in Rydberg collisions 844 fractional parentage 117–119 excitations 1115 – measurement of 615 – coefficients of 117 Thomas–Fermi approximation fine-structure constant 3 fractional revival 1072 1115 finite basis set method 230, 714 fragmented condensate 1114 –sea 1109 finite element method 144 frame transformation 517, 792, 975, – temperature 1109 finite group action 24, 25 985 Index Subject – vacuum 107 finite matrix method Franck–Condon – virtual photon method 1377, 1380 – for atoms and molecules 351 – factor 525 Fermi’s golden rule 215, 320, 919, Floquet theory 726, 1086 effective, for dissociative 1014 – for atoms in a laser field 726 recombination 809 Fermi–Dirac statistics 1109 fluctuation potential 332 sum rule 525 fermion 76, 94, 115 fluence spectrum 1374 – mapping 542 – anticommutator 1109 fluorescence efficiency 1250 – overlap 579 – commutation relations 115 fluorescence process 904 – principle 285, 525, 540, 887, 935 Fermi-symmetric molecule 507 –incomets 1251 –region 540 Feshbach projection operator 393, fluorescence yield 921 Franson interferometer 1197 710, 715, 722 fluorescent scattering 1285 Fraunhofer Feshbach resonance 392, 395, 396, flux–velocity contour map 976 – diffraction 1133 542, 710, 1111 Fock expansion 200 black sphere 684 – vibrational predissociation and Fock matrix for – limit 1133 radiative stabilization mechanism Dirac–Hartree–Fock–Breit method free electron gas 302 570 – Breit interaction 352 free induction decay 1068 Feynman causal propagator 330, – Coulomb interaction 352 free radicals 1336 333 – density matrix 352 frequency Feynman diagram 107, 359 – one-electron Hamiltonian 351 –comb 458 Feynman–Vernon–Hellwarth picture Fock state 1108, 1176 – pulling 1027 1003 Fokker–Planck equation 1093, – shifter, laser 1043 field 1154, 1158 – stabilization 1042 – atoms in 227 – damped harmonic oscillator – standard 186, 456, 1104 – classical 1168 1154 frequency comb, optical 631 – dipole coupling 1169 forbidden bands 286 – application to spectroscopy 631 – electromagnetic 1168 forbidden transition 187, 192 Fresnel – nonclassical features 1179 – molecular 530 – diffraction 1133 – operator 1108 form factor 791, 838, 916 – formula 1131 – quantization 1142 – connection with generalized – number 1029, 1030 – quantum 1168 oscillator strength 838 – regime 1133 –shift 256, 257 – expressions for discrete transitions – zone plate 1133 – states 1162 858 fullerene 593, 594 – theory, classical 1110 – general trends 858 – buckled 598 filter, optical 651 – inelastic 1377 – endohedral complexes 595 1482 Subject Index

– formation 595 –lowering 92 – SU(2) – rotational spectrum of 506 –raising 92 parametrization of representation functions, representation of 135 – weight 92 functions 18 fundamental constants 455, 460 geometric phase 1136 representation functions 21 furnace method 262 germanium clusters 597 representation, orthogonality furry bound interaction picture g-factor properties 21 329 – electron 429 representation, symmetry fusion plasma 1303 – hydrogenic carbon 432, 437 relations 23 fusion, nuclear 1360 – hydrogenic oxygen 432, 437 solid harmonics 60 GHZ test of nonlocality 1199 –U(2) spin 96 G giant clusters 595 –U(2n) spin orbital 96 Gibbs free energy 576 – Abelian 76 gain clamping 1025, 1026 Glauber approximation 716, 757 – dynamical 87 gain coefficient 1023 Glauber–Sudarshan distribution noncompact 87 gain media 1023 1149 – Euclidean 89 – homogeneously broadened global warming 1293 –Lie 327 1025–1027, 1033 glory and rainbow scattering 662, –Lorentz 89, 327, 328 – inhomogeneously broadened 679, 681, 887, 976 – molecular symmetry 493 1026, 1027, 1033 – glory diffraction oscillations 681 – octahedral 498 gain saturation 1025, 1026 – rotational rainbow 977 – orthogonal 493 Galerkin method 144 godparent 117 – parametrized SO(3, R) ujc Index Subject Galilean invariant cross section 790 Goldstone diagram 107 representations 20 gas phase collisions and chemistry gradient force 1094, 1096 – parametrized SU(2) representations 561, 576 Grassman algebra 97 20 – astrophysical applications 1235, gravitational wave detection 1206 – Poincaré 327, 328 1247, 1265 –LIGO 1206 – representation theory 92 –clusters 590 –LISA 1207 – rotation 77, 88, 493 gauge – quantum nondemolition 1206 – semisimple 76 – choices 414 – resonant mass-detector 1206 – simple 76 –invariance 401 Green’s function 111, 395, 401, 710 – symplectic 77 – length and velocity 215, 380, 724 – continuum distorted wave 776, – tetrahedral 498 – symmetry 1114 777 –U(n) orbital 96 – transformation 227 – Coulomb 159 – unitary 76 Gaunt factor 823 – Coulomb Dirac 161 group action – semicalssical representation 838 – four-point 405 – Hilbert spaces 26 Gaussian – Hartree–Fock propagator 366 – matrix group actions 26 – beam 1029 – in formal scattering theory 146 – relation to angular momentum – chaotic field 1079 – potential scattering 112 theory 26 – quadrature 140 – propagator 333 group and Lie algebra realizations – state 1217 – radiative corrections 408 27 – units 1 – radiative transitions 406 group delay 1203 Gegenbauer polynomial 16, 169, – Thomas process 865 group generators 75, 77 841 – two-point 402 group reduction 79 Gel’fand tableaux 93 greenhouse gases 1296 group velocity 1025, 1071, 1130 Gel’fand–Paldus tableau 96 Greenstein effect, in comets 1252 – dispersion Gel’fand–Tsetlin canonical chain Gross–Pitaevskii equation (GPE) cancellation of 1202 93 1110 pulse propagation 1055 Gell–Mann and Low formula 111 – numerical methods 1113 – in dispersive medium generalized gradient approximation group 1020 (GGA) 302 – SO(3) – single photon 1202 generalized oscillator strength 790, Euler–Rodrigues parameters of – superluminal 1203 931, 954, 1377 representation functions 18, 21 gyromagnetic ratio 999 – connection with form factor 838 representation, orthogonality gyro-rotor generator properties 21 – perturbed, diagram 510 – atomic operators as 76 representation, symmetry – spherical, diagram 510 – commuting 77 relations 23 – symmetric, diagram 510 Subject Index 1483

H – electron capture resonance 932 Hong–Ou–Mandel interferometer – electron scattering processes 933 1190, 1191 Hadamard gate 1221 – energy structure and notation 177 – ultrafast measurements 1202 Hahn–Banach theorem 1217 – ground-state expectation values Hönl–London factors 527 halfway house VCDW 779 (table) 208 –sumrules 528 halogen molecule scattering 979 – ionization energy (table) 211 Hook method 262 Hamilton optics 1130 – ionization of 791 hot atom chemistry 1397 Hamilton–Jacobi equation 782 – isotope shift (table) 207 HRTOF 980 Hanbury–Brown and Twiss effect – nonrelativistic eigenvalue (table) Hubble Space Telescope 1248 1031, 1146, 1147, 1186 205, 206 Hugenholtz diagram 107 Hanle effect 130, 265 – nonrelativistic energies for He-like Hund’s coupling cases 528 harmonic generation 1056, 1082 ions 207 Husimi’s function 1151 – by elliptically polarized fields – oscillator strength (table) 216, Huygens principle 1133 1083 217 hydrodynamic escape mechanism – conversion efficiency 1056 – quantum defect extrapolation 1287 – higher-order 1061, 1062 (table) 212 hydrogen 437 –third 1057 – singlet-triplet mixing (table) 217 –atom 459 harmonic oscillator – threshold ionization of 784, 785 – atomic beam 968 –damped 1153, 1154, 1157 – total energies for 208 – electron capture 944 – length scale 1110 helium clusters 601 – electron impact excitation of 699 harmonic plateau 1082 helium-like ions 302 – fine structure 444 harmonium 92 – energy structure and notation 177 – group theory of 81, 88 Index Subject harpoon mechanism 978 Hellmann–Feynman theorem 303, – infrared lines of 882 harpooning distance 978 766 – ionization by proton impact 793 Hartree energy 5 Helmholtz equation 1129 –Lambshift 444 Hartree term 404 hemispherical analyzer 910 – O(4) symmetry 156 Hartree–Fock approximation 106, Henry α parameter 1028 – radio lines of 882 308, 309, 401 Hessian matrix 469 – SO(4) symmetry 89 –diagrams 364 heterodyne detection 1148 – SO(4,2) symmetry 90 – multiconfiguration 313, 315 hidden variables 1196 hydrogenic atoms 184, 437 – time dependent 756, 1359, 1362 high energy-density physics (HEDP) – algebraic approach to 91 Hartree–Fock diagrams 108 1305 – electric dipole transition integrals Hausdorff formula 110 high field seeker 1129 837 healing length 1111 highly stripped ions 264, 269, 1359 – excited state energies in magnetic heat bath 1152 – in astrophysics 1238 fields (table) 231 heat capacity, ideal gas 968 Hilbert transform 1012 – expectation values (table) 214 heats of formation 577 Hohenberg–Kohn theorem 475 – ground state energies in magnetic Heaviside–Lorentz units 1 Hohenberg–Kohn variational fields (table) 230 – natural 4 principle 301 – Monte Carlo calculations for 871 heavy particle scattering 754, 775 hole burning 629 – N-dimensional 91 – analytical approximations 757 – spatial 1012, 1026, 1027, 1030 – nuclear size correction (table) 230 – dynamics of 873 – spectral 1012, 1027, 1030 – perturbations of 91 – forced impulse method 756 hollow cathode 644 – structure and notation 176 – independent event model 756 –lamp 263 hydrogenic ions 184, 194 – independent particle model 756 Holstein–Biberman theory 287 Hylleraas functions 201, 393 – many-electron treatments 756 Holtsmark formula 1306 – Hamiltonian matrix elements 204 – numerical calculations 757 homodyne detection 1147 – integral recursion relations 204 heavy-ion storage ring 275 homogeneous broadening 1011, – integrals involving 202 Hegerfeldt’s paradox 1202 1025, 1026, 1103 Hylleraas–Undheim–MacDonald height parameter 698 homologous sequence 185 theorem 201, 309, 759 Heisenberg correspondence principle homomorphism hyperfine splitting 839 – SU(2) → SO(3, R) 11 – hydrogeen 422 helicity, photon 695 homopause 1260 – muonium 421 helium – characteristics of planets and hyperfine structure 253, 319, 506, –2s2p1P 0 autoionization states satellites 1260 1364 394 homosphere 1260 – anomalies 259 1484 Subject Index

