Demtröder Atoms, Molecules and Photons

Transcription

1 Demtröder Atoms, Molecules and Photons

2 GRADUATE TEXTS IN PHYSICS Graduate Texts in Physics publishes core learning/teaching material for graduate- and advanced-level undergraduate courses on topics of current and emerging fields within physics, both pure and applied. These textbooks serve students at the MS- or PhD-level and their instructors as comprehensive sources of principles, definitions, derivations, experiments and applications (as relevant) for their mastery and teaching, respectively. International in scope and relevance, the textbooks correspond to course syllabi sufficiently to serve as required reading. Their didactic style, comprehensiveness and coverage of fundamental material also make them suitable as introductions or references for scientists entering, or requiring timely knowledge of, a research field. Series Editors Professor Richard Needs Cavendish Laboratory JJ Thomson Avenue Cambridge CB3 0HE, UK rn11@cam.ac.uk Professor William T. Rhodes Florida Atlantic University Imaging Technology Center Department of Electrical Engineering 777 Glades Road SE, Room 456 Boca Raton, FL 33431, USA wrhodes@fau.edu Professor H. Eugene Stanley Boston University Center for Polymer Studies Department of Physics 590 Commonwealth Avenue, Room 204B Boston, MA 02215, USA hes@bu.edu

3 Wolfgang Demtröder Atoms, Molecules and Photons An Introduction to Atomic-, Molecularand Quantum-Physics With677Figuresand42Tables 123

4 Professor Dr. Wolfgang Demtröder Universität Kaiserslautern FB Physik Erwin-Schrödinger-Str Kaiserslautern Germany ISSN e-issn ISBN e-isbn DOI / Springer Heidelberg Dordrecht London New York Library of Congress Control Number: c Springer-Verlag Berlin Heidelberg 2006, 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Integra Software Services Pvt. Ltd., Pondicherry Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 Preface to the Second Edition The first edition of this textbook had found a friendly acceptance. This second edition does not change the concept of the representation which combines the experimental techniques for the investigation of atoms and molecules and their results that have lead to the development of quantum physics. Some new developments in laser physics and quantum optics have been inserted in Chapter 12 in order to give the reader some ideas about the frontiers in these fields regarding experimental techniques and physical insight. This second edition represents a thoroughly revised version of the first edition, which, unfortunately, contained a lot of errors and misprints. I am grateful to many readers who have informed me about such errors and who offered corrections and improvements of the representation for a better understanding. I am particularly indebted to Dr. Nico Dam, Raboud University Nijmegen, Netherland and Prof. Zamik Rosenwaks, Ben Gurion University, Israel, who have sent me an extensive correction list. The author hopes, that this new edition will be well accepted and that critical readers will send their comments or ideas about possible improvements. I thank Dr. Th. Schneider, Springer Verlag for his continuous interest and encouragement. Kaiserslautern, October 2010 Wolfgang Demtröder

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7 Preface to the First Edition The detailed understanding of matter, its phase transitions and its interaction with radiation could be only reached, after its microscopic structure determined by the kind of atoms or molecules as basic constituents of matter had been investigated. This knowledge allowed the controlled optimization of characteristic properties of matter. Atomic physics therefore represents not only an area of important fundamental research, but has furthermore many applications which have essentially formed our present technical world. The understanding of materials and their use in daily life, has major impact of our culture and our attitude towards nature and our environment. This textbook is aimed as an introduction to the microscopic world of atoms, molecules and photons. It illustrates how our knowledge about the microscopic structure of matter and radiation came about and which crucial experiments forced an extension and refinement of existing classical theories, culminating in the development of quantum theory, which is now accepted as the basic theory of atomic and molecular physics. The book therefore starts with a short historical review about the role of experiments for correcting erroneous ideas and proving the existence of atoms and molecules. The close interaction between experiments and theory has been one of the reasons for the rapid development of atomic physics in the 19 th and 20 th centuries. Examples are the kinetic theory of gases, which could be completely understood by the assumption of moving atoms in the gas, or the postulation of energy quanta in the radiation field, which could explain the discrepancy between measurements of the spectral energy distribution of thermal radiation fields and classical electrodynamics. The new ideas of quantum physics and their corroboration by experiments are discussed in Chap. 3 while the fundamental equations of quantum mechanics and their applications to some simple examples are explained in Chap. 4. A theory can be best understood by applications to a real situation. In Chap. 5 the quantum theory of the simplest real system, namely the hydrogen atom, is presented. Here it is again illustrated, that experiments enforced an extension of quantum mechanics to quantum electrodynamics in order to understand all experimental results. The description of larger atoms with many electrons is treated in Chap. 6, which also reduces the chemical properties of chemical elements to the structure of the electron shells and explains why all elements can be arranged in a periodic table. The important subject of interaction of matter with radiation is discussed in Chap. 7. This prepares the ground for the explanation of lasers, treated in Chap. 8. Molecules, consisting of two or more atoms, form the basis for the great variety of our world. They are discussed in Chaps. 9 and 10. In particular the question, why and how atoms can form stable molecules, and which kind of interaction occurs,

