Download Atoms, Molecules and Optical Physics 1 and 2

Ingolf V. Hertel and Claus-Peter Schulz
Humboldt Universität zu Berlin and Max Born Institute Berlin-Adlershof
Atoms, Molecules and
Optical Physics
January 13, 2014
Springer
7:57 h (UTC+1)
Volume II
Molecules and Photons – Spectroscopy
and Collisions
Preface
The two textbooks on Atomic, Molecular and Optical (AMO) physics presented here aim at providing something like the canonical knowledge of modern atomic and molecular physics and to opening a first entry into optical
physics and quantum optics. All of these topics constitute a vital area of
active and highly productive research in physics. And in spite of, or perhaps
even because of its remarkable history the field continues to constitute an indispensable basis for any more profound understanding of nearly all branches
of modern physics, physical chemistry and partially even biological and material sciences. Specifically the latter appear to become more and more based
on genuine molecular concepts.
These textbooks address on the one hand advanced students of physics
and physical chemistry, who have to study these topics within their respective
curricula. At the same time, however, they should be useful to all those who
discover in different contexts that they miss some essential basics from this
field and who seek for suitable means to acquire that knowledge. Of course
these books also address quite specifically the PhD-student or the young
researcher who starts for the first time his or her own activities in the field –
or just wants to know more about it. They will find here reliable knowledge
and stimulating challenges for their own work. We thus have tried not only
to provide the essential basics for working with these topics, but whenever
possible also to inform the interested reader about the present state-of-the-art
and to allow him a glimpse on today’s cutting edge research.
The general remarks as well as details about formats, notation, units, and
typography outlined in the preface to Vol. 1 (Hertel and Schulz, 2014)
are equally valid for the present Vol. 2. In the following we just give a guide
through the contents, as the the readers will find many topics and details far
beyond the standard textbooks and routine teachings on AMO science.
Chapter 11 resumes the discussion of light (comprising in the broadest
sense the whole electromagnetic spectrum) and photons, key themes of these
two volumes. The focus is here on lasers (one of the most important tools
of modern AMO physics), Gaussian beams, polarization and nonlinear proi
ii
Preface
cesses. In the following Chap. 12 the emphasis is on the properties of photons
and coherence. In addition to discussing some basics of quantum optics and
its applications, we also complete now the theory of photon induced transitions (Chap. 4) and introduce field quantization which allows us to treat
spontaneous emission.
After these preparations we are ready to enter into molecular physics
and modern molecular spectroscopy. We start in Chap. 13 with diatomic
molecules, the most simple prototypes, and enhance our view with ‘real’
polyatomic molecules in Chap. 14 – with a brief excursion into the subject of
symmetries. While along this way we have already encountered various comparatively simple examples of molecular spectroscopy, Chapter 15 leads us
deep into a variety of sophisticated modern methods of spectroscopy. The field
is dominated today by laser based methods, but we also gain some insights
e.g. into the possibilities of photoelectron spectroscopy.
Three quite detailed Chapters 16-??coll3 are devoted to the present status
in the physics of electronic, atomic, molecular and ionic collisions (including
collisional ionization) – a topic of great practical importance and with demanding intellectual challenges, both from an experimental and theoretical
view point. Chapter 19 gives a down to earth manual for using the density
matrix. It also gives a brief look on the theory of measurement, including
a powerful method to analyze radiation patterns from anisotropically populated mixtures of excited states. Finally, making use of these concepts, an
introduction of the optical Bloch equations is given in Chap. 20, which again
addresses many exciting facets of quantum optics with interesting examples.
A possible extension of the two volumes published now is under consideration. Such a Vol. 3 would approach modern research even more closely
and illuminate some particularly hot and rapidly developing areas such as
ultra-cold matter and quantum gases, ultrafast dynamics, attosecond physics,
cluster spectroscopy and similar themes.
We wish all our readers an exciting and stimulating reading as well as
efficient understanding and successful learning. In several readings, we have
tried to produce text, mathematical formulas and figures as free from errors
as possible. Clearly, this can only be an approximate process. Thus, we encourage the readers to kindly communicate any critical comments, errors or
simply even typos which they may discover – and to make suggestions for
improvements wherever it appears advisable. We shall correct such errors at
the web-site http://staff.mbi-berlin.de/AMO/book-homepage/ if and as
soon as they become known to us.