– depolarization effects of 697 intensity quantities see also inversion symmetry 493 – energy splittings 254 oscillator strengths etc. 193 – of wave functions 516 – intensities 255 – atomic inverted medium optical pumping – normal 258 multiplet values 193 1014 – tetrahedral nuclear 505 regularities, scaling 194 Ioffe–Pritchard trap 1116 hypergeometric function 34, 162 systematic trends, sequences ion beam spectroscopy 269 hypergeometric series form of 194 ion crystal 1102 WCG-coefficients 35 – molecular 518 ion–atom collisions 789 hyperpolarizability 1053 fits to experiment 520 – differential 948 hyperradius 782 interaction picture 111, 124 – dynamics of 765 hyperspherical coordinates 398, 781 interaction-free measurement 1194 – electron spectroscopy 948 – in ion–atom collisions 772 interference – electron spectrum 959, 960 – between atomic BECs 1189 – high energy cross section 790 I – Buckyball 1188 – low energy 943 – Feynman rules 1190 – multi-electron 957 imaginary time 1114 – filter 651 – nonperturbative processes 955 imaging – Franson interferometer 1197 – pertubative processes 951 – ion–molecule reactions 991 – fringes 1135 – photon spectroscopy 947 impact parameter approximation – in de Broglie optics 1135 – quasifree electron 961 751, 776 – low-intensity 1186 – reactions 761 impulse approximation 795, 845 – matter–wave 1188 – recoil momentum spectroscopy ujc Index Subject – quantal – porphyrine 1188 948 weak binding condition 849 – single-photon 1188 – relativistic 1359 – semiquantal 851 – two-photon, or fourth-order – state selective 947 inclusive process 755 1190 – translational energy spectroscopy independent interferometer 947 – event model 756 – division of amplitude 1135 ion–atom interchange 580 – particle model (IPM) 755 – division of wavefront 1135 ion–dipole reactions 564 – processes approximation 831 – Hong–Ou–Mandel 1190 ionic clusters 596 index of refraction 999, 1009, 1070 – loop 1135 ionic reactions, table of 576 – complex 1011, 1014 – Mach–Zehnder 1135 ionization 779, 951, 962 infinitesimal generators 12 – optical Ramsey 1137 – adiabatic 1362 information content – scanning Michelson 609 – balance – single photon 1200 – stimulated Raman 1137 in plasmas 1308 Infrared Space Observatory 1245 – three-grating 1135 – by high energy particles (cross infrared spectral region, definition – young double slit 1135 section table) 1378 181, 607 intermediate coupling 181 –chamber 650 infrared spectroscopy 607 internal conversion – classical 240 inhomogeneous broadening 1012, – in predissociation 536 scaling 1085 1025, 1026 International Ultraviolet Explorer – cross section inner shell processes 951 1248 Born series method 719 inner shell vacancy rearrangement interpolated functions, derivatives of distorted wave method 719 387 141 exterior complex scaling (ECS) instability, thermodynamical 1115 interpolation 135 method 718 integral approximation 139 – Chebyshev 137 pseudostate method 718 – adaptive quadrature 140 – cubic spline 136 time-dependent close coupling – compsite quadrature 140 – iterated 136 method 718 – Gaussian quadrature 140 – Lagrange 136 –diffusive 1085 – polynomial quadrature 139 – orthogonal function 137 – double 780 integral cross section 930 – rational function 136 binary encounter approximation integral equations 146 intersection, conical 486 for 855 – numerical methods 141 interstellar gas clouds 576 – electron impact 790, 935, 969, integral transforms 146 – molecules observed in 1240 970, 1268, 1328 integral, atomic and molecular 105 intersystem transition, atomic 177 empirical formula for 969 integration in imaginary time intrinsic relaxation 1071 – electron scattering theory of 717 1114 invariance groups (algebras) 87 –field 240, 242 Subject Index 1485

– free-free transition picture 795 irreducible tensor operator 38, 127 Kepler realization of SO(4) 89 – in heavy particle scattering 753, –algebraof 39 kernel function 147 755, 758 – examples 40 kinematic analysis, scattering 985 – in ion–atom collisions 789 – unit tensor operators 40 Kirkwood function 1151 – mechanism 935 – Wigner–Eckart theorem 39 Klein–Gordon equation 91 – Monte Carlo method for 869, 870 irreducible tensor operators 224 Kleinman symmetry 1052 – multiphoton (REMPI) 970, 1078 irreversible process 125 Klein–Nishina cross section 919 – multiple 1081 isentropic expansion 967 Klots unimolecular decay theory – multistep 1080 isobaric nuclei 1358 568 – nonperturbative 1081 isoelectronic sequence 185 K-matrix 707 – of light target atoms 952 isoionic sequence 185 Kohn variational method 713, 783 – potential isolated pentagon rule 595 Kohn–Sham method 302, 475 in Hartree–Fock approximation isolated resonance approximation Koopman’s theorem 311, 351 313 831 Kramers cross section, for of clusters 591, 596, 598 isomer shift 257 photoionization 818 of ground state atoms (table) isomers 594, 595, 597 Kramers–Henneberger frame 182 isonuclear sequence 185 transformation 726, 1083 – projectile electrons 796 isoscalar factor 82 Kramers–Kronig relation 866 – stabilization in intense laser fields isotope separation 1080 Kroll–Watson formula 725 1083 isotope shift 200, 256, 318 Kronecker product 79 –Stark 240 – residual 257 – reduction 31 – state-selective field 240 isotopic labeling 580, 581 krypton, one-electron 264 Index Subject – strong field approximations isotropic harmonic oscillator 90 1087 L – surface 969 J – tunneling 240, 1081 ladder operator 88 – yield spectrum for molecular Jackson–Schiff correction factor, in Lagrange interpolation 136 hydrogen 1393 electron capture 859 Lagrange multiplier – yield, definition 1394 Jacobi coordinates 540 – in Hartree–Fock theory 310 ionizing radiation 915, 1389 Jacobi polynomials 15 Laguerre polynomial 166 – charged particles 951, 1391 – relation to SU(2) group Lamb dip 629, 1027 – condensed matter effects 1396 representations 21 –inverted 1016 – neutrons 1391 Jacobian, frame transformation 975 – stabilization 1027 – photons 915, 1391 Jacquinot advantage, in Fourier Lamb shift 1159 – track structures 1395 transform spectroscopy 611 – helium 208 ion–molecule reaction 563, 564, Jacquinot stop 612 – hydrogen 444 581, 983, 1274 Jahn–Teller effect 536 Lamb–Dicke regime 1101 – atmospheric 1272 Jaynes–Cummings model 1002, Landau critical velocity 1118 – cross section 987 1175, 1226 Landau level 227 – ideal experiment 984 Jeans escape mechanism 1287 – relativistic 228 – imaging 991 Jeffrey–Born phase function 663, Landau–Dyhne formula 1083 – in interstellar clouds 1241 673 Landau–Lifshitz cross section 663, – instrumentation 985 Jeffreys connection formula 783 680 – kinematic analysis 985 Jellium model 590 Landau–Zener model 764, 769, 979 – product formation rate 984 Josephson effect 1121 – charge transfer 943 ion–neutral reaction 575, 579 – transition probability 242, 811 ionosphere, electron density profile K Landé g-value 184, 229 1279 Langevin equation ionospheric KAM torus 1085 – damped harmonic oscillator 1157 – density profiles 1277 Kapitza–Dirac effect 1134 – quantum mechanical 1157 – regions 1271 – geometry of 1134 Langevin orbiting 946 ion-pair formation, in Rydberg – near-resonant 1133 Langevin rate coefficient 564, 806, collisions 836 Kato cusp condition 200 1274 ion–quadrupole interactions 1274 – in Thomas–Fermi theory 299 Laplace–Runge–Lenz vector 89 irreducible representation 78 Keldysh parameter 1081 Larmor precession – of SO(2,1) 88 Kepler orbits 869 –usedasaclock 1203 1486 Subject Index

