E. Richard CohenDavid R. LideGeorge L. TriggEditors

AIP Physics Desk ReferenceThird Edition

With 125 Illustrations

Springer

Contents

Preface to the Third Edition vPreface to the First Edition viiContributors xxxiTable of Fundamental Physical Constants xxxv

1. Symbols, Units, and Nomenclature 1E. Richard Cohen1.1 Physical Quantities 2

1.1.1 Symbols for quantities 21.1.2 Symbols for units 2

1.2 Physical Units 31.2.1 Base units 31.2.2 Dimension 3

1.3 The International System of Units (Systeme International, SI) 41.3.1 Base units 41.3.2 Conversion factors to SI units 6

1.4 Recommended Symbols for Physical Quantities 81.4.1 General physics 81.4.2 Quantum mechanics 181.4.3 Crystallography 181.4.4 Nuclear and fundamental particles 19

1.5 Nomenclature Conventions in Nuclear Physics 201.5.1 Nuclide 201.5.2 Characterization of interactions 20

1.6 References 21

2. Mathematical Basics 22E. Richard Cohen *2.1 Factorials 242.2 Progression and Series 242.3 Means 242.4 Summation Formulas 252.5 Binomial Theorem 252.6 Quadratic Equation 252.7 Differentiation 26

2.7.1 Taylor series 26

ix

§ CONTENTS

2.8 Integration 272.9 Logarithmic functions 28

2.9.1 Series 282.10 Exponential Functions 28

2.10.1 Derivatives 282.10.2 Integrals 29

2.11 Trigonometric Functions 292.11.1 Series expansions 302.11.2 Derivatives 302.11.3 Integrals 302.11.4 Plane triangles 312.11.5 Spherical triangles 31

2.12 Inverse Trigonometric Functions 322.12.1 Series expansions 322.12.2 Derivatives 322.12.3 Integrals 32

2.13 Hyperbolic Functions 332.13.1 Series expansions 342.13.2 Derivatives 342.13.3 Integrals 34

2.14 Inverse Hyperbolic Functions 352.14.1 Series expansions 352.14.2 Derivatives 352.14.3 Integrals 36

2.15 Gamma Function 362.15.1 Definite integrals 37

2.16 DeltaFunction 382.17 Vector Algebra 39

2.17.1 Notation 392.17.2 Dot product (scalar product or inner product) 392.17.3 Cross product (vector product or outer product) 392.17.4 Vector identities 392.17.5 Vector linear equations 402.17.6 Differential operators 40

2.18 Orthogonal Coordinate Systems 432.18.1 Gradient of/ , V / 432.18.2 Divergence of A, V-A 432.18.3 Curl of A, V x A - 432.18.4 Projected derivative, components of A «VB 442.18.5 Divergence of a tensor VT 452.18.6 Scalar LaplacianV2/ 462.18.7 Vector Laplacian V2A 46

2.19 Fourier Series and Fourier Transforms 472.19.1 Orthogonality condition 47

CONTENTS Xi

2.19.2 Completeness • 482.19.3 Convolution 48

2.20 Laplace Transforms 482.20.1 General properties 482.20.2 Linearity 482.20.3 Differentiation 482.20.4 Bessel functions 492.20.5 Spherical harmonics 532.20.6 Potential at ri due to a unit source at T2 532.20.7 Clebsch-Gordan (Wigner) coefficients 55

2.21 References 56

3. Acoustics 60Robert T. Beyer3.1 Important Acoustical Units 623.2 Oscillations of a Linear System 63

3.2.1 Analogies 653.3 General Linear Acoustics; Wave Propagation in Fluids 65

3.3.1 Plane waves 653.3.2 Spherical waves 663.3.3 Reflection and transmission 673.3.4 Velocity and attenuation of sound 67

3.4 High-Intensity Sound; Nonlinear Acoustics 723.4.1 Lagrangian form of wave equation 723.4.2 Solutions of Eulerian wave equation 733.4.3 Burgers' equation and other approximations 743.4.4 Radiation pressure 74