As further reading we recommend for comparison or for a deeper look into
some specialties the textbooks listed below. .
Berlin Adlershof, January 2014
Ingolf V. Hertel and Claus-Peter Schulz
References
iii
Acronyms and terminology
AMO: ‘Atomic, molecular and optical’, physics.
References
Atkins, P. W. and R. S. Friedman: 2010. Molecular Quantum Mechanics.
Oxford: Oxford University Press, 2nd edn.
Bergmann, L. and C. Schaefer: 1997. Constituents of Matter - Atoms,
Molecules, Nuclei and Particles. Berlin, New York: Walter der Gruyter,
902 pages.
Blum, K.: 2012. Density Matrix Theory and Applications. Atomic, Optical,
and Plasma Physics 64. Berlin, Heidelberg: Springer Verlag, 3rd edn., 343
pages.
Born, M. and E. Wolf: 2006. Principles of Optics. Cambridge University
Press, 7th (expanded) edn.
Bransden, B. H. and C. J. Joachain: 2003. The Physics of Atoms and
Molecules. Prentice Hall Professional.
Brink, D. M. and G. R. Satchler: 1994. Angular Momentum. Oxford:
Oxford University Press, 3 edn., 182 pages.
Demtröder, W.: 2010. Atoms, Molecules and Photons. Berlin, Heidelberg,
New York: Springer, 2nd edn.
Demtröder, W.: 2008a. Laser Spectroscopy, vol. 1: Basic Principles. Berlin,
New York: Springer, 4 edn., 457 pages.
Demtröder, W.: 2008b. Laser Spectroscopy, vol. 2: Experimental Techniques. Berlin, New York: Springer, 4 edn., 697 pages.
Drake, G. W. F., ed.: 2006. Handbook of Atomic, Molecular and Optical
Physics. Heidelberg, New York: Springer.
Edmonds, A. R.: 1996. Angular Momentum in Quantum Mechanics. Princeton, NJ, USA: Princeton University Press, 154 pages.
Hertel, I. V. and C. P. Schulz: 2014. Atoms, Molecules and Optical Physics
1; Atoms and Spectroscopy, vol. 1 of Springer-Textbook. Berlin Heidelberg:
Springer, 1st edn.
Loudon, R.: 2000. Quantum Theory of Light. Oxford, New York: Oxford
University Press, 3rd edn.
Mukamel, S.: 1999. Principles of Nonlinear Optical Spectroscopy. Oxford:
Oxford University Press, 576 pages.
Steinfeld, J. I.: 2005. Molecules and Radiation - 2nd Edition, An Introduction to Modern Molecular Spectroscopy. Mineola, NY: Dover Edition.
Weissbluth, M.: 1978. Atoms and Molecules. Student Edition. New York,
London, Toronto, Syndey, San Francisco: Academic Press, 713 pages.
Acknowledgements
Over the past years, many colleagues have encouraged and stimulated us
to move forward with this work, and helped with many critical hints and
suggestions. Most importantly, we have received a lot of helpful material and
state of the art data for inclusion in these textbooks.
We would like to thank all those who have in one or the other way contributed to close a certain gap in the standard textbook literature in this
area – that is at least what we hope to have achieved. Specifically we mention Robert Bittl, Wolfgang Demtroeder, Melanie Dornhaus, Kai Godehusen,
Uwe Griebner, Hartmut Hotop, Marsha Lester, John P. Maier, Reinhardt
Morgenstern, Hans-Hermann Ritze, Horst Schmidt-Boecking, Ernst J. Schumacher, Guenter Steinmeyer, Joachim Ullrich, Marc Vrakking und Roland
Wester ; their contributions are specifically noted in the respective lists of
references.
Of course, there all other sources are documented which we have used for
informations and which have provided data which we have used to generate
the figures in these books.
One of us (IVH) is particularly grateful to the Max-Born-Institute for
providing the necessary resources (including computer facilities, library access, and office space etc.) for continuing the work on this book after official
retirement.
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Volume II Molecules and Photons – Spectroscopy and Collisions
Preface Vol. 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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11 Lasers, light beams and light pulses . . . . . . . . . . . . . . . . . . . . . . .