laser –ring 626 – metal vapor 1037 – atmosperic transmission 1041 – selective excitation 265 – methyl fluoride 1037 – beam quality 624 – short-pulsed 1038 – mixed gas 1037 – categories (table) 1035 – single-mode 1025 – molecular 1037 – coherent states 1030 – spectroscopy –N2O 1038 – combustion diagnostics 1337 far-infrared 616 –N2 1038 – configuration 623 ultraviolet 641 – Nd-doped fiber 1042 – designs 625 visible region 623 – Nd–YAG 1038 – diagnostics 1335, 1341 – stability parameters 625 – Ne, Ar, Kr, Xe 1036 – Doppler velocimetry 1337 – sub-picosecond 626, 1040 – neutral atom 1036 – emission – theory – nuclear pumped 1046 spectral range of 1036 semiclassical 1025, 1027 – organic dye 1044 – excitation 939 – tunable (table) 628 – particle beam-pumped 1046 –eyesafe 1041 – vacuum ultraviolet 645 – quantum well 1043, 1044 –field – without inversion 1080 – Raman fiber 1042 collisions in 723 laser types – rare earth chelate 1045 – fluctuations 1079 –He−Ne 1023 – rare earth ion 1040 – frequency conversion techniques – alexandrite 1040 – rhodamine 6G 1043 645 – ammonia 1037 –ring 1042 difference-frequency mixing –ArF 1038 – ruby 1040 645 – chemical 1039 – semiconductor 1043 ujc Index Subject stimulated anti-Stokes Raman – chemical-oxygen-iodine (COIL) high power 1047 scattering 645 1039 – solid state 1039 sum-frequency mixing 645 –CN− 1042 dye 1043, 1045 third harmonic generation 646 –CO 1038 excimer 1039, 1043 –gain 623 –CO2 1037 thin-disk 1046 – gain media (tables) 627 – colliding-pulse 1045 – soliton 1043 – interaction with matter 628 – color center 1042 – stoichiometric 1041 – linewidth 1028 – copper vapor 1037 – strained layer 1044 – magnetic resonance (LMR) –Cr–LiCaAlF6 1040 – TEA 1038 spectrometer 618 –Cr–LiSaAlF6 1040 – thulium 1041 – medical applications of 1041 – cyanide 1037 – Ti-sapphire 1040 – microscopic 1175 – deuterium fluoride-CO2 1039 – transition metal ion 1040 – mode – dye 1038 – vertical cavity surface emitting Fox–Li computations 1028 –erbium 1041 1044 frequencies 1027 – excimer 1036, 1038 – water vapor 1037 Gaussian 1029 –extremeUV 1046 –XeCl 1038 longitudinal 1026, 1028 –fiber 1041 –XeF 1038 transverse 1028, 1033 – fluorine 1038 – X-ray 1046 – multimode 1030 – free electron 1046, 1047 –ZnSe 1044 – nonlinear mixing 1039 –GaAlAs 1043 laser, fixed frequency (table) – oscillator and beam parameters –GaAs 1044 627 623 –gas 1036 laser-cooled ions 1226 – oscillator geometries 624 – germanium oxide 1039 laser-induced bound states 1084 – output intensity 1025 – gold vapor 1037 laser-induced continuum structure – photolysis –H2 1038 1080 in molecular beams 968 –He–Cd 1037 laser-induced fluorescence (LIF) – population inversion 623 –He–Ne 1036 970, 1339 – principles of operation 623 – heterostructure 1043 – detector 970 – pumping method 626, 1041 – holmium 1041 – in ion–molecule reactions 989 – resonator 625, 1028 – hydrogen fluoride 1039 – wavelength table 1339 concentric 1029 – inorganic rare earth liquid 1045 laser-induced transparency 1080 hemispherical 1029 –ion 1036 laser-produced plasma 643 stable 1028, 1030 –KrF 1038 lattice permutation 79 symmetric confocal 1028 – lead salt 1044 Lau effect 1133 unstable 1028, 1030 – liquid 1044 Laue geometry 1134 Subject Index 1487 lead LIGO gravitational wave observatory line profile, Voigt function 910 – photon scattering by 917 1206 line radiation source 644 – photon–atom scattering by limit theorem, for generalized line shape (1 keV–1MeV) 916 oscillator strength 931 – Breit–Wigner 396, 672 leap-frogging 263 Lindemann mechanism 562 – Doppler 279, 973, 1011, 1023, least dissipation, principle of line broadening 103, 279, 875 1284 814 – adiabatic approximation 885, 886 –Fano 395, 911, 1079 least squares, method of 137 – asymmetric line shapes 282 – Gaussian 195, 911 Legendre function 169 – bound states and other quantum – Lorentzian 195, 279, 624, 876, Legendre polynomial 903 effects 286 911, 921, 1000, 1012, 1025, 1170, Lennard–Jones potential 564 – bound–free and free–bound 1284 – scattering by 681, 683 transitions 887 – Shore 905 lens, atomic 1132, 1133 – by atom–atom collisions 884, 886 – Voigt 279, 911 lepton charge 402, 403 – by charged particles 879 profile 1012 lepton scattering – by electrons 881, 883, 886 line strength 187, 321, 837 – tests of quantum electrodynamics – by field of static ions 881 – connection with oscillator strength 416 – classical oscillator approximation 838 level shift 280 – hyperfine structure 255 –acStark 1002 – coefficient 284 – molecular 515 – and width 629 – collisional 875, 1011 – relative (table) 193 – Bloch–Siegert 1001 – collisional narrowing 1013 – semiclassical representation 838 – light 1002 – cross section 878 line width Index Subject – operator 102 – Doppler 195, 282, 1011, 1012 – Doppler 1023 – transformation 102 – effective Gaunt factor 880 – homogeneous 1023 level width 759, 921 – empirical formulae 879 – inhomogeneous 1066 level-crossing method – impact approximation 281, 875, – Lorentzian 1027 265 882 line, atomic spectral 177 Levinson’s theorem 668 and line strength sn 839 linear algebra, computational 148 Lie algebra 75 – in hydrogen and hydrogenic ions linear algebraic equations method – classification of 76 880 714 – realizations 87 – inhomogeneous 1012 linear energy transfer 1395 – semisimple 76 – interaction potentials 280 linear optics 1225 Lie algebra action 25, 26 – ion impact 880 linear spectroscopy 1009 – Hilbert spaces 26 – neutral atom 875 linear-response method 110 – matrix group actions 26 – one-perturber 885 linkage, of transition rates 263 – relation to angular momentum – overlapping lines 875 linked cluster theorem 108, 337 theory 26 – perturbation theory for 878 linked diagram 108, 109 Lie group 77, 327 –power 1011 Liouville equation 124 Lieber diagram 864 – pressure 195, 279, 875 – quantum 1150 ligand shell 593 unified theories of 888 Liouville operator 223 light – quadratic Stark 878 Liouville space 223 – pressure 1094 – quasistatic approximation 284 Lippmann–Schwinger equation – scattering – quasistatic theory 282 112, 713 Rayleigh 915, 1006 – resonance 195, 878 – distorted wave 777 resonant 1006 – satellite features 285 LISA gravitational wave observatory stimulated 1059 – semiclassical theory 876 1207 –shift 1002 – shift and width operator for 876 lithium-like ions – source – simple formulae 877 – dielectronic recombination 831 infrared 608 –Stark 196, 875, 877 local density approximation (LDA) ultraviolet 642 widths, hydrogen 196 302 – speed of 1 – van der Waals 195, 877 local oscillator 1148 – strings 1047 – Voigt profile 1015 local realism – velocity of 1010 – width and shift 884 – disproof of, without inequalities light–matter interaction 723, 997 matrices 876 1199 – quantized fields 997 – WKB approximation 887 – three-particle gedanken experiment – semiclassical 997 line intensity 186 1199 1488 Subject Index

local thermodynamic equilibrium electron 429 – damped harmonic oscillator 1153, (LTE) 263, 1304 of clusters 592 1154 local-density approximation 1114 – multipole 258, 997 – damped two-level atom 1154, locked dipole approximation 564, –trap 1099, 1116 1155 578, 687, 1274 – white dwarf in squeezed bath 1154 locking, of magnetic moment 592 presence of helium in 233 – recombination theory 816 locking-radius model 693 magneton 998 master oscillator power amplifier log derivative method 765 magneto-optical (MOPA) 1044, 1046 logarithmic negativity 1218 – diffraction 1135 master theorems London phase distribution 1145 –trap 457, 1098, 1103 – MacMahon form 64 long range interactions 365 magnetron cooling 1102 – Schwinger form 64 – capture theories 563 magnetron motion 1101 material science 1397 Lorentz Majorana transition 1099, 1116 mathematical constants (table) 6 – approximation 1053 Mandel Q parameter 1144 mathematical functions –atom 999 Mandel’s formula, for photon – digital library of 153 – group 327, 328 counting 1030 Maxwell equations 3, 1142 homogeneous 89 Manley–Rowe relations 1055 – absorptive 1070 proper 327 many-body calculations, relativistic –dispersive 1070 – local field 1053 350 Maxwell–Bloch equations 1069, – transformation 326 many-body perturbation theory 1070 boosts 326 (MBPT) 105, 353, 359, 401 McCall-Hahn area theorem 1070, ujc Index Subject discrete 326 – configuration mixing 367 1071 infinitesimal 327 – correspondence rules 362 mean energy loss per collision 1380 rotations 326 –diagrams 360 mean field approximation 1129 –triplet 229 – effective interelectron interaction mean free path 1319 Lorentzian line shape 876, 1012 369 mean speed, thermal 824 Lorentz–Lorenz corrections 1025 – electron and vacancy states 362 mean-field theory 1110, 1113 LoSurdo–Stark effect 92 – electron scattering 367 measurement low field seeker 1129 – electron–vacancy states 370 – quantum theory of 1189 luminosity, atmosphere 1284 – Hartree–Fock approximation 364 – weak 1195 – one-particle states 366 measurement-induced nonlinearities M – photoionization diagrams 385 1225 – photon emission 374 mechanical effects of radiation Møller operator (matrix) 779 – role of the Pauli principle 362, 1127 Møller–Plesset perturbation theory 367 mercury clusters 592 106, 472 – summation of sequences 363 merged beam method 830, 946, 991 Mach number 968 many-body theory 105 – form factor 946 Mach–Zehnder interferometer 1135 – relativistic 334 mesosphere Mackay icosahedra 599 Markov approximation 125 – terrestial 1261 macroscopic wave function 1110, maser metal cluster 590 1114 – microscopic 1175 – molecules 593 magic angle 225, 934 – threshold 1179 metal-fullerene clusters 595 – pseudomagic 902 mass polarization 199 metal–insulator–metal (MIM) diode magic numbers 590, 601 mass ratios 617 magic squares – measurement of 1105 metallocarbohedrenes 593 – addition of angular momentum mass shift 199, 256 metallofullerenes 595 63 – normal 199, 256, 318 metastable atoms 320 magnetic – reduced 257 – electron scattering by 939 – dipole interaction 997, 999 – specific 199, 256, 318 – in atomic beams 932, 935, 939, motional correction 1127 mass transfer cross section 863 968, 1132 – dipole transition 187, 192 Massey parameter 742 –incomets 1253 –field Massey–Mohr cross section 663, – in discharges 1329 atoms in 227, 247 680 – in planetary atmospheres 1281 in neutron stars 230 master equation 125, 1004, 1010, Metropolis algorithm 150 – mirror 1132 1092, 1152, 1159, 1162 Michelson interferometer –moment – correlation functions 1156 –(diagram) 609 Subject Index 1489

– distribution of modulation – ab initio methods 762 – valence universal 110 frequencies 611 – adiabatic states 762 multibeam resonance 1134 microcanonical ensemble 871 – approximation methods 467 multichannel quantum defect theory microchannel plate 649 – empirical estimates 764 711 microelectromechanical systems – fitting experimental energies 520 – multiphoton processes 1078 (MEMS) 1047 – nuclear motion 480 multiconfiguration Hartree–Fock micromaser 1174, 1178 – rotation 467 approximation 313, 315 – quantum nondemolition experiment – rotational-vibrational 481 – Breit–Pauli interaction 316 1194 – vibration 467 multiconfigurational self-consistent microstructure fabrication 1332 – wave function 107, 468, 516 field theory 474 microwave cavities 1174 – weakly interacting systems 476, multi-electron Milky Way galaxy, age 1358 482 – excitation 922 Milne detailed balance 822 molecular symmetry 491, 516 – transitions 957 minimax method molecule, compound 1365 multilayer coating 651 – for autoionizing states 316 molecules in intense laser fields multipactor discharge mode 1332 minimum uncertainty state 1144 1084 multiphoton process 628, 1072, Minkowski space 326 Mollow spectrum 1161 1077 mirror images momentum space wave function – multi-electron effects 1079 – radiating atoms and 1170 – quantum defect representation – rate enhancement 1080 mirror, atomic 1131 841 – strong field 1080 mixed states 123 momentum spectroscopy 922 – weak field 1078 mobility momentum transfer multiple fragmentation 550 Index Subject – coefficient 806, 1323 – collision frequency 1280 multiple lasers, excitation by 1080 – of ions in a gas 666 – cross section 661, 708, 930, 933, multiple path occupation 498 mode locking 1031, 1045 1265, 1307 multiplet 177 mode pulling 1027 Monte Carlo integration 151 multiplex advantage, in Fourier model potentials – relation to random number transform spectroscopy 610 – scattering results for 684 distributions 151 multiplexed detection 267, 610 –tableof 685 Monte Carlo method 149 multiplicity 176, 177 modulation – classical trajectory 869 multipole – cross-phase 1057 exotic projectiles 873 – effects 912 – self-phase 1057 heavy particle dynamics 873 – expansion 997 molecular beam 933, 967 hydrogenic targets 869, 871 –moments 221 – angular momentum polarization many-electron targets 870 multireference (MR) CC theory 110 studies 968 multiply-charged projectiles multireference configuration – beam splitters 1134 870 interaction theory 474 – epitaxy 1044 nonhydrogenic one-electron muon 1359 – reagent preparation 968 models 870 – atomic capture 1361, 1362 – sources 967 pseudo-one-electron targets – lifetime 1359 molecular clock 979 872 – scattering 754 molecular clouds state-selective electron capture muon-catalyzed fusion 1359 – carbon chemistry of 1239 872 –cycle 1361 –dark 1239 – dense plasmas 1313 – experimental methods 1368 –diffuse 1238 – for line broadening 888 – muon loss 1367 molecular clusters 602 Morse potential, scattering by 688 – reactions and energy release 1360 molecular dynamics 491, 537 most probable energy loss 1373, muonic atom – simulation 1374, 1381, 1382 – cascade 1364 dense plasmas 1313 MOT 1098, 1103 – elastic scattering 1364 molecular formation, resonant 1361 motional correction – formation 1362 molecular fragmentation 537, 803, – magnetic dipole interaction 1127 – helium 1367 969, 1084 Mott insulator 1123, 1227 – hydrogen 1362 – pattern 969 Mott scattering 938 – hyperfine transitions 1364 molecular orbital X-rays 962 Mott term, stopping power 1380 – isotopic transfer 1364 molecular spectra 491 MR CC – sticking 1367 – measurement of 615 – state selective 110 – stripping 1368 molecular structure 467 – state universal 110 muonic molecule 1490 Subject Index