3.5 Atmospheric Acoustics 753.5.1 Velocity of sound in air 753.5.2 Refraction in a fluid medium 753.5.3 Attenuation in atmosphere 753.5.4 Doppler effect 75

3.6 Underwater Sound 763.7 Acoustic Transmission in Solids 77

3.7.1 Velocity in an extended polycrystalline solid 773.7.2 Configurational dispersion in a solid rod 773.7.3 Attenuation of sound in solids 77

3.8 Molecular Acoustics; Relaxation Processes 783.8.1 Propagation of sound 783.8.2 Excess sound attenuation in liquids 793.8.3 Ultrasonic propagation at very low temperatures 79

3.9 Bubbles, Cavitation, Sonoluminescence 803.9.1 Cavitation 803.9.2 Sonoluminescence 81

ENTS

3.10 Nondestructive Testing, Ultrasonic Imaging 813.10.1 , Nondestructive testing 813.10.2 JJltrasonic imaging 81

3.11 Noise and Its Control 813.11.1 Active suppression of noise 82

3.12 Room and, Architectural Acoustics 833.12.1 Sabine's formula 833.12.2 Practical architectural acoustics 83

3.13 Physiological and Psychological Acoustics 853.13.1 Loudness and loudness level 853.13.2 Auditory sensation area 863.13.3 Masking 863.13.4 Temporary threshold shift (TTS) 863.13.5 Pitch 873.13.6 Binaural hearing 873.13.7 Audiogram 87

3.14 Speech Communication 883.15 Bioacoustics 883.16 Musical Acoustics 89

3.16.1 Resonance frequencies for an organ pipe 893.16.2 Resonance frequencies for a rectangular membrane 893.16.3 Resonance frequencies for a circular membrane 89

3.17 Acoustical Measurements and Instruments 893.17.1 Absolute measurement of sound intensity 903.17.2 Calibration of microphones 903.17.3 Frequency measurement 903.17.4 Acoustic filter 91

3.18 References 91

4. Astronomy 93Jay M. Pasachoff4.1 Basic Data 944.2 Solar Systems 954.3 Stars and the Milky Way 1004.4 Time and Planetary Positions 112

5. Astrophysics and Cosmology 119Virginia Trimble5.1 Stellar Astronomy 120

5.1.1 Stellar structure and evolution 1205.1.2 Stellar atmospheres 1215.1.3 Nuclear reactions, energy generation, and nucleosynthesis . . 123

5.2 Binary Stars 1275.2.1 Significance 1275.2.2 Evolution of binary stars 128

CONTENTS Xiii

5.3 Star Clusters, Interstellar Medium, and The Milky Way 1285.3.1 Star clusters 1285.3.2 The galactic center 1305.3.3 The Milky Way: General properties 1305.3.4 Backgrounds 130

5.4 Galaxies 1315.4.1 Types and their properties 1315.4.2 Dark matter 1335.4.3 Formation and evolution of galaxies 1345.4.4 Collective properties, clustering, and large-scale structure . . . 135

5.5 High-Energy Astrophysics 1365.5.1 Basic physical mechanisms 1365.5.2 Neutron stars and black holes as endpoints of stellar evolution 1375.5.3 Pulsars and x-ray binaries 1375.5.4 Supernovae 1385.5.5 Quasars and other active galaxies 1395.5.6 Gamma ray bursters 140

5.6 Cosmology 1415.6.1 Evidence that the universe is expanding and experienced a Big

Bang 1415.6.2 The Friedmann-Robertson-Walker metric 1415.6.3 Big-Bang nucleosynthesis 1425.6.4 "Best values" of the parameters for a relativistic universe . . . 1435.6.5 Connections with particle physics 144

|, 5.7 References 144

6. Atomic and Molecular Collision Processes 145M. R. Flannery6.1 Introduction 1476.2 Collisions 148

6.2.1 Differential and integral cross sections 1486.2.2 Collision rates, collision frequency, and path length 1496.2.3 Energy and angular momentum: Center of mass and relative . 150