11.1 Lasers – a brief introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.1.1 Basic principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.1.2 FABRY-PÉROT resonator . . . . . . . . . . . . . . . . . . . . . . . . . .
11.1.3 Stable, transverse modes and diffraction losses . . . . . . .
11.1.4 The amplifying medium . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.1.5 Threshold condition and stationary state . . . . . . . . . . . .
11.1.6 Laser rate equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.1.7 Line profiles and hole burning . . . . . . . . . . . . . . . . . . . . . .
11.2 Gaussian beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.1 Diffraction limited profile of a laser beam . . . . . . . . . . . .
11.2.2 FAUNHOFER diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.3 Ray transfer matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.4 Focussing a Gaussian beam . . . . . . . . . . . . . . . . . . . . . . . .
11.2.5 Measuring beam profiles with a razor blade . . . . . . . . . .
11.2.6 The M2 factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.3 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.3.1 Polarization and time dependent intensity . . . . . . . . . . .
11.3.2 Lambda-quarter and half-wave plates . . . . . . . . . . . . . . .
11.3.3 STOKES parameters, partially polarized light . . . . . . . . .
11.4 Wave-packets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.4.1 Description of laser pulses . . . . . . . . . . . . . . . . . . . . . . . . .
11.4.2 Spatial and temporal intensity distribution . . . . . . . . . .
11.4.3 Frequency combs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5 Measuring durations of short laser pulses . . . . . . . . . . . . . . . . .
11.5.1 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5.2 Correlation functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5.3 Interferometric measurement . . . . . . . . . . . . . . . . . . . . . . .
11.5.4 Experimental examples . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.6 Nonlinear processes in Gaussian laser beams . . . . . . . . . . . . . . .
11.6.1 General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.6.2 Cylindrical geometry (2D geometry) . . . . . . . . . . . . . . . .
11.6.3 Conical geometry (3D geometry) . . . . . . . . . . . . . . . . . . .
11.6.4 Spatially resolved measurements . . . . . . . . . . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Contents
12 Coherence and photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1 Some basics for quantum optics . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.2 First-order degree of coherence . . . . . . . . . . . . . . . . . . . .
12.1.3 Quasi-monochromatic light . . . . . . . . . . . . . . . . . . . . . . . .
12.1.4 Temporal or longitudinal coherence . . . . . . . . . . . . . . . . .
12.1.5 Higher-order degree of coherence . . . . . . . . . . . . . . . . . . .
12.1.6 Photon “bunching” experiments . . . . . . . . . . . . . . . . . . . .
12.1.7 Spatial or lateral coherence . . . . . . . . . . . . . . . . . . . . . . . .
12.1.8 Astronomical interferometry . . . . . . . . . . . . . . . . . . . . . . .
12.1.9 HANBURY BROWN-TWISS stellar interferometer . . . . . .
12.1.10 Bunching and anti-bunching . . . . . . . . . . . . . . . . . . . . . .
12.2 Photons, photon states, and radiation modes . . . . . . . . . . . . . . .
12.2.1 Towards quantization of the radiation field . . . . . . . . . .
12.2.2 Modes of the radiation field . . . . . . . . . . . . . . . . . . . . . . . .
12.2.3 Density of states and black body radiation . . . . . . . . . . .
12.2.4 Number of photons per mode . . . . . . . . . . . . . . . . . . . . . .
12.2.5 The multi-mode field and energy . . . . . . . . . . . . . . . . . . .
12.3 Field quantization and optical transitions . . . . . . . . . . . . . . . . . .
12.3.1 Second quantization and photon number states . . . . . . .
12.3.2 The electric field operator . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.3 GLAUBER states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.4 Addendum for multi-mode states . . . . . . . . . . . . . . . . . . .
12.3.5 Interaction Hamiltonian for dipole transitions . . . . . . . .
12.3.6 Perturbation theory and spontaneous emission . . . . . .
12.3.7 Spontaneous emission in a cavity . . . . . . . . . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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13 Diatomic molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.1 Characteristic energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.1.1 Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.1.2 Electronic energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.1.3 Vibrational energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.1.4 Rotational energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.2 Born-Oppenheimer approximation . . . . . . . . . . . . . . . . . . . . . .
13.2.1 Molecular potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.2.2 General form of molecular potentials . . . . . . . . . . . . . . . .