– Auger formation 1364 noise nuclear electric quadrupole moment – energy corrections 1365 – colored 1157 255, 258, 320 – nuclear fusion rate 1366 – operator 1157 nuclear magnetic dipole moment – resonant formation 1365 – white 1157 255, 259, 319 – rovibrational energy levels 1361 nonadiabatic nuclear motion – scaling 1360 – coupling 742, 744 – in molecular scattering 722 – three-body formation 1366 – scattering theory 723 – in molecules 480 mutual neutralization 575, 576, – transition 535, 551, 761, 1129 nuclear polarization 439 584, 800, 810, 1330 relativistically induced 478 nuclear reactions – cross section 811 nonclassical fields 1143 – astrophysical factor 1359, 1366 – Landau–Zener probability 811 nonclassical light – Coulomb barrier 1359 – rate coefficient 811 – atomic cascade source 1186 – cross sections 1359 noncrossing rule 470, 743, 810 – electronic screening of 1359 N nonlinear nuclear scattering 917 – atom optics 1126 nuclear size effect 318, 443 nanocapsules 596 – mixing 1039 – for hydrogenic atoms (table) 230 nanocavity laser 1047 – optics 629, 1051 – in atoms 1356 natural enabled by ultra-intense laser – quantum electrodynamic 1358 – coordinate system 127 pulses 1062 – relativistic 1357 – frame 694 enabled by ultrashort laser pulses nuclear spin 560 – orbital expansion 316 1062 nuclear spin and statistics ujc Index Subject – width 911 focused beam effects 1056 – in molecules 522 near-edge X-ray absorption fine wave equation 1053 nuclei structure (NEXAFS) 1351 – polarization 1051 – isobaric 1358 nebular equilibrium 1309 – refractive index 1052 number negative coefficient 1052 – of photons 1142 – energy states 330 in an atomic vapor 1058 – operator 1108, 1142 –glow 1327 intensity-dependent 1052 – states 1143, 1162 – ions 369, 578, 1330 mechanisms 1052 numerical differentiation 140 autodetachment from 320, 391 – Schrödinger equation 1111 numerical integration 147 cluster 603 pulse propagation 1055 Numerov method 141, 236 harpoon mechanism 979 – susceptibility 629, 1051 Nyquist frequency 139 photodetachment from 387, 946 quantum mechanical expression neutral–molecule reactions 563 1053 O neutral–neutral reactions 564 relation to hyperpolarizability neutrino mass 1358 1053 occasional proportional feedback neutron diffraction 1133 tensor properties 1052 technique 1033 neutron optics 1125 nonlocal transients 1074 Ochkur approximation 716 neutron stars, magnetic fields 230 nonlocality 1216 octahedral rotor, semirigid 500 neutrons, ultracold 1131 – GHZ test 1199 octahedral symmetry, molecular Neville’s algorithm 136 –Hardytest 1199 499 Newton diagram 975, 985 – in quantum measurement 1195 one-and-a-half centered expansion nightglow 1284 nonreactive scattering 555 (OHCE) 758 – spectrum of Venus 1287 normal modes 1142 one-particle density operator 1114 nightside ionospheres 1277 normal ordering operator 105 one-particle operator 1108 noble gas normal product of operators 105 one-way quantum computer 1226 –clusters 599 normal product with contractions onions 595 – compounds with diatoms 482 105 Oort cloud 1247 – discharge 644 normalization opacity project 1241 – electron scattering by 368, 1320 – incoming wave 381 open shell 393 – harmonic generation in 1082 – of continuum wave functions 668, operator – lasers 1036 790, 821 – annihilation/creation 76, 94, 115, – photoionization 384, 912 northern aurae, spectrum of Jupiter 118, 330 – scattering lengths for 669 1289 – commutation relations 330, 331 noble metal clusters 590 novae 1236 – conjugation 118 no-cloning theorem 1200, 1216 nuclear charge distribution 340 – non-commuting 330, 354 Subject Index 1491

– normal ordering 330 orientation 222, 693 – in de Broglie optics 1130 –ordering – atomic 936 paraxial wave equation 1028 antinormal 1148 – density matrix formalism 128 parent term, atomic structure 179 normal 105, 330, 1146, 1148 – from spin-orbit interaction 129 parity 176, 557, 560 s-ordered 1148 – in electron capture 770 – combined with rotations 493 symmetric 1148 – in molecular beams 969 – molecular structure and selection – quasiparticle 120 Ornstein–Uhlenbeck process 1079 rules 521 – representation of 116 orthopositronium decay rate 422 – selection rule 901 – time evolution 124 oscillator strength 186, 187, 261, partial Oppenheimer–Brinkman–Kramers 321, 1004, 1011 – cross section 908 (OBK) approximation 777, 859, – absorption 186, 878 – transposition 1217 955 – bound–free 822 – wave expansion 667, 706 optical – connection with line strength 838 particle identification – Bloch equations 1003, 1066 – definition 215 –PID 1384 with decay 1004 – finite nuclear mass effects 215 particle–hole interaction – cavities – generalized 790, 838, 931, 1377 – in photoionization 384 strong cavities 1174 – helium (table) 216, 217 – interchannel interactions 385 –depth 1267 – length and velocity forms 215 – intrachannel interactions 384 – Earnshaw theorem 1098 – measurement of 262, 264 – virtual double excitations 385 – emission cross section 934 – molecular 524 partition sum 125 – excitation 237 – silicon Paschen–Back effect 229 –force 1093 comparison of atomic and solid – relativistic 229 Index Subject – frequency comb 631 1375 path integral Monte Carlo method – lattice 1096, 1121, 1226 –sumrule 205, 524 – dense plasmas 1313 – material 651 – time-resolved measurement 265 Paul trap 1099 coating 651 Ostwald’s step rule 602 – electrode configuration and interference filter 651 output coupling 1026 voltages 1100 multichannel plates 651 overtone bands 526 Pauli multilayer coating 651 oxygen – correlations (blocking) 755 polarizer 652 – green – matrices 10, 94 thin film 651 spectrum of Venus 1289 – principle 498 window 651 – quenching reactions 484 – pseudo-spin operator 1001 – molasses 1095, 1098 ozone peaking approximation σ +– σ − 1098, 1099 – hole 1299 – in quantal impulse approximation corkscrew 1098 – stratospheric 848 lin  lin 1098 depletion 1293, 1300 Pearson-7 function 910 lin ⊥ lin 1097 destruction 1298 pendellösung oscillations 1134 – nutation 1067 formation 1298 pendular states 969 – parametric oscillator 630, 1056 Penning ionization 836 – potential 392, 683, 710, 715 P Penning trap 1101 second order 716 perfect crystal – pumping 221, 224 PADDS (Perpendicular ADDS) 973 – neutron interaction with 1127 diode laser 1041 Padé approximation 137 perfect scattering experiment 133, in molecular beams 968 pair production 693, 696 – theorem 665 – electron–positron 1359 periodic orbit 542 in quantal impulse approximation Paldus tableau 96 permeability of vacuum 1 848 papier mâché 595 permittivity of vacuum 1 –trap 1096, 1116 parabolic coordinates 155, 232 permutation symmetry optics, near-field 1133 parabolic quantum number 238 –full 1052 orbital collapse 312 paramagnetic clusters 592 – intrinsic 1052 orbitally forbidden transitions 531 parametric – of wave functions 516 orbiting and spiraling collisions 662 – amplification 1056 persistent current 1118 Orbiting Astronomical Observatory – oscillation 1056 perturbation theory 101, 359 1248 squeezed light generation 1145 – central field 92 orbit–orbit interaction 308 – process 1055 – continuum distorted wave order parameter 1114 paraxial approximation third-order 777 1492 Subject Index

– degenerate 336 – atmospheric 1289 – Cooper minimum 383 – diagrammatic 107, 359 photodetachment – cross section 382, 386 – Epstein–Nesbet 106 – double electron 785 – delayed maximum 383 – expansions 102, 104, 109 – from H−,He−,andK− 785 – diagrammatic perturbation theory – for state multipoles 129 – mirroring of resonance profiles in 361 – large order 91 alternative partial cross sections – double photoionization of He 387 – Møller–Plesset 106 388 – electron correlation effects 904 – many-body 105, 359 –ofH−,Li−,andNa− 388 – field-induced oscillatory structure –matrix 101 –oftheK-shell of He− and Li− 388 241 – multiphoton processes 1078 photodetection theory 1147 – high photon energy behavior of the – principal term 104 photodiode 649 partial cross sections 383, 384 – Rayleigh–Schrödinger 104, 335 photodissociation 1267, 1294 –incomets 1254 – renormalization term 104 – absorption cross section 537 – interaction Hamiltonian 379 – time-independent 101 – anisotropy parameter 538 – mirroring of resonance profiles in – Z-dependent 313 – branching ratios 537 alternative partial cross sections perturbed stationary state (PSS) – direct 535 388 method 757 – experimental techniques 539 – multiple excitation 374 Peterkop semiclassical theory 782 –incomets 1254 – multiple ionization processes 906 Peterkop theorem 717 – indirect 535 – non-dipole effects 387 Petermann Kfactor 1028 – interstellar 1238 – of positive ions 388 Pfaffians – molecular 535 – of Rydberg atoms 240, 242 ujc Index Subject – skew symmetric matrices 65 – partial cross section 537 – particle–hole interaction effects phase – predissociation 384 – contrast imaging 1117 electronic 535 – polarization effects 387 –diffusion 1028, 1122 rotational 535 – post collision interactions 906 model 1079 vibrational 535 – random phase approximation for – dispersion 1122 – quantum yields 537 371 – matching 630, 1083 – rates of 1239 – rates of 1239 of nonlinear optical processes – selection rules 536 – relativistic and spin-dependent 1054 – state-resolved 973 effects 387, 911 – operator 1145 photodissociative ionization 1267 – relaxation effects 387 hermitian 1146 photoelectric effect 901, 916 – resonances 385, 386, 904 operational 1146 – angular distribution 902 – theoretical methods for 371, 386 sine and cosine 1146 – dipole approximation 901 – threshold laws 906 –shift 666–668, 708, 1135 – experimental methods 907 – two-electron 922 binary encounter approximation – open-shell atoms 902 – wave function boundary conditions 852 – spin analysis 901, 903 381 Born S-wave 673 photoelectron photoionized clouds dispersive 1136 – angular distribution 904 – modeling 1245 effective range expansion 668, – energy analysis 906 photoionized gas 708 – spectrometry 908 – processes in 1235 eigenphase sum 710 – spectroscopy photomultiplier tube 649 geometric 1136 operational modes 909 photon near resonances 710 spectrum 901 – antibunching 1162 quantum defect equation 708 – spectrum 910 – bandpass 911 topological 1136 correlation satellites 906 – bunching 1030 – space averaging method 1087 photographic plate 649 and antibunching 1147 – space theory photoionization 379, 918, 970, – cloning 1200 of gas phase reactions 565 1236, 1267, 1294 – correlation 1146, 1147, 1186 – velocity 1130 –5s2 electrons 372 – counting photoabsorption – angular distribution 902 Mandel’s formula 1030 –4d10 subshell threshold 372 anisotropy parameter 903 – density of states 215 – by ionic clusters 596 asymmetry parameter 387 – distribution photoassociation 1119 – anisotropy parameter 902 Poissonian 1144 – spectroscopy 1103 – configuration interaction effects squeezed state 1145 photochemical processes 906 – echo 1069 Subject Index 1493