1 6.2.4 Elastic scattering 1516.2.5 Inelastic scattering 1516.2.6 Reactive scattering 1516.2.7 Center-of-mass to laboratory crgss-section conversion . . . . 151

6.3 General Collision Properties 1536.3.1 Momentum transfer 1536.3.2 Momentum transfer cross section 1536.3.3 Energy transfer 1546.3.4 Energy transfer cross sections 1566.3.5 Atomic units 159

r 6.3.6 Energy conversion factors 159I 6.3.7 Rydberg properties 160

)dv CONTENTS

6.4 Equilibrium Distributions 1636.4.1 Maxwell velocity distribution for free particles 1636.4.2 Two temperature Maxwell distributions 1646.4.3 Boltzmann distribution 1656.4.4 Classical statistical weights 1676.4.5 Association/dissociation equation 1716.4.6 Saha's ionization equations 1716.4.7 Macroscopic detailed balance 1736.4.8 Planck's equilibrium distribution 1746.4.9 Boltzmann equation 175

6.5 Macroscopic Rate Coefficients 1756.5.1 Scattering rate 1756.5.2 Energy transfer rate 1766.5.3 Transport cross sections and collision integrals 177

6.6 Quantal Transition Rates and Cross Sections 1786.6.1 Microscopic rate of transitions 1786.6.2 Detailed balance between rates 1796.6.3 Energy density of continuum states 1806.6.4 Inelastic cross sections 1816.6.5 Detailed balance between cross sections 1826.6.6 Examples of detailed balance 1826.6.7 Four useful expressions for the cross section 183

6.7 Born Cross Sections 1866.7.1 Fermi golden rules 1876.7.2 Ion (electron)-atom collisions 1886.7.3 Atom-atom collisions 1896.7.4 Quantal and classical impulse cross sections 1896.7.5 Atomic form factor and generalized oscillator strength . . . . 1906.7.6 Form factors for atomic hydrogen 1916.7.7 Rotational excitation 1926.7.8 List of Born cross sections for model potentials 193

6.8 Quantal Potential Scattering 1946.8.1 Partial wave expansion 1956.8.2 Scattering amplitudes 1966.8.3 Integral cross sections 1976.8.4 Differential cross sections 1976.8.5 Optical theorem 1996.8.6 Levinson's theorem 2006.8.7 Partial wave expansion for transport cross sections 2006.8.8 Born phase shifts 2016.8.9 Coulomb scattering 202

6.9 Collisions between Identical Particles 2026.9.1 Fermion and Boson scattering 203

CONTENTS XV

6.9.2 Coulomb scattering of two identical particles 2046.9.3 Scattering of identical atoms 205

6.10 Classical Potential Scattering 2066.10.1 Deflection functions 2066.10.2 Classical cross sections 2076.10.3 Orbiting cross sections 209

6.11 Quantal Inelastic Heavy-Particle Collisions 2116.11.1 Adiabatic formulation (kinetic coupling scheme) 2116.11.2 Diabatic formulation (potential coupling scheme) 2126.11.3 Inelastic scattering by a central field 2136.11.4 Two-state treatment 2146.11.5 Exact resonance 2156.11.6 Partial wave analysis 2176.11.7 Close coupling equations for electron-atom (ion) collisions . . 217

6.12 Semiclassical Inelastic Scattering 2196.12.1 Classical path theory 2206.12.2 Landau-Zener cross section 2216.12.3 Eikonal theories 221

6.13 Long-Range Interactions 2246.13.1 Polarization, electrostatic, and dispersion interactions 224

6.14 Radiative Processes 2256.14.1 Photon scattering by free and bound electrons 2256.14.2 Radiative emission rate 2286.14.3 Cross section for radiative recombination 2336.14.4 Radiative recombination rate 2346.14.5 Dielectronic recombination cross section 2366.14.6 Bremsstrahlung 2366.14.7 Bremsstrahlung cross section 2376.14.8 Dipole transition matrix elements 237