13.2.3 Nuclear wave functions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.2.4 Harmonic potential and harmonic oscillator . . . . . . . . . .
13.2.5 Morse potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.2.6 VAN DER WAALS molecules . . . . . . . . . . . . . . . . . . . . . . .
13.3 Nuclear motion: rotation and vibration . . . . . . . . . . . . . . . . . . . .
13.3.1 SCHRÖDINGER equation . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.3.2 Rigid rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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13.3.3 Population of rotational levels and nuclear spin . . . . . .
13.3.4 Specific heat capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.3.5 Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.3.6 Non-rigid rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.3.7 DUNHAM coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.4 Dipole transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.4.1 Rotational transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.4.2 Centrifugal distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.4.3 STARK effect: polar molecules in an electric field . . . . . .
13.4.4 Vibrational transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.4.5 Vibration-rotation spectra . . . . . . . . . . . . . . . . . . . . . . . . .
13.4.6 RYDBERG-KLEIN-REES method . . . . . . . . . . . . . . . . . . . .
13.5 Molecular orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.5.1 Variational method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.5.2 Specialization for H+
2 .............................
13.5.3 Charge exchange in the H+
2 system . . . . . . . . . . . . . . . . .
13.5.4 MOs for homonuclear molecules . . . . . . . . . . . . . . . . . . . .
13.6 Construction of total angular momentum states . . . . . . . . . . . .
13.6.1 Total orbital angular momentum . . . . . . . . . . . . . . . . . . .
13.6.2 Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.6.3 Total angular momentum . . . . . . . . . . . . . . . . . . . . . . . . . .
13.6.4 HUND’s coupling cases . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.6.5 Reflection symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.6.6 Lambda-type doubling . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.6.7 Example H2 – MO ansatz . . . . . . . . . . . . . . . . . . . . . . . . .
13.6.8 Valence bond theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.6.9 Nitrogen and oxygen molecule . . . . . . . . . . . . . . . . . . . . .
13.7 Heteronuclear molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.7.1 Energy terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.7.2 Filling the orbitals with electrons . . . . . . . . . . . . . . . . . . .
13.7.3 Lithiumhydrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13.7.4 Alkali halides: ionic bonding . . . . . . . . . . . . . . . . . . . . . . .
13.7.5 Nitrogen monoxide, NO . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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14 Polyatomic molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.1 Rotation of polyatomic molecules . . . . . . . . . . . . . . . . . . . . . . . . .
14.1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.1.2 Spherical rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.1.3 Symmetric rigid rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.1.4 Asymmetric rigid rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.2 Vibrational modes of polyatomic molecules . . . . . . . . . . . . . . . .
14.2.1 Normal modes of vibration . . . . . . . . . . . . . . . . . . . . . . . .
14.2.2 Energies and transitions of normal modes . . . . . . . . . . .
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14.2.3 Linear, triatomic molecules AB2 . . . . . . . . . . . . . . . . . . . .
14.2.4 Nonlinear triatomic molecules AB2 . . . . . . . . . . . . . . . . .
14.2.5 Inversion vibration in ammonia . . . . . . . . . . . . . . . . . . . .
14.3 Symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.3.1 Symmetry operations and elements . . . . . . . . . . . . . . . . .
14.3.2 Point groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.3.3 Eigenstates of polyatomic molecules . . . . . . . . . . . . . . . .
14.3.4 JAHN-TELLER effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.4 Electronic states of some polyatomic molecules . . . . . . . . . . . . .
14.4.1 A first example: H2 O . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.4.2 Hybridization – sp3 orbitals . . . . . . . . . . . . . . . . . . . . . . .
14.4.3 Electronic states of NH3 . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.4.4 sp2 hybrid orbitals forming double bonds from . . . . . .
14.4.5 Triple bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.5 Conjugated molecules and the HÜCKEL method . . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15 Molecular spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.2 Microwave spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.3 Infrared spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.3.2 FOURIER transform infrared spectroscopy . . . . . . . . . . .
15.3.3 Infrared action spectroscopy . . . . . . . . . . . . . . . . . . . . . . .
15.4 Electronic spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.4.1 FRANCK-CONDON factors . . . . . . . . . . . . . . . . . . . . . . . . .