– indivisibility 1186 plasmon excitation 1375 positron scattering 731, 873 – information content of 1200 plethysm 80 – annihilation 732 – number Pluvinage wave function 780 angular correlation 732 average 1179 Pockels effect 1061 – atomic hydrogen 735 intracavity 1178 Poincaré resonances 735 variance normalized 1179 – group 328 – atoms 736 – occupation number 238 – sphere 696 – Born approximation 733 – recoil effects 1091 – transformation 327 – close-coupling approximation – sources, single 1182 Poisson distribution 1012 734 – statistics 1030 – sub-Poissonian fields 1144 – convergent close-coupling method Bose–Einstein distribution Poisson sum formula 675 735 1030 polarizability 110 – eikonal-Born series 734 Poisson distribution 1030 – complex 999 – ionization 735, 780 – teleportation of 1200 – frequency dependent 366 Wannier threshold law 735 photon–atom scattering – hydrogenic 213, 232 – noble gases 735 (1 keV–1MeV) 915 – relativistic, for hydrogen 233 Ramsauer minimum 736 – elastic 916 polarization 934 – optical potentials 734 – inelastic 918 – correlation 937 –Oregap 732 – lead, cross section for 916 – effect 939 – positronium formation 731 photonic – ellipse 694 – potential scattering 733 – bandgaps 1173 nonlinear rotation 1059 – variational method 735 superluminal tunneling 1203 – entanglement 1196 – Wigner cusp 735 Index Subject – crystal fibers 1047 – in heavy atom scattering 700 positronium 731 photon-number resolving – in optical transitions 265 – Thomas peak 867 photodetectors 1225 – interaction 946 post collision interaction 925 photorefractive effect 1061 –ofmedium 3 – photoionization 907 physical constants 1 – optical 125, 131, 695 postion senitive detectors (PSD) –tableof 2 – particle scattering phenomena 267 physisorption 592, 1351 126, 693 potential energy curves (PEC) 742, planar imaging, two-dimensional – photon 331 744 1339 – potential 669, 707, 708 potential energy surface (PES) 467, plane wave Born approximation – redistribution 286 518, 535, 742, 744, 978, 984, 987, (PWBA) 757, 951 – relaxation 221 1336 planetary atmospheres 576 – spectroscopy 1016 – analytic derivative technique 471 planetary nebulae 1236 –spin 125, 130 – for chemical reaction 987, 991 planets polarized – intersection of 470 – exobase properties (table) 1289 – atoms 222 – perturbations of 476 plasma – beams, collisions involving 125, potential scattering 976, 977 – diagnostics 872 699, 938 – hard-core 669 – etching 1331 – electrons 938 – laser field effects 724 – frequency 1000, 1305 – light 999 – modified Coulomb 669 – laser induced 1303 and atomic multipoles 224 – polarization potential 669 plasma conditions, diagram 1304 production of 642, 652 – van der Waals 669 plasma physics 1303 –target 938 power broadening 1005, 1011 – collisional processes in dense polarizer 652 predissociation 535 plasma 1311 polyatomic molecules pre-master equation 1162 – ionization balance 1308 – electron scattering by 723 pressure broadening 279 – one-component model 1306 polynomial quadrature 139 principal axes 559 – radiative processes in dense ponderomotive energy 1080, 1096, probability density function 1374 processes 1311 1100 processes, electron driven 940 – two-component model 1306 population inversion 1014, 1023 product growth method 945 plasma screening population representation 222 product imaging 973, 980 – Debye model 1306 population trapping 1079 – detection 973 – ion-sphere model 1306 positive partial transpose 1217 product kinetic energy distribution – Thomas–Fermi model 1310 positron pair production 1359 973 plasmoid mode 1332 positron production 962 product quantum state 984 1494 Subject Index

– distribution 973 definition of 211 – theory of measurement 1180 projectile continuum distorted wave in momentum space wave reality of the wave function approximation (PCDW) 777 functions 841 1195 projectile electrons 796 multichannel 726 – trajectory 1159 projection operator 101, 710, 716 parameters 312 –well 1043 – formalism 392 relativistic and finite mass – Zeno effect 1193 – hole 394 corrections to 211 quantum-cascade laser 1047 – quasiprojectors 394 relativistic theory 353 quantum-mechanical correlation propagator 407 Rydberg series 312 1216 – electron 333 semiclassical representation quasi-elastic collisions, -and – one-body 402 837 J-mixing 836 – photon 333 theory 235 quasi-electron 368 – two-body 405 use in radial integrals 837 quasifree electron model – two-point 409 – degenerate gas 1107 – of Rydberg atom collisions 842 propensity rules 693 – electrodynamics 1358 quasiparticle 120 protected measurements 1195 electron factors 416 quasi-probability distribution 1148 proton charge radius 443 equations of motion 329 – Cahill and Glauber 1149 proton transfer 579 fine structure 420 – Kirkwood 1151 proton–helium scattering 865 helium-like ions 208 – P function 1149 pseudocrossing 743 hyperfine structure 421 – positive P 1149 pseudopotential 300, 1110 lepton scattering 416 – Q, Husimi 1151 ujc Index Subject – method 396, 397 many-electron ions 425 – Wigner 1149 results 398 muon g factors 416 quasiprojection operators 394 pseudostate expansion 715, 759 one-electron ions 424 quasispin 81 pulse area theorem 1067 perturbation theory 331 – bosons 118 pulse compression 1031, 1045 precision tests 423 – conjugation 118 pulse propagation, resonant 1069 two-photon interactions 425 – dependence on electron number pulse shaper 552 –eraser 1191 119 pump mechanisms 1023, 1024 – error correction 1224 – fermions 117 pump–probe experiment 548 – field theory 401, 1107 – half-filled shell 119 pump–probe resonance 1073 –fluid 601 – spin-quasispin interchange 119 – information processing 1162 – triple tensors 118 Q – interference 1144 quasisteady state 802 – interrogation 1194 qubits 1216 Q-switching 1030, 1031 – jumps 1104 –self 1045 – key distribution 1219 R quadrature operator 1143 – liquid 599 quadrature states 1148 – localization 1085 Rabi frequency 1001, 1010, 1023, – rotated 1148 – Monte Carlo formalism 1159 1066, 1128 quadrupole interaction – Monte Carlo method – generalized 1001, 1067 – electric 998 dense plasmas 1313 – power dependent 629 quadrupole moment 110 –networks 1222 – two-photon 1073 quadrupole potential 575 – nondemolition experiment 1181, – vacuum 1002 quadrupole tensor 999 1193 Rabi oscillations 1067, 1176, 1177 quantization 115 gravitational radiation detection –damped 1067 – of circulation 1118 1206 Racah quantized field effects 1141 – number 176, 411 – coefficients quantum molecular 518 definition 43 – beats 129, 267 – optics 997 fundamental identities 44 time integration of 130 – phase 1145 orthogonality 43 – chaos 1085 transition 1123 recurrance relations 46 – cryptography – random walks 1223 relation to hypergeometric series with entangled pairs 1201 – regression hypothesis 1156 46 – defect 184, 211, 237, 240, 242, – scars 1086 relation to 313, 872 – search algorithm 1223 Wigner–Clebsch–Gordan analytic continuation 708 – teleportation 1200, 1219 coefficients 43 Subject Index 1495