8 VIII Preface to the First Edition is treated in more detail. In Chap. 11 the different experimental techniques for the investigation of atoms and molecules are presented, in order to give the reader a feeling for the inventive ideas and the necessary experimental skill for their realization. The last chapter presents a short overview on recent developments in atomic and molecular physics, which shall demonstrate that physics will be never a complete and finalized field. There is still much to explore and new ideas and scientific enthusiasm is needed, to push the border of our knowledge further ahead. Some examples in this chapter also illustrate possible important applications of new ideas such as the quantum computer or new techniques of frequency metrology used in the world wide global positioning system GPS. Many people have helped to publish this book. First of all I would like to thank the team of LE-TeX, who have made the layout. In particular Uwe Matrisch, who has looked after the editing process and who has taken care of many handwritten remarks and corrections of the author with great patience. Dr. Schneider from Springer-Verlag has always supported this project, although it took longer as anticipated. Many thanks go to all colleagues who have given their permission to reproduce figures or tables. This book is an extended version of volume 3 of a German textbook consisting of 4 volumes. The authors hopes, that it will find a comparable good acceptance as the German version. He will be grateful for any reply of readers, giving corrections of possible errors or hints to improvements. Any of such replies will be answered as soon as possible. A textbook lives from the active collaboration of its readers and the author looks foreward to a lively correspondence with his readers. He hopes that this book can contribute to a better understanding of this fascinating field of atoms, molecules and photons. Kaiserslautern, August 2005 Wolfgang Demtröder

9 Contents 1. Introduction 1.1 Contents and Importance of Atomic Physics Molecules: Building Blocks of Nature Survey on the Concept of this Textbook The Concept of the Atom 2.1 Historical Development Experimental and Theoretical Proofs for the Existence of Atoms Dalton s Law of Constant Proportions The Law of Gay-Lussac and the Definition of the Mole Experimental Methods for the Determination of Avogadro s Constant The Importance of Kinetic Gas Theory for the Concept of Atoms Can One See Atoms? Brownian Motion Cloud Chamber Microscopes with Atomic Resolution The Size of Atoms The Size of Atoms in the Van der Waals Equation Atomic Size Estimation from Transport Coefficients Atomic Volumes from X-Ray Diffraction Comparison of the Different Methods The Electric Structure of Atoms Cathode Rays and Kanalstrahlen Measurement of the Elementary Charge e How to Produce Free Electrons Generation of Free Ions The Mass of the Electron How Neutral is the Atom? Electron and Ion Optics Refraction of Electron Beams Electron Optics in Axially Symmetric Fields... 47

10 X Contents Electrostatic Electron Lenses Magnetic Lenses Applications of Electron and Ion Optics Atomic Masses and Mass Spectrometers J.J. Thomson s Parabola Spectrograph Velocity-Independent Focusing Focusing of Ions with Different Angles of Incidence Mass Spectrometer with Double Focusing Time-of-Flight Mass Spectrometer Quadrupole Mass Spectrometer Ion-Cyclotron-Resonance Spectrometer Isotopes The Structure of Atoms Integral and Differential Cross Sections Basic Concepts of Classical Scattering Determination of the Charge Distribution within the Atom from Scattering Experiments Thomson s Atomic Model The Rutherford Atomic Model Rutherford s Scattering Formula Summary Problems Development of Quantum Physics 3.1 Experimental Hints to the Particle Character of Electromagnetic Radiation Blackbody Radiation Cavity Modes Planck s Radiation Law Wien s Law Stefan Boltzmann s Radiation Law Photoelectric Effect Compton Effect Properties of Photons Photons in Gravitational Fields Wave and Particle Aspects of Light Wave Properties of Particles De Broglie Wavelength and Electron Diffraction Diffraction and Interference of Atoms Bragg Reflection and the Neutron Spectrometer Neutron and Atom Interferometry Application of Particle Waves Matter Waves and Wave Functions Wave Packets The Statistical Interpretation of Wave Functions Heisenberg s Uncertainty Principle