6.15 Atomic and Molecular Databases 2386.16 General References 2396.17 References 240

7. Atomic Spectroscopy 242Wolfgang L. Wiese7.1 Introduction » 2437.2 Photon Energies, Frequencies, and Wavelengths 243

7.2.1 Photon energy 2437.2.2 Frequency, wavelength, wavenumber 2447.2.3 Spectral wavelength ranges 2447.2.4 Wavelengths in air 2447.2.5 Wavelength standards 2447.2.6 Energy conversion factors 245

7.3 Atomic States, Atomic Shell Structure 245

CONTENTS

7.3.1 Quantum numbers 2457.3.2 Pauli exclusion principle, atomic shells 245

7.4 The Hydrogen Spectrum 2467.5 Alkali Spectra 2467.6 Atomic States and Spectra for Many-Electron Atoms 247

7.6.1 Typical features, general quantum designations 2477.6.2 Russell-Saunders or LS-coupling 2477.6.3 Customary notation, sample case 2487.6.4 Other coupling schemes 248

7.7 Atomic Structure Hierarchies, Selection Rules for Discrete Transitions 2507.7.1 Atomic structure hierarchies 2507.7.2 Selection rules for discrete transitions 251

7.8 Spectral Line Intensities, Atomic Transition Probabilities,/-Values,and Line Strengths 2527.8.1 Emission intensities 2527.8.2 Absorption intensities 2527.8.3 Line strengths 2527.8.4 Relationships among A, f, and S 2537.8.5 Relationships between spectral line and multiplet values . . . 2547.8.6 Tabulations 254

7.9 Atomic (Radiative) Lifetimes 2577.10 Scaling, Systematic Trends (Regularities), and Important Characteristics

of Spectra 2587.10.1 Hydrogenic (one-electron) species 2587.10.2 Atoms and ions with two or more electrons 2597.10.3 Important characteristics of complex spectra . . . . ; . . . . 259

7.11 Spectral Line Shapes, Widths, and Shifts 2607.11.1 Doppler broadening 2607.11.2 Pressure broadening 261

7.12 Spectral Continuum Radiation 2627.12.1 Hydrogenic species 2627.12.2 Many-electron systems 263

7.13 Sources of Spectroscopic Data 2637.14 References 263

8. Biological Physics 265Elias Greenbaum and Victor Bloomfield8.1 Introduction 2678.2 Intermolecular Forces < 267

8.2.1 Elementary electrostatic and dispersion interactions 2678.2.2 Force fields 2688.2.3 Interactions in water 2688.2.4 Ionic solutions and polyelectrolytes 269

8.3 Nucleic Acids 2698.3.1 Structures of nucleic acid bases and nucleotides 269

CONTENTS XVii

8.3.2 Energetics of bending and twisting 2718.3.3 Supercoiled DNA 271

8.4 Proteins and Amino Acids 2728.4.1 Peptide bond and polypeptide conformations 2738.4.2 Helix-coil transition and protein folding 274

8.5 Binding Thermodynamics 2748.6 Nuclear Magnetic Resonance 2758.7 Electron Paramagnetic Resonance 2788.8 Thermodynamics, Mitochrondria, and Chloroplasts 280

8.8.1 Free-energy change of a chemical reaction 2808.8.2 Electrical and chemical work 2818.8.3 Ion gradients, active transport, and ATP synthesis 2828.8.4 Mitochondria 2838.8.5 Chloroplasts 284

8.9 Signaling and Transport Across Cell Membranes 2848.9.1 Receptors 2878.9.2 Transporters 2888.9.3 Channels and pumps 288

8.10 Electrophysiology 2898.10.1 Impulses in nerve and muscle cells 2898.10.2 Properties of nerve and muscle cells 2898.10.3 Axons: The cable model 2918.10.4 Models for membrane current density 291