Schwinger–Bargmann generating – thermal model 571 Raman–Nath approximation 1131 function 44 modified 571 Rampsberger–Rice–Karplus–Marcus symmetries 45 radiative corrections 353, 416 (RRKM) theory 542, 568 – commutation relations 116 radiative damping Ramsauer–Townsend effect 669, – invariant operator 42 – Lorentz atom 999 1320 – lemma 82 radiative electron capture 961 random number generation 149 – operators radiative forces 1171 – Metropolis algorithm 150 Biedenharn–Elliott identity 50 radiative lifetime 194, 237, 264 – nonuniform 150 – reciprocity relation 83 – cavity effects 238, 1168 – rejection method 150 radial coupling 745 – finite temperature effects 238 – transformation method 150 – matrix elements 766 – measurement of 265 random phase approximation 365, radial Dirac equation – np2PJ states 266 401, 663 – boundary conditions 340, 341 radiative line strength 187 rate coefficient 556, 576, 578 – free electron radiative processes 353 rate constant progressive waves 343 radiative recoil 444 – in combustion reactions 1336 standing waves 343 radiative recombination 576, 800, – state-to-state 984 radial Dirac equation for bound states 817, 1236, 1274 –thermal 984 – approximation by finite elements – collisional 801, 802 rate equation 125 350 – cross sections for 817, 819, 821 – approximation 1005, 1013, 1014, – approximation by spinor basis set – electron energy loss rate 817, 819 1024, 1025 345 – Gaunt factor 823 – chemical 578 G-spinors 348, 349 – normalization of continuum wave rate laws 561 Index Subject L-spinors 347 function 821 Rayleigh (unit) 1286 S-spinors 348 – photon emission probability 819 Rayleigh scattering 915, 916, 1006 variational collapse 349 – radiated power 817, 819 Rayleigh–Ritz variational principle – finite difference methods –rate 817, 822 144, 200 deferred correction 344 – scaling laws 823 r-centroid 526 double shooting 344 – three-body collisional 800 reactance matrix 556 – variational derivation radiative self-interference forces reaction 967 Rayleigh quotient 345 1172 – association 570 radial integrals radiative shifts 1171 – barrier 563 – hydrogenic, for dipole transitions radiative stabilization 391, 570, – bimolecular 563 837 578, 943 – competition with association 572 – semiclassical quantum defect radiative transition 187, 215 – complex 562 representation 837 – molecular 520 – coordinate 563, 761 radial wave functions – moment matrix 520 – energetics 576 – for H and Na 236 –rate 186, 187 – ion–molecule 563, 983 radiating atoms hydrogen (table) 195 – ion–neutral 575 – and mirror images 1170 hydrogenic matrix elements 836 – neutral–molecule 563 – in resonators 1170 – selection rules 187 –path 483 – in waveguides 1169 – theory 215 curvature 483 radiation absorption 1390 radio frequency heating 1102 – spontaneity 577 radiation detectors 1374, 1389 rainbow angle 677, 977 – termolecular 562 radiation dose 1375 Raman cooling 1105 – unimolecular 562 radiation physics 1390 Raman linewidths 1338 reactive scattering 684, 967, 978 – cross sections for 1374, 1392 Raman process 1017 reactive sphere model, for radiation reaction 999 – Auger 924 recombination processes 804 radiation theory Raman scattering 630 rebound collision 988 – semiclassical 1025 – radiationless 924 rebound reaction 979 radiation therapy 1383 – stimulated 630, 1059 recoil radiation trapping 287, 934, 1011 anti-Stokes field 1059 – corrections 418 – multiple component lines 290 Stokes field 1059 – in heavy particle scattering 754 radiationless transition 920 – stimulated, Stokes amplification in – ion momentum spectroscopy 873 radiation–matter interactions 1389 1055 – ion momentum spectroscopy radiative association 561, 570, 582, – X-ray 924 (RIMS) 955 1239 Raman sideband cooling 1105 – peak 953 1496 Subject Index

recombination 583 – coefficient of 1131 resolvent operator 103, 336 – coefficient 1330 refraction resonance – destruction rates 801 –lawof 1131 – Auger 905 – dielectronic 829 refractive index 1023, 1027, 1030 – autoionizing 391, 904 – distributions used in 811 – nonlinear 1032 –Bragg 1134 – electron–ion 829, 1330 Regge generating function 34 – Breit–Wigner parameters 396 vibrational populations in 584 regions of nonadiabatic coupling – double 1080 – high gas density theory 815 (NAR) 742 –giant 371, 591 diffusional-drift 806 relative flow technique 933 – in electron scattering 932 – ion–ion 584 relativistic binding energy 231 – intensity-induced 1080 – Langevin rate 806 relativistic corrections 460 – isolated 830 – microscopic methods 812 – asymptotic expansions for 214 – laser 1001, 1009, 1058, 1066, bottleneck method 815 – Darwin term 709 1078, 1095, 1134 diffusion theory 814 – for helium 208 electric/magnetic 618 master equations 816 – hydrogenic atoms in strong fields – line broadening 195, 877 time dependent 813 231 – mirroring of resonance profiles time independent 814 – mass-correction term 709 388 trapping radius method 815 –software 354 – overlapping 832 – nonequilibrium theory 815 – spin–orbit potential 709 – photoionization 386, 904 – processes of 1330 relativistic effective Hamiltonian – pump-probe 1073 – production rates 801 – Breit–Pauli 335 – quasi-Landau 241 ujc Index Subject – radiative 829, 1330 – Dirac–Coulomb 335 – scattering 671 –rate 806 – Dirac–Coulomb–Breit 335 – shape parameter 395 – theory – nonrelativistic limit 335 – strong field mixing 240 macroscopic methods 803 relativistic effects – Thomas peak 867 – Thomson theory of 807 – magnetic field 228 – two-beam 1134 – three-body 800, 829, 1330 – Thomas–Fermi theory for 303 – two-photon (diagram) 1072 – tidal 800 relativistic recoil 438 – width and shift 394, 710, 1172 – variational principle for 814 – Hamiltonian for 209 resonance fluorescence 265, 1160 – working formulae 802, 805 relaxation 1003, 1065 – coherent intensity 1160 recoupling theory – density matrix formalism 125 – incoherent intensity 1160 – commutation andf association of – effective Hamiltonian 1004 – photon antibunching 1162 symbols 59 – homogeneous 1066 – photon correlations 1162 – construction of transformation – inhomogeneous 1068 – spectrum 1161 coefficients 58 – intrinsic 1071 resonance scattering 391, 672, 710, – unsolved problems 59 – observed levels 1003, 1004 1284 recoupling theory and 3n − j – operator 1004 – on surfaces 1346 coefficients – unobserved levels 1003 resonance theory 391, 722 – composite systems 54 relaxation rate – multichannel 710 recurrence relations – longitudinal 1004, 1010 resonant capture-stabilization model j (β) – dmm functions 22 – transverse 1004, 1010 803 red giant 1241 Renner–Teller effect 480, 536 resonant enhanced multiphoton reduced density operator 1152, renormalization 332 photoionization (REMPI) 970, 1159 – theory 414 1078 reduced mass representation theory resonant photoionization – electronic, for light nuclei 207 – bosonic 94 – detector 970 reflection – fermionic 94 resonant pulse propagation 1069 – critical angle 1131 – universal enveloping algebra 97 resonant Raman effect 911, 924 –lawof 1131 reservoir 1151, 1162 resonant rearrangement collision – principle 542 – squeezed 1152 925 – symmetry 694 – theory 1162 resonant transfer 961 conservation of in scattering –thermal 1152 resonant-mass detector 1206 697 resolution resonators, radiating atoms in 1170 –total 1131 – in Fourier transform spectroscopy revivals 550 – total mirror 1131 611 Riemann zeta function 5 reflectivity – in photon experiments 910 rigid rotor 29, 492 Subject Index 1497

– asymmetric 493 rovibrational coupling 491 Rydberg wave packet 1071 symmetry analysis 498 rovibrational structure 95, 503 – free evolution (diagram) 1072 – eigenvalue graph 493 –diagram 504 – symmetric 29 Rowland circle 647 S representation function 29 Runge–Kutta method 142 Ritz formula 185 Runge–Lenz vector 81 saddle-point method R-matrix 1366 Russell–Saunders (LS) coupling – for autoionizing states 316 – fixed nuclei 723 177, 179 Sagnac effect 1136 – method 712 – allowed LS terms 178 Saha distribution, definition 802 R-matrix–Floquet method 726 Russian doll 505, 595 Saha–Boltzmann formula 1308 rock salt lattice 596 Rutherford cross section 671, 686, satellite lines 887 Rodrigues formula 167 1375, 1376 saturable absorption rotating frame Rydberg atom 1174 – optical nonlinearities 1058 – molecular 517 – in electric fields 238 saturation 1005 – optical 242, 1001 – in magnetic fields 241 – in ion–molecule reactions 582 rotating wave approximation 1001, – in microwave fields 242 – laser 1015 1010, 1093, 1128, 1169 – microwave ionization 1084 – parameter 1005 rotation – optical excitation 237 – spectroscopy 1015 – dynamics – radiative lifetimes 237 scale height 1260 semiclassical 494 – wave functions for 235 scaled-energy spectroscopy 248 – group Rydberg atom collisions 243, 836 scaling transformation 90 SU(2) group (SO(3, R)) 10 – binary encounter approximation scattering Index Subject Clebsch–Gordan series 337 852 – electron irreducible representations – Born approximation 858 by atoms in laser field 725 (irreps) 337 capture 859 by ions in laser field 725 Lie algebra SO(3) 88 – classical impulse approximation scattering (see collisions, light – matrices 18 849 scattering, and particular – parametrization – classical scattering theory for 841 processes) 1006 Euler angles 19 – elastic n → n  transitions 844 scattering amplitude 664, 671, 672, rotation matrices 517, 559 – fine structure transitions 844 674, 675, 679, 706, 707, 769, 771, – as generalized Fourier transforms – inelastic n → n transitions 843 882, 915, 917, 930, 936, 938 493 Born results for 843 – Born, second 866 – as rigid rotor eigenfunctions 492 – inelastic n, changing transitions – capture 955 rotational branch strengths 526 842 – continuum distorted wave 783 rotational branches, molecular 521 – momentum distribution functions – distorted wave strong potential rotational coupling matrix elements 840 Born (DSPB) 795 766, 767 – quantal impulse approximation – for polarization phenomena 701 rotational energy surface 494 845, 849 – impulse approximation for 848 – asymmetrical gyro-rotor, diagram – quasi-elastic mixing transitions –spinflip 701 511 844 scattering equations 743 –diagram 495, 501 – quasifree electron model 842 scattering length 708, 1110, 1111, – multiple 507 – semiquantal impulse approximation 1119, 1127 – octahedral and tetrahedral 500 851 – effective 1119 – quadrupole 508 – spatial distribution functions 840 – in elastic scattering 668 – scalar monopole 508 – types of collision processes 836 –sign 1111 – spherical gyro-rotor, diagram Rydberg constant 5 – s-wave 1129 508 Rydberg formula 184, 905 – tuning 1119 – vector dipole 508 Rydberg states 829 – use of, in Rydberg collisions 842 rotational excitation, theory 722 – autoionizing 244 – values for noble gas atoms 669 rotational invariants – basic properties 836 scattering matrix 555 – solid harmonic expansions 14 –high 237, 239 scattering signal calculation 971 rotational scattering 977 –inclusters 600 scattering theory rotational structure 497 – in laser fields 726 – adiabatic nuclei approximation – octahedral and tetrahedral 500 – quantum nondemolition experiment 722 rotational symmetry 1194 – angular momentum recoupling – molecular 517 Rydberg unit 5 709 1498 Subject Index