15.4.2 Selection rules for electronic transitions . . . . . . . . . . . . .
15.4.3 Radiationless transitions . . . . . . . . . . . . . . . . . . . . . . . . . .
15.4.4 Rotational excitation in electronic transitions . . . . . . . .
15.4.5 Classical emission and absorption spectroscopy . . . . . . .
15.5 Laser spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.5.1 Laser induced fluorescence . . . . . . . . . . . . . . . . . . . . . . . . .
15.5.2 REMPI for a ‘simple’ triatomic molecule . . . . . . . . . . . .
15.5.3 Cavity ring down spectroscopy . . . . . . . . . . . . . . . . . . . . .
15.5.4 Spectroscopy of small free biomolecules . . . . . . . . . . . . .
15.5.5 Other important methods . . . . . . . . . . . . . . . . . . . . . . . . .
15.6 RAMAN spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.6.2 Classical interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.6.3 Quantum mechanical theory . . . . . . . . . . . . . . . . . . . . . . .
15.6.4 Experimental aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.6.5 Examples of RAMAN spectra . . . . . . . . . . . . . . . . . . . . . . .
15.6.6 Nuclear spin statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.7 Nonlinear spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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956
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978
978
980
984
987
987
991
993
995
996
1000
1000
1002
1010
1013
1017
1018
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1020
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15.7.1 Some basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.7.2 An example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.8 Photoelectron spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.8.1 Experimental basis and the principle of PES . . . . . . . . .
15.8.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.8.3 TPES, PFI, ZEKE, KETOF, MATI . . . . . . . . . . . . . . . .
15.8.4 PES for negative ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.8.5 PEPICO, TPEPICO and variations . . . . . . . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1033
1037
1039
1039
1042
1047
1049
1050
1056
1061
16 Basics of atomic collision physics: elastic processes . . . . . . . .
16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16.1.1 Integral and total cross sections . . . . . . . . . . . . . . . . . . . .
16.1.2 Principle of detailed balance . . . . . . . . . . . . . . . . . . . . . . .
16.1.3 Integral elastic cross sections . . . . . . . . . . . . . . . . . . . . . . .
16.2 Differential cross sections and kinematics . . . . . . . . . . . . . . . . . .
16.2.1 Experimental considerations . . . . . . . . . . . . . . . . . . . . . . .
16.2.2 Collision kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16.2.3 Mass selection of atomic clusters . . . . . . . . . . . . . . . . . . .
16.3 Elastic scattering and classical theory . . . . . . . . . . . . . . . . . . . . .
16.3.1 The differential cross section . . . . . . . . . . . . . . . . . . . . . . .
16.3.2 The optical rainbow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16.3.3 The classical deflection function . . . . . . . . . . . . . . . . . . . .
16.3.4 Rainbows and other remarkable oscillations . . . . . . . . . .
16.4 Quantum theory of elastic scattering . . . . . . . . . . . . . . . . . . . . . .
16.4.1 General formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16.4.2 Angular momentum and impact parameter . . . . . . . . . .
16.4.3 Partial wave expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16.4.4 Semiclassical approximation . . . . . . . . . . . . . . . . . . . . . . .
16.4.5 Scattering phase shifts at low kinetic energies . . . . . . .
16.4.6 Scattering matrices for pedestrians . . . . . . . . . . . . . . . . .
16.5 Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16.5.1 Types and phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16.5.2 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16.5.3 An example: electron helium scattering . . . . . . . . . . . . . .
16.6 BORN approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1069
1071
1073
1075
1079
1079
1082
1086
1088
1089
1089
1092
1095
1104
1105
1107
1109
1111
1114
1118
1122
1122
1124
1127
1131
1134
1135
17 Inelastic collisions – a first overview . . . . . . . . . . . . . . . . . . . . . .
17.1 Simple models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17.1.1 Reactions without threshold energy . . . . . . . . . . . . . . . . .
17.1.2 The absorbing sphere model . . . . . . . . . . . . . . . . . . . . . . .
17.1.3 An example: charge exchange . . . . . . . . . . . . . . . . . . . . . .
1139
1139
1139
1141
1142
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17.1.4 MASSEY criterium for inelastic collisions . . . . . . . . . . . .