8.11 Photobiophysics 2938.12 Muscle and Contractility 2958.13 Characterizing Biopolymers in Solution 297

8.13.1 Sedimentation and diffusion 2978.13.2 Sedimentation equilibrium 2988.13.3 Rotational motion 2988.13.4 Frictional coefficients 2988.13.5 Electrophoresis and gel electrophoresis 2988.13.6 Scattering 2988.13.7 Dynamic light scattering 300

8.14 Biophysics, the Health Sciences, and Emerging Technology 3008.15 References 304

8.15.1 General references 3048.15.2 On-line resources , 3048.15.3 Specific references 304

9. Crystallography 306George A. Jeffrey and Vicky Lynn Karen9.1 Historical Sketch 3079.2 Crystal Data and Symmetry 309

9.2.1 Crystal system, space group, lattice constants, andstructure type 309

9.2.2 Reduced cells 3159.2.3 Physical properties of crystals 316

9.3 Crystal Diffraction 3169.3.1 Conditions for diffraction 3169.3.2 Single-crystal diffractometer 3199.3.3 Absorption 3219.3.4 X-ray absorption corrections 3219.3.5 Extinction 3239.3.6 Multiple reflections 3239.3.7 Diffraction by perfect crystals 3249.3.8 "Borrmann" or "anomalous transmission" effect 3249.3.9 Kossel and Kikuchi lines 3249.3.10 Powder diffractometry 3259.3.11 Powder diffraction profile refinement: Rietveld method . . . . 326

9.4 Structure Factor 3269.4.1 Atomic scattering factors/, (s) 3269.4.2 Dispersion corrections for x-ray atomic scattering factors . . . 3289.4.3 Geometrical structure factor 3319.4.4 Unitary and normalized structure factors 332

9.5 Thermal Motion 3329.6 Diffracting Density Function 3359.7 Phase Problem 336

9.7.1 Phase-solving methods 3369.7.2 Patterson synthesis 3379.7.3 Direct methods 337

9.8 Crystal Structure Refinement: Method of Least Squares 3379.9 References 3399.10 Appendix: Crystallographic Data Sources 343

9.10.1 Introduction 3439.10.2 Categories, quality, and description 3439.10.3 Major sources of crystallographic data 344

10. Earth, Ocean, and Atmosphere Physics 349Ferris Webster10.1 Introduction 35010.2 Properties of Planet Earth 350

10.2.1 Planetary dimensions and constants , . . 35010.2.2 Ocean areas, volumes, and depths 351

10.3 Ocean 35310.3.1 Seawater properties 35310.3.2 Air-sea interaction 35910.3.3 Tides 36010.3.4 Waves 36110.3.5 Geophysical fluid dynamics 362

10.4 Atmosphere 363

w

CONTENTS Xix

10.4.1 Principal atmospheric constituents 36310.4.2 Properties of moist air 36310.4.3 Properties of dry air 36410.4.4 U.S. Standard Atmosphere (1976) 365

10.5 Global Climate 37010.5.1 Earth's radiation balance 37010.5.2 Global temperature trends 37110.5.3 Atmospheric CO2 concentrations 374

10.6 References 375

11. Electricity and Magnetism 376David J. Griffiths11.1 Introduction 37711.2 Electrostatics 37711.3 Magnetostatics 38011.4 Electrodynamics 38211.5 Conservation Laws 38611.6 Electromagnetic Waves 38711.7 Radiation 39011.8 Relativistic Formulation 39311.9 Circuits 39511.10 Units 39811.11 References 400

12. Elementary Particles 402H. Schellman12.1 The Standard Model 403

12.1.1 Fundamental fermions 40312.1.2 Electroweak couplings 40412.1.3 Electroweak Lagrangian 40412.1.4 Cabibbo-Kobayashi-Maskawa mixing matrix 40512.1.5 CP violation in the kaon system 40612.1.6 Neutrino masses and mixing 40712.1.7 Strong interactions 408