– atom–atom 753 – semiclassical 663, 675, 835 – for ionization 783 – autodetachment 391 – Thomas process 863 – Monte Carlo 871 – autoionization 391 – variational methods 713 semiclassical quantum defect – basic definitions 741 – Wannier method 781 representation 837 –Born 714, 716 Schawlow–Townes formula 1028 semiclassical theory – charge exchange 761 Schiff cross section 663 – Young’s two slit experiment, – charge transfer 753, 775 Schmidt model 459 exclusion of 1185 – classical 659, 835, 841, 976 Schrödinger equation 109, 235, 307 semiconductor clusters 597, 598 – classical trajectory method 869 – asymptotic form 200 semiconductor laser 1028, 1029, – close-coupling 706 – cusp conditions for 200 1033 – continuum distorted wave method – for Zeeman effect 227 semirigid rotor 491 775 – hydrogenic 153 seniority 81, 117, 308, 350, 351 – coordinate systems 694 – many-electron 308 separability criterion 1216 – density matrix formalism 126, – mathematical properties of 200 separatrix curve 496 695 – momentum space 156 series limit 185 – distorted wave 716 – parabolic coordinates 155 series summation formula 5 – elastic 659, 976 – radial solutions of 667 Seya–Namioka design 647 quantum amplitudes for 664 – spherical coordinates 153 shakedown process 906, 925 – electron–atom 367, 705 – three body 199 shakeoff process 908, 922, 1358 – electron–ion recombination 800, computational methods for 200 shakeup process 906, 922, 1358 829 – time-dependent 1078 shallowest ascent path 469 ujc Index Subject – electron–molecule 720 direct integration of 1086 Shannon’s information entropy 233 – energy loss straggling 1375, 1392 solution of 724 shape resonance 672 – energy transfer cross section, for – two-electron 199 – in surface scattering 1346 Coulomb potentials 841 Schrödinger’s cat 1144 Shavitt graph 96 – identical particles 666 Schwartz inequality 1146 shell structure – intermediate and high energy 714 Schwinger generating function 34, – group theory of 80 – ion–atom collisions 753, 761 45 – mixed configurations 80 – ion–atom ionization 789 Schwinger g-value 184 shelving state 1104 – laboratory frame representation Schwinger variational method 713 Sherman function 938 720 Schwinger–Bargmann generating shocked gas, interstellar 1243 – line broadening 279, 875 function 44 Shor’s algorithm 1223 – linear algebraic equations method Schwinger–Wu generating function Shore profile 905 714 51 shot noise 1188 – mass transfer 863 second quantization 105, 115 SI units 1 – model potential formulae 684 selection rules Sil variational principle 778 – molecular frame representation – for electron impact excitation 932 silicon 721 – for molecular radiative transitions –clusters 597 – Monte Carlo method 869 521 – oscillator strength spectrum 1375 – normalization choices 668, 790, – for nonadiabatic coupling 745 – photodiode 650 821 – for photoionization 381 – proton scattering cross section – optical potential 715 – for radiative transitions 187 1377 – orbiting and spiraling collisions self-consistent field method single active electron approximation 662 – energy derivatives 472 1086 – orientation and alignment 123, – for molecules 471 single, double, triple, quadruple 693 self-energy 208, 414, 439 (SDTQ) replacements 316 – photoionization 379 self-focusing 1058 single-atom detection 1080 – potential scattering 112, 669 – critical power 1058 single-atom laser 1033 – reactive 561, 978, 984 self-imaging 1133 single-centered expansion 757 ionic 576 self-induced transparency 1005 single-ion trap 457 – recombination 800, 829 self-pulsing instability 1033 single-particle model 902 – regions of validity (diagram) 871 self-trapping 1058 single-photon sources 1182 – relativistic effects 708 semiclassical approximation 675, singlet states 1218 – resonant 391, 671, 924 783, 835, 951, 997 singlet–triplet mixing – R-matrix 712, 714, 723 – for heavy particle scattering 754, – helium mixing angles 216 – Rydberg atom collisions 835 757 – scattering phase difference 700 Subject Index 1499

– spin-flip cross section 667 – resolution 101 – three-level 1016 sinusoidal variation 1171 spectrometer 647 – time-resolved 539, 643 Sisyphus effect 1097, 1098 – Fourier transform 608, 648 – translational energy 947 –originof 1096 – grazing incidence grating 648 –two-level 1015 size extensivity 472 – normal incidence grating 648 – two-photon 1017 Slater determinant 115, 350, 471 – spatial heterodyned 648 – ultraviolet 641 Slater integral 309 spectrometry – wavelength and frequency Slater rules 106 – photoelectron 908 standards 186 Slater-type orbital 317 spectroscopic data, atomic 197 – wavelength ranges 185 slice imaging 980 spectroscopic factor 366 spectrum generating algebras 87 slow light 1020, 1205 spectroscopic notation 176–179 speed of light 1 slowly varying envelope spectroscopy Spencer–Fano equation 1392 approximation 1000 – accelerator based 265, 269, 1359 spherical harmonics – in de Broglie optics 1130 – atomic 175 – angular momentum operator S-matrix 707, 882 – Auger 1346 actions 53 – impact parameter 877 – beam-foil 269 – definition 15 – near a resonance 710 – beam-gas 270 – spinor 53 SN1987A (supernova) 1242 – beam-laser 271 –tableof 69 Snell’s law 1131 – cavity ring-down 1342 –tensor 52 sodium, energy levels of 237 – cold-target recoil-ion momentum – vector 53 solar corona 922 spherical top 499 – emissivity of 1238 – Doppler 539 – Hamiltonian for 493 Index Subject solar radiation – Doppler-free 1015 spin groups spin(m) 94 – interaction with the atmosphere – electron emission 948 spin magnetic moment 998 1265 – electron energy loss 1345 spin polarimetry 908 solar wind 1266 – Fourier transform 608, 615, 648 spin-dependent effects solid harmonics 12 – hole-burning 629, 1015 – in collisions 129 – orthogonality 13 – infrared 607 – on radiative transitions in helium – product 13 absorption, defined 608 216 –table 69 emission, defined 608 – on scattering 938 – vector addition rule 13 – intensity versus line position 515 molecular 530 solids –iontrap 272 spin-dependent operators 97 – impurity spectroscopy in 1012 –Lambdip 629 spin-flip amplitude 667, 700, 938 soliton – laser 623 spinor representation 94 – in dispersive nonlinear media electric resonance (LER) 616 spin–orbit interaction 177, 308, 1058 magnetic resonance (LMR) 335, 938 – laser 1033 616, 618 spinorial invariant 15 – optical pulse 1070, 1074 – linear 1012 spin-polarized projectiles, scattering solvent shell 600, 603 –momentum 922 of 130, 699, 938 Sommerfeld parameter 1359 – nonlinear 1015 spin–rotation Hamiltonian 519 space physics 1397 –ofclusters 590 spline, cubic 136 space shuttle environment 576 – photoassociation 1103 split-step method 1113 space-fixed coordinates 557 – photoelectron 901 spontaneous decay 1010 space-fixed frame 742 angle-resolved 1346 spontaneous emission 1013, 1159 spark 644 ultraviolet 1346 –rateof 215, 1169 spatial coherence length 1138 X-ray 1348 – suppression of 1168, 1172 special functions 162 – polarization 1016 – Wigner–Weisskopf theory 1159 spectator stripping 979 – pump/probe 1015 spontaneous symmetry breaking spectator vacancy 921 – Raman 1060 – in molecules 501, 506 spectral – recoil ion momentum 873, 948, spontaneously broken symmetry – aliasing 610 955 1114 – density 1170 – saturation 1015 squeeze operator 1144 – line series 185 – selection rules 187 squeezed state 1144 – method, analysis of data 139 –Stark 238 – gravitational radiation detection – range of laser emission 1036 – submillimeter and far-infrared 1206 – redistribution 286 615 – two-mode, or twin-beam 1187 1500 Subject Index

squeezing stopping power 959, 1379 superluminal communication, – amplitude 1188 – at small speeds 1380 impossibility of 1200 – number 1188 straggling 1374 superluminal group delays 1203 – quadrature 1187, 1188 – energy loss 1381 superluminal velocity standard quantum limit (SQL) 1188 extremely thin absorbers 1382 – in tunneling 1203 Stark thick absorbers 1381, 1383 supermultiplet 178 – ionization 231 thin absorbers 1381 supernova 1242, 1245 – parameter 969 – Monte Carlo method 1384 – ejecta 1242 – representation 881 – multiple scattering 1384 – SN1987A 1242 –shift 231, 239, 493 – range 1383 – X-ray spectrum of 1236 dynamic (ac) 1002, 1073, 1080 straggling function 1374 supersonic hydrogenic 92 – analytic methods 1383 – beam 967, 1138 linear 231 stratosphere – expansion 967 quadratic 232 – terrestial 1261 surface third order 233 stripping reaction 978, 989 – extended X-ray absorption fine – spectroscopy 238 strong coupling structure (SEXAFS) 1349 – switching 240, 241 – cavity QED 1173 – ionization detector 969 state multipole – correspondence principle 840 – of intersection 479 – definition 127 – detecting and trapping atoms –physics 1343 – for coupled systems 129 1182 surface-hopping approximation 752 – symmetry properties 127 – in experiments 1174 surfaces, atomic processes on 1344, ujc Index Subject – time evolution 129 – open optical cavities 1174 1351 – transformation properties 127 strong interaction 418 – adsorption and desorption 1352 stationary phase approximation strong-field processes 1077 – Auger spectroscopy 1346 284, 675 strontium, Rydberg states of – chemisorption 1352 – superluminal group delays 1203 244 – impact scattering 1345 statistical STU parameters 700 – inverse photoemission spectroscopy – adiabatic channel model (SACM) Stückelberg 1347 752 – angle 1002, 1128 – photoelectron spectroscopy 1346 –analysisofdata 138 – oscillations 770 – resonance scattering 1345 – weight (level, term) 187 – phase 749 – X-ray absorption 1349 steepest descent, method of 168 Sturmian basis set 759 – X-ray photoelectron spectroscopy stellar atmospheres 1241 Sturmian expansion 796 1348 – circumstellar shells 1241 Sturmian functions 154 swarm method 947 Stern–Gerlach effect subexcitation electrons 1390 s-wave 1110 – atom optical 1128, 1134 submillimeter spectroscopy 615 Swings effect, in comets 1251 –inverse 1137 sub-Poissonian fields 1144 symmetric resonance 750 Stieltjes imaging 1358 sum frequency generation 1054, symmetric rotator stimulated emission 1023 1056 – angular momentum operators 30 stimulated raman adiabatic passage – nonlinear polarization 1054 – body frame components 30 (STIRAP) 1019 sum rule 393 – inertial frame components 30 stochastic differential equations – momentum space wave function – wave functions 30 1158 840 symmetric top 492, 519, 559 – Ito approach 1158 – oscillator strength 205 –energylevels 492 – Stratonovich approach 1158 –radialintegral 837 – Hamiltonian 492 stochastic integrals 1158 supercontinuum light – transition moments for 530 stochastic model, laser 1079 – generation of 1062 symmetry Stokes amplification supercontinuum radiation 644 – breaking 1114 – stimulated Raman scattering 1055 superelastic scattering 936, 937 –CPTtest 429, 430 Stokes parameter 126, 131, 695 superfine splitting 497 – dynamical 87 – angle-differential 126, 131 superfine structure 494, 501, 506 – groups (algebras) 87 – definition 131, 132 – octahedral 502 molecular 493, 498, 522 – generalized 126, 131 superfluid 1117, 1118 – oscillations 666 –integrated 126, 131 – Fermion 1120 synchrotron radiation 642, 907 Stokes vector 695 – strongly interacting 1120 – insertion devices 918 – density matrix representation 696 superhyperfine structure 505 – monochromator 908 Subject Index 1501