11 Contents XI Dispersion of the Wave Packet Uncertainty Relation for Energy and Time The Quantum Structure of Atoms Atomic Spectra Bohr s Atomic Model The Stability of Atoms Franck Hertz Experiment What are the Differences Between Classical and Quantum Physics? Classical Particle Paths Versus Probability Densities in Quantum Physics Interference Phenomena with Light Waves and Matter Waves The Effect of the Measuring Process The Importance of Quantum Physics for our Concept of Nature Summary Problems Basic Concepts of Quantum Mechanics 4.1 The Schrödinger Equation Some Examples The Free Particle Potential Barrier Tunnel Effect Particle in a Potential Box Harmonic Oscillator Two-and Three-Dimensional Problems Particle in a Two-dimensional Box Particle in a Spherically Symmetric Potential Expectation Values and Operators Operators and Eigenvalues Angular Momentum in Quantum Mechanics Summary Problems The Hydrogen Atom 5.1 Schrödinger Equation for One-electron Systems Separation of the Center of Mass and Relative Motion Solution of the Radial Equation Quantum Numbers and Wave Functions of the H Atom Spatial Distributions and Expectation Values of the Electron in Different Quantum States

12 XII Contents 5.2 The Normal Zeeman Effect Comparison of Schrödinger Theory with Experimental Results Relativistic Correction of Energy Terms The Electron Spin The Stern Gerlach Experiment Experimental Confirmation of Electron Spin Einstein de Haas Effect Spin-Orbit Coupling and Fine Structure Anomalous Zeeman Effect Hyperfine Structure Basic Considerations Fermi-contact Interaction Magnetic Dipole-Dipole Interaction Zeeman Effect of Hyperfine Structure Levels Complete Description of the Hydrogen Atom Total Wave Function and Quantum Numbers Term Assignment and Level Scheme Lamb Shift Correspondence Principle The Electron Model and its Problems Summary Problems Atoms with More Than One Electron 6.1 The Helium Atom Approximation Models Symmetry of the Wave Function Consideration of the Electron Spin The Pauli Principle Energy Levels of the Helium Atom Helium Spectrum Building-up Principle of the Electron Shell for Larger Atoms The Model of Electron Shells Successive Building-up of Electron Shells for Atoms with Increasing Nuclear Charge Atomic Volumes and Ionization Energies The Periodic System of the Elements Alkali Atoms Theoretical Models for Multielectron Atoms The Model of Independent Electrons The Hartree Method The Hartree Fock Method Configuration Interaction Electron Configurations and Couplings of Angular Momenta Coupling Schemes for Electronic Angular Momenta Electron Configuration and Atomic States

13 Contents XIII 6.6 Excited Atomic States Single Electron Excitation Simultaneous Excitation of Two Electrons Inner-Shell Excitation and the Auger Process Rydberg States Planetary Atoms Exotic Atoms Muonic Atoms Pionic and Kaonic Atoms Anti-hydrogen Atoms and Other Anti-atoms Positronium and Muonium Summary Problems Emission and Absorption of Electromagnetic Radiation by Atoms 7.1 Transition Probabilities Induced and Spontaneous Transitions, Einstein Coefficients Transition Probabilities, Einstein Coefficients and Matrix Elements Transition Probabilities for Absorption and Induced Emission Selection Rules Selection Rules for Spontaneous Emission Selection Rules for the Magnetic Quantum Number Parity Selection Rules Selection Rules for Induced Absorption and Emission Selection Rules for the Spin Quantum Number Higher Order Multipole Transitions Magnetic Dipole Transitions Two-Photon-Transitions Lifetimes of Excited States Line Profiles of Spectral Lines Natural Linewidth Doppler Broadening Collision Broadening X-Rays Bremsstrahlung Characteristic X-Ray-Radiation Scattering and Absorption of X-Rays X-ray Fluorescence Measurements of X-Ray Wavelengths Continuous Absorption and Emission Spectra Photoionization Recombination Radiation Summary Problems