12.2 Selected Particle Properties 40812.3 Kinematics 410

12.3.1 Relativistic kinematics of reactions and decays 41012.3.2 Boost of a four-vector 41112.3.3 Decay length distribution 41112.3.4 Two-body decays 41112.3.5 Three-body decays 41112.3.6 Two-body reactions 41212.3.7 Mandelstam variables 41212.3.8 Transformations between the laboratory and the center

of mass frames 413

XX CONTENTS

12.3.9 In specific frames 41312.3.10 Lepton scattering 41312.3.11 Inclusive particle production 414

12.4 Decays and Cross Sections 41412.4.1 Lepton scattering 41412.4.2 e+e~ scattering 41612.4.3 Resonance production 41612.4.4 Hadron scattering 41712.4.5 Fragmentation 41712.4.6 Typical interaction cross sections 417

12.5 Particle Detectors 41812.5.1 Cherenkov radiation 41812.5.2 Ionization energy loss 41812.5.3 Multiple scattering through small angles 41912.5.4 Charged particle trajectories 41912.5.5 Calorimetry 424

12.6 References 424

13. Fluid Dynamics 425Stavros Tavoularis13.1 Introduction 42613.2 Properties of Common Fluids 42713.3 Mathematical Description 429

13.3.1 Equations of motion 42913.3.2 Dimensionless parameters 43113.3.3 Some laminar solutions 433

13.4 Instability, Transition, and Turbulence 43413.4.1 Hydrodynamic stability 43413.4.2 Transition 43413.4.3 Turbulence 435

13.5 Friction and Drag 43513.6 Gas Dynamics 437

13.6.1 Wave propagation in fluids 43713.6.2 One-dimensional, isentropic, compressible flow 43713.6.3 Shockwaves 438

13.7 Measurement in Fluids 43913.7.1 Bulk flow measurement 43913.7.2 Flow visualization 43913.7.3 Pressure measurement 43913.7.4 Velocity measurement 44013.7.5 Temperature measurement 44013.7.6 The fluid mechanics laboratory 441

13.8 References 441

CONTENTS XXi

14. Mechanics 444Florian Scheck14.1 Introduction 44514.2 Newtonian Mechanics 445

14.2.1 Newton's laws and inertial frames 44514.2.2 Kepler's laws for planetary motion 44714.2.3 Phase space and determinism 448

14.3 Canonical Mechanics 45014.3.1 Lagrangian functions and Euler-Lagrange equations 45014.3.2 Hamiltonian systems 45114.3.3 Canonical transformations and Hamilton-Jacobi equation . . . 45214.3.4 Action-angle variables, manifolds of motion 454

14.4 Rigid Bodies 45514.4.1 The inertia tensor 45514.4.2 Euler's equations 45714.4.3 Spinning tops 458

14.5 Relativistic Kinematics 45814.5.1 Lorentz transformations and decomposition theorem 45914.5.2 Causal orbits, energy, and momentum 46014.5.3 Time dilatation and scale contraction 46114.5.4 Motion of free particles in SRT and GRT 462

14.6 Hamiltonian Dynamical Systems 46414.6.1 Long-term behavior of mechanical systems 46414.6.2 Deterministic chaos in Hamiltonian systems 465

14.7 References 465

15. Medical Physics 467William R. Hendee and Michael Yester15.1 Introduction 469

15.1.1 Imaging 46915.2 Ionizing Radiation: X- and y-Rays 470

15.2.1 Interaction of x- and y-rays with tissue 47015.2.2 X-ray dosage 47215.2.3 X-ray image contrast 478

15.3 Ionizing Radiation: Electrons 47815.4 Health Risks 48015.5 Ultrasound > 48015.6 Magnetic Resonance 48015.7 Brachytherapy .< 48315.8 Nuclear Medicine 48715.9 References 489