17.2 Excitation functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17.2.1 Impact excitation by electrons and protons . . . . . . . . . .
17.2.2 Electron impact excitation of He . . . . . . . . . . . . . . . . . . .
17.2.3 Finer details in e− + He impact excitation . . . . . . . . . . .
17.2.4 Electron collisions with rare gases . . . . . . . . . . . . . . . . . .
17.2.5 Electron impact at atomic mercury – the
FRANCK-HERTZ experiment . . . . . . . . . . . . . . . . . . . . . . .
17.2.6 Molecular excitation by electron impact . . . . . . . . . . . . .
17.2.7 Threshold laws for excitation and ionization . . . . . . . . .
17.3 Scattering theory for the multichannel problem . . . . . . . . . . . . .
17.3.1 General formulation of the problem . . . . . . . . . . . . . . . . .
17.3.2 Potential matrix and coupling elements . . . . . . . . . . . . .
17.3.3 The adiabatic representation . . . . . . . . . . . . . . . . . . . . . . .
17.3.4 The diabatic representation . . . . . . . . . . . . . . . . . . . . . . . .
17.4 Semiclassical approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17.4.1 Time dependent SCHRÖDINGER equation . . . . . . . . . . . .
17.4.2 Coupling elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17.4.3 Solution of the coupled differential equations . . . . . . . . .
17.4.4 LANDAU-ZENER formula . . . . . . . . . . . . . . . . . . . . . . . . . .
17.4.5 A simple example: Na+ +Na(3p) . . . . . . . . . . . . . . . . . . . .
17.4.6 STÜCKELBERG oscillations . . . . . . . . . . . . . . . . . . . . . . . .
17.5 Collision processes with highly charged ions (HCI) . . . . . . . . . .
17.5.1 Above-barrier model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17.5.2 An experiment on electron exchange . . . . . . . . . . . . . . . .
17.5.3 HCI collisions and ultrafast dynamics . . . . . . . . . . . . . . .
17.6 Surface hopping, conical intersections and reactions . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1146
1146
1147
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1164
1167
1170
1170
1172
1174
1175
1178
1182
1186
1187
1190
1192
1193
1196
1197
18 Electron impact excitation and ionization . . . . . . . . . . . . . . . . .
18.1 Formal scattering theory and applications . . . . . . . . . . . . . . . . .
18.1.1 Close-coupling equations . . . . . . . . . . . . . . . . . . . . . . . . . .
18.1.2 Theoretical methods and experimental examples . . . . .
18.2 BORN approximation for inelastic collisions . . . . . . . . . . . . . . . .
18.2.1 FBA scattering amplitude . . . . . . . . . . . . . . . . . . . . . . . . .
18.2.2 Cross sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18.2.3 BORN approximation and RUTHERFORD scattering . . .
18.2.4 An example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18.3 Generalized oscillator strength . . . . . . . . . . . . . . . . . . . . . . . . . . .
18.3.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18.3.2 Expansion for small momentum transfer . . . . . . . . . . . . .
18.3.3 Explicit evaluation of GOS for an example . . . . . . . . . .
18.3.4 Integral inelastic cross sections . . . . . . . . . . . . . . . . . . . . .
18.4 Electron impact ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1203
1203
1207
1213
1213
1215
1216
1217
1218
1218
1219
1221
1222
1222
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18.4.1
18.4.2
18.4.3
18.4.4
Integral cross sections and the LOTZ formula . . . . . . . . .
SDCS: Energy partitioning between the electrons . . . .
Behaviour at the ionization threshold . . . . . . . . . . . . . . .
DDCS: Double-differential cross section
and the BORN-BETHE approximation . . . . . . . . . . . . . . .
18.4.5 TDCS: Triple-differential cross sections . . . . . . . . . . . . . .
18.4.6 Electron momentum spectroscopy (EMS) . . . . . . . . . . . .
18.5 Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1227
1229
1232
1237
1246
1251
1255
1257
19 The density matrix – a first approach . . . . . . . . . . . . . . . . . . . . .
19.1 Some terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19.1.1 Pure and mixed states . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19.1.2 Density operator and density matrix . . . . . . . . . . . . . . . .