14 XIV Contents 8. Lasers 8.1 Physical Principles Threshold Condition Generation of Population Inversion The Frequency Spectrum of Induced Emission Optical Resonators The Quality Factor of Resonators Open Optical Resonators Modes of Open Resonators Diffraction Losses of Open Resonators The Frequency Spectrum of Optical Resonators Single Mode Lasers Different Types of Lasers Solid-state Lasers Semiconductor Lasers Dye Lasers Gas Lasers Nonlinear Optics Optical Frequency Doubling Phase Matching Optical Frequency Mixing Generation of Short Laser Pulses Q-Switched Lasers Mode-Locking of Lasers Optical Pulse Compression Measurements of Ultrashort Optical Pulses Summary Problems Diatomic Molecules 9.1 The H + 2 Molecular Ion The Exact Solution for the Rigid H + 2 Molecule Molecular Orbitals and LCAO Approximations Improvements to the LCAO ansatz The H 2 Molecule Molecular Orbital Approximation The Heitler London Method Comparison Between the Two Approximations Improvements to the Approximations Electronic States of Diatomic Molecules The Energetic Order of Electronic States Symmetry Properties of Electronic States Electronic Angular Momenta Electron Spins, Multiplicity and Fine Structure Splittings

15 Contents XV Electron Configurations and Molecular Ground States Excited Molecular States Excimers Correlation Diagrams The Physical Reasons for Molecular Binding The Chemical Bond Multipole Interaction Induced Dipole Moments and van der Waals Potential General Expansion of the Interaction Potential The Morse Potential Different Binding Types Rotation and Vibration of Diatomic Molecules The Born-Oppenheimer Approximation The Rigid Rotor Centrifugal Distortion The Influence of the Electron Motion Vibrations of Diatomic Molecules Interaction Between Rotation and Vibration The Dunham Expansion Rotational Barrier Spectra of Diatomic Molecules Transition Matrix Elements Vibrational-Rotational Transitions The Structure of Electronic Transitions Continuous Spectra Summary Problems Polyatomic Molecules 10.1 Electronic States of Polyatomic Molecules The H 2 O Molecule Hybridization The CO 2 Molecule Walsh Diagrams Molecules with more than Three Atoms The NH 3 Molecule Formaldehyde and Other H 2 AB Molecules Aromatic Molecules and π-electron Systems Rotation of Polyatomic Molecules Rotation of Symmetric Top Molecules Asymmetric Rotor Molecules Vibrations of Polyatomic Molecules Normal Vibrations Quantitative Treatment Couplings Between Vibrations and Rotations

16 XVI Contents 10.5 Spectra of Polyatomic Molecules Vibrational Transitions within the Same Electronic State Rotational Structure of Vibrational Bands Electronic Transitions Clusters Production of Clusters Physical Properties of Clusters Chemical Reactions First Order Reactions Second Order Reactions Exothermic and Endothermic Reactions Determination of Absolute Reaction Rates Molecular Dynamics and Wave Packets Summary Problems Experimental Techniques in Atomic and Molecular Physics 11.1 Basic Principles of Spectroscopic Techniques Spectroscopic Instruments Spectrometers Interferometers Detectors Microwave Spectroscopy Infrared Spectroscopy Infrared Spectrometers Fourier Transform Spectroscopy Laser Spectroscopy Laser-Absorption Spectroscopy Optoacoustic Spectroscopy Optogalvanic Spectroscopy Cavity-Ringdown Spectroscopy Laser-Induced Fluorescence Spectroscopy Ionization Spectroscopy Laser Spectroscopy in Molecular Beams Nonlinear Laser Spectroscopy Saturation Spectroscopy Doppler-Free Two-Photon Spectroscopy Raman Spectroscopy Basic Principles Coherent Anti-Stokes Raman Spectroscopy Spectroscopy with Synchrotron Radiation Electron Spectroscopy Experiments on Electron Scattering Photoelectron Spectroscopy ZEKE Spectroscopy

17 Contents XVII 11.9 Measurements of Magnetic and Electric Moments in Atoms and Molecules The Rabi-Method of Radio-Frequency Spectroscopy Stark-Spectroscopy Investigations of Atomic and Molecular Collisions Elastic Scattering Inelastic Scattering Reactive Scattering Time-Resolved Measurements of Atoms and Molecules Lifetime Measurements Fast Relaxation Processes in Atoms and Molecules Summary Problems Modern Developments in Atomic and Molecular Physics 12.1 Optical Cooling and Trapping of Atoms Photon Recoil Optical Cooling of Atoms Optical Trapping of Atoms Bose Einstein Condensation Molecular Spectroscopy in a MOT Time-resolved Spectroscopy in the Femtosecond Range Time-resolved Molecular Vibrations Femtosecond Transition State Dynamics Coherent Control Optical Metrology with New Techniques Frequency Comb Atomic Clocks with Trapped Ions Squeezing New Trends in Quantum Optics Which Way Experiments The Einstein Podolski Rosen Paradox Schrödinger s Cat Entanglement and Quantum Bits Quantum Gates Summary Problems Chronological Table for the Development of Atomic and Molecular Physics Solutions to the Exercises References Subject Index