16. Molecular Spectroscopy and Structure 492Peter F. Bernath16.1 Introduction 493

XXH CONTENTS

16.2 Rotational Spectroscopy 49316.2.1 Diatomics 49416.2.2 Linear Molecules 49816.2.3 Symmetric tops 49816.2.4 Asymmetric tops 49916.2.5 Spherical tops 502

16.3 Vibrational Spectroscopy 50216.3.1 Diatomics 50316.3.2 Linear molecules 50716.3.3 Symmetric tops 50916.3.4 Asymmetric tops 51116.3.5 Spherical tops 51116.3.6 Raman Spectroscopy 512

16.4 Electronic Spectra 51316.4.1 Diatomics 51416.4.2 Polyatomics 517

16.5 Structure Determination 51716.6 References 520

17. Nonlinear Physics and Complexity 522Paul Manneville17.1 Dynamical Systems and Bifurcations 523

17.1.1 Preliminaries 52317.1.2 Tangent dynamics and center-manifold reduction 52517.1.3 Bifurcations 527

17.2 Chaos and Fractals 52917.2.1 The nature of chaos 53117.2.2 Fractal properties and dimensions 53217.2.3 Routes to chaos 53417.2.4 Applied nonlinear dynamics 535

17.3 Space-Time Dynamical Systems 53617.3.1 Classification of instabilities and the modeling issue 53617.3.2 Continuous approach to space-time behavior 53717.3.3 Discrete approach to space-time behavior 539

17.4 References 542

18. Nuclear Physics / . . 544Kenneth S. Krane18.1 Nuclear Properties ; 545

18.1.1 Size and shape of nuclei 54518.1.2 Mass and binding energy 54618.1.3 Electromagnetic moments 54618.1.4 Isospin in nuclei 548

18.2 Radioactive Decay 54918.2.1 Radioactive decay laws 549

CONTENTS XXiii

18.2.2 Alpha decay 55018.2.3 Beta decay 55118.2.4 Gamma decay 55218.2.5 Internal conversion 55318.2.6 Units for radioactivity 554

18.3 Nuclear Models 55518.3.1 The shell model 55518.3.2 The deformed shell model 55618.3.3 The collective model 556

18.4 Interaction of Nuclear Radiation with Matter 55918.4.1 Heavy charged particles 55918.4.2 Electrons 56018.4.3 Electromagnetic radiation 56118.4.4 Neutrons 562

18.5 Nuclear Reactions 56318.5.1 Nonrelativistic kinematics 56318.5.2 Cross sections 564

18.6 Compilations of nuclear data 56518.7 References 566

19. Optics 568Joseph Reader19.1 Reflection and Refraction 570

19.1.1 Reflection 57019.1.2 Index of refraction 57019.1.3 Refraction at a plane surface 57219.1.4 Coefficients of reflectance and transmittance 57219.1.5 Reflectance and transmittance at normal incidence 57319.1.6 Brewster's angle of reflection 57319.1.7 Total internal reflection 57419.1.8 Beam displacement by a plane parallel plate 57519.1.9 Prisms 57519.1.10 Refraction at a spherical surface 576

19.2 Absorption 57719.2.1 Internal transmittance and total transmittance 57719.2.2 Optical density * 577

19.3 Lenses 57819.3.1 Imaging by lenses 57819.3.2 Minimum focal distance 58019.3.3 Lens power and F-number 58019.3.4 Lens maker's formula 58019.3.5 Thin lenses in combination 58019.3.6 Ray tracing for lenses 581

19.4 Mirrors 581

XXiv CONTENTS

19.4.1 Imaging by mirrors 58119.4.2 Ray tracing for mirrors 583

19.5 Diffraction 58319.5.1 Diffraction by a single slit 58319.5.2 Diffraction at a circular aperture 58419.5.3 Resolving power of a telescope 58419.5.4 Resolving power of a microscope 585

19.6 Interference 58619.6.1 Double slit intensity distribution 