19.1.3 Matrix representation for selected examples . . . . . . . . . .
19.1.4 Coherence and degree of polarization . . . . . . . . . . . . . . .
19.2 Theory of measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19.2.1 State selector and analyzer . . . . . . . . . . . . . . . . . . . . . . . .
19.2.2 Interaction experiment with state selection . . . . . . . . . .
19.3 Selected examples of the density matrix . . . . . . . . . . . . . . . . . . .
19.3.1 Polarization matrix and STOKES parameters . . . . . . . . .
19.3.2 Atom in an isolated 1 P state . . . . . . . . . . . . . . . . . . . . . . .
19.4 Angular distribution and polarization of radiation . . . . . . . . . .
19.4.1 Formulation of the problem . . . . . . . . . . . . . . . . . . . . . . . .
19.4.2 General discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19.4.3 Details of the evaluation . . . . . . . . . . . . . . . . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1265
1265
1271
1272
1275
1278
1278
1280
1286
1286
1292
1301
1301
1306
1309
1313
1313
20 Optical BLOCH equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.1 Open questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.2 Two level system in quasi-monochromatic light . . . . . . . . . . . .
20.2.1 Dressed states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.2.2 RABI frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.2.3 Rotating wave approximation . . . . . . . . . . . . . . . . . . . . . .
20.2.4 The coupled system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.3.1 MOLLOW triplet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.3.2 AUTLER-TOWNES effect . . . . . . . . . . . . . . . . . . . . . . . . . .
20.4 Quantum systems in strong electromagnetic fields . . . . . . . . . .
20.4.1 Temporal evolution of the density matrix . . . . . . . . . . . .
20.4.2 Optical BLOCH equations for a two state system . . . . .
20.5 Excitation with continuous wave (cw) light . . . . . . . . . . . . . . . .
20.5.1 Relaxed steady state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1315
1315
1319
1319
1320
1321
1322
1324
1324
1326
1328
1328
1329
1332
1332
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20.5.2 Saturation broadening . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.5.3 Broad band and narrow band excitation . . . . . . . . . . . . .
20.5.4 Rate equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.5.5 Continuous excitation without relaxation . . . . . . . . . . . .
20.5.6 Continuous excitation with relaxation . . . . . . . . . . . . . .
20.6 BLOCH equations and short pulse spectroscopy . . . . . . . . . . . . .
20.6.1 Excitation with ultrafast laser pulses . . . . . . . . . . . . . . . .
20.6.2 Ultrafast spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.6.3 Rate equations and optical BLOCH equations . . . . . . . .
20.7 STIRAP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.7.1 Three level system in two laser fields . . . . . . . . . . . . . . . .
20.7.2 Energy splitting and state evolution . . . . . . . . . . . . . . . .
20.7.3 Experimental realization . . . . . . . . . . . . . . . . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1332
1334
1335
1336
1338
1339
1339
1341
1342
1347
1347
1349
1351
1355
1355
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1359
K
First BORN approximation for e+Na(3s)→e+Na(3p) . . . . . .
K.1 Evaluation of the generalized oscillator strength . . . . . . . . . . . .
K.2 Integration of the differential cross section . . . . . . . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1362
1362
1365
1365
1366
L
Guiding, detecting and energy analysis of electrons and
ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L.1 SEM, channeltron, microchannel plate . . . . . . . . . . . . . . . . . . . .
L.2 Index of refraction, lenses and directional intensity . . . . . . . . . .
L.3 Hemispherical energy selector . . . . . . . . . . . . . . . . . . . . . . . . . . . .
L.4 Magnetic bottle and other time of flight methods . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1367
1367
1372
1374
1377
1379
1380
M Statistical tensor and state multipoles . . . . . . . . . . . . . . . . . . .
M.1 Multipole expansion of the density matrix . . . . . . . . . . . . . . . . .
M.2 State multipoles and expectation values of multipole tensor
operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
M.3 Recoupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1382
1382
N
1390
1390
1393
1396
1397
1398
Optical pumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
N.1 A standard case: Na(3 2 S1/2 ↔ 3 2 P3/2 ) . . . . . . . . . . . . . . . . . . . .
N.2 Multipole moments and their experimental detection . . . . . . . .
N.3 Optical pumping with two frequencies . . . . . . . . . . . . . . . . . . . . .
Acronyms and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1385
1387
1389