– polarization property 643 – terrestial 1261 throughput advantage, in Fourier – sources 918 Thomas peak 777, 865–867 transform spectroscopy 611 – spectral property 642 Thomas process 863 tidal recombination 800 – temporal property 642, 643 – classical 863 tight-binding approximation 1122 – undulator 643 – diagram for mass transfer 864 tilting transformation 90 – wiggler 643 – equations of constraint 864 time evolution operator 124 – interference effects 867 time of flight technique 935 T – off-energy-shell 866 time orbiting potential trap 1116 – quantum 864 time reversal symmetry 516 tableaux, outer product 79 Thomas ridge 865 time-independent perturbation theory Talbot effect 1133 Thomas–Fermi approximation 101 target continuum distorted wave 1111, 1115, 1310 time-of-flight (TOF) technique 935 approximation (TCDW) 777 Thomas–Fermi theory 295, 1358 time-of-flight analyzer 910 target recoil method, for electron – Dirac exchange correction 299 time-of-flight imaging 1117 scattering 933 – gradient expansion for the kinetic time-ordered operator 111, 331 target, excited, scattering from 936 energy 298, 302 T-matrix 707, 882 Taylor expansion 135 – no-binding result for molecules Tokamak 872 Taylor series algorithm 142 295 tomographic reconstruction 974 teleportation of photons 1200 – nonrelativistic energy expansion Tomonaga–Schwinger equation 111 tensor construction 116 300 TOP trap 1116 tensor coupled forms 116 – relativistic effects 303 topological phase 1136 tensor harmonics (table) 69 – von Weizsäcker correction 298 total angular momentum of the Index Subject tensor operator Thomas–Reiche–Kuhn sum rule composite system –algebra 37 205, 1004 – SU(2) transformation properties coupling of tensor operator 39 Thomson scattering 1006 55 properties of tensor operator 39 – cross section 919 – uncoupled and coupled basis tensor operator 37 differential 919 vectors 55 universal enveloping algebra 38 – nuclear 917 total cross section 930 Wigner Operators 40 Thomson theory of recombination total internal reflection, frustrated Wigner–Eckart theorem 39 807 1203 – for coupled systems 129 three-level processes 1016 total photoionization cross section – irreducible 38, 127 three-level systems 1018 908 tensor representation 94 – special effects in 1018 trajectory tensor spherical harmonics three-point vertex – in Monte Carlo calculations 873 – angular momentum operator – irreducible 407 transfer excitation 753 actions 52 – reducible 406 transfer ionization 753, 943 term series 184 threshold transit time broadening 1103 term value 184 – analytic continuation through transition array 178 term, atomic structure 176, 178 708, 793 transition moment matrix termolecular recombination 800 threshold cross section – orbital and spin selection rules ternary reactions, ion–molecule 581 – for photodetachment 387 523 tetrahedral symmetry, molecular – for photoionization 383, 384, transition probability, collisional 499 386, 818, 906, 923 – approximate formulae 750 thermal beam method 945 Auger decay effect 906, 923, – double passage 749 thermal coherence time 1138 925 – Landau–Zener model 746 thermal equilibrium delayed maximum 384, 386 – molecular 518 – density matrix for 125 – orbiting (shape) resonances 672 – multiple passage 751 thermal model threshold law – Nikitin model 747 – of radiative association 571 – Wannier 717, 781, 906 – nonadiabatic 744 thermal state 1177 – Wigner 781, 906 – Rosen–Zener–Demkov model thermal wavelength 1138 threshold, laser 748 thermochemistry 1335 – condition for 1023 – single passage 746 thermodynamical instability 1115 –gain 1023 transition state 575 thermosphere – population difference 1023 – barrier 563 – model for the Earth and planets – second threshold 1033 – loose 567 1274 threshold, maser 1179 – theory 1502 Subject Index

bimolecular statistical 566 triple-centered expansion 758 ultraviolet spectral region unimolecular statistical 568 tritium – definition 641 – tight 567 – β-decay 1358 – near ultraviolet 641 translation factor 761 troposphere, terrestial 1261 – vacuum ultraviolet 641 translational energy spectroscopy tunneling 871, 1360 uncertainty principle 947 – dynamic 494, 497 – energy–time form 1189 transmission matrix 555 matrix eigenvector table 503 – in cryptography 1201 transmission method, for electron – Hamiltonian matrix for 497 – number-phase form 1193 scattering 933 – in binary reactions 580 undulator 643, 907 transmittivity – ionization 240, 1081 unimolecular decay 566, 568 – coefficient of 1131 – reaction mechanism 569 –thermal 568 transparency – resonance 672 unimolecular reactions 544 – induced 1074 – RRKM correction 569 unit tensor operators – self-induced 1070 – superluminal delay time 1203 – coupling laws 41 transport cross section 665 – transmission probability for 1203 unitary group approach (UGA) 92, transverse diffusion 1095 – Wigner correction to 569 471 trap tunneling time unitary group U(n) 92 – frequency 1110 – definitions 1203 – generators of 92, 471 – optical 1116 – interpretation of 1204 unitary irreducible representations trapped ion method 946 – measurement using dieletric mirror 18 trapping 1203, 1204 units ujc Index Subject –atom 1096, 1098, 1099, 1103, – weak measurement approach – atomic 3 1116 1205 physical quantities in (table) 5 – axial motion 1101 twin beams and twin pulses 1145 – electromagnetic 1 – cyclotron motion 1101 two-beam resonance 1134 – Gaussian 1 –diffusion 1093 two-centered expansion 758 – Heaviside–Lorentz 1 – dipole force 1096 two-level atom 1000 natural units 4 – Earnshaw theorem 1098, 1099 –damped 1154, 1155 – in atomic spectroscopy 176 – electron 1104 – density matrix 1010 –SI 1 – Ioffe–Pritchard trap 1116 – model Hamiltonian 1001, 1010 – systems of 1 – ion chaos 1102 – squeezed bath 1154 universal set of quantum gates 1225 – ion crystal 1102 – steady state 1005 universe, early, molecular processes – ion phase transitions 1102 two-loop corrections 441 in 1244 – Lamb-Dicke regime 1101 two-particle operator 1108 unrestricted Hartree–Fock (UHF) – linear trap 1100 two-photon 110 – magnetic 1099, 1116 – absorption 1058 up-conversion pumping 1041 – magneto-optical 1098, 1103 – coherence 1073 uranium – magnetron motion 1101 – corrections 441 – fully stripped 1359 – many ions 1102 – laser 1033 – micromotion 1100, 1101 – process 1017 V – molecule 1096 – resonance 1072 – of charged particles 1099, 1101 two-state approximation vacancy production 953 – Penning trap 1101 – for collisions 743 – K-shell 952 – quantization of motion 1100 two-step mechanism – rotational coupling 956 – quantum theory 1094, 1097 – for heavy particle scattering 756 vacancy states – race track 1100 two-step process 1017 – nomenclature 920 – radius method, for recombination two-time correlation functions 1156 vacuum diagrams 107 processes 815 vacuum fluctuations 1159, 1186 – secular motion 1100, 1101 U vacuum polarization 330, 353, 415, – semiclassical theory 1093, 1097 440 – state 1073, 1179 U(n) Casimir operators 93 – current 330 – sympathetic cooling 1103 U(n) representation theory 92 vacuum splitting 1177 – time orbiting potential trap 1116 Ugo Fano 1397 vacuum state 330, 1143 –TOPtrap 1116 ultracold collisions 1103 –energy 330 – trap frequencies 1100, 1104 ultrafast electron diffraction 551 van Cittert–Zernike theorem 1138 triple tensors 118 ultrashort pulse generation 1032 van der Waals force 282, 570, 599 Subject Index 1503

– in neutral–neutral reactions 564 Wang transformation 519 – Wigner’s form 33 – unretarded limit 1172 Wannier exciton 600, 601 Wigner–Eckart theorem 39, 82, variable phase method 673 Wannier method 781, 782 119, 128 variation of constants method 112 – ridge 782 Wigner–Weisskopf theory of variational method 144 – threshold law 717, 781, 784, 906 spontaneous emission 1159 – for capture rate 565 Wannier state 1122 Wilkinson microwave anisotropy – Kohn 713 warm dense matter (WDM) 1303 probe 1244 – Kohn–Sham 302 warming, of troposphere 1296 Winans–Stückelberg vibrational wave – Schwinger 713 water clusters 603 function 809 – transition state 567 Watson Hamiltonian 481 window, optical 651 variational principle wave function witness operator 1217 – for bound state wave functions – coupled cluster expansion for WKB approximation 1130, 1359 200, 309 109 – in de Broglie optics 1130 – for charge transfer 778 wave function collapse work function 591 – for recombination processes 814 – energy-time uncertainty relation – Hohenberg–Kohn 301 1190 X – Rayleigh–Ritz 200 – speed of 1197 –Sil 778 wave operator 336 xenon vector coupling coefficients 31 wave packet – photoionization of 387 vector solid harmonics – coherent 1071 X-ray – angular momentum operator waveguide – absorption 1349 actions 53 – atomic 1132 EXAFS 1376 Index Subject vectors of zero length 14 – radiating atoms in 1169 ionizing effects of 1391 velocity distribution, thermal 1011 wavelength standards 186 – diffraction 551 velocity mapping 980 wave–particle duality 1185, 1191 – emission 921 velocity-selective coherent weak coupling detector correction for 1385 population trapping 1105 – experiments on 1172 – pulses 551 vertical external cavity weak interaction 417 surface-emitting laser (VECSEL) weak measurement 1195 Y 1047 – approach to tunneling times vertical-cavity surface-emitting 1205 Young double slit 1135 laser (VCSEL) 1047 Weber bar 1206 Young tableau 79, 80 vibrational Weight, highest and vector 93 – excitation, theory 722 Weyl dimension formula 93 Z –period 547 white noise 1079 – scattering 977 Wick’s theorem 105, 332, 337 Zeeman effect 92, 228, 241, 493 – structure 480 Wiener–Khintchine theorem – anomalous 228 – transitions 526 1146 – classification of energy levels – wave packet 548, 549 wiggler 643, 907, 919 229 vibron model 95 Wigner – energy tabulation 230, 231 virial theorem 298 – causality condition 668 – Landé g-value 229 virus coat, symmetry of 506 – coefficient 560 – nonrelativistic theory 228 viscosity cross section 661 – function 1093, 1149 – normal 229 Voigt function 910 – threshold law 781, 906 – quadratic 230 Voigt line shape 279, 1012 – tunneling correction 569 – quadratic relativistic 230 Voi gt pr ofil e 1015 Wigner–Clebsch–Gordan coefficients – strong field 230 Vol kov s t a t e 1087 31 – weak field 228 Volkov wave function 724 – combinatorial definition 61 intermediate-coupling g-value von Neumann entropy 1217 – discretized representation functions 184 von Neumann rejection method, for 37 Landé g-value 184 random numbers 150 – Kronecker product reduction Lorentz unit 184 vortex 1117 32 magnetic splitting factor g W – Racah’s form 33 183 – tensor product space construction Schwinger g-value 184 Wadsworth mount 647 33 Zeeman slower 1103 waiting time probability 1181 – Van der Warden’s form 33 zone plate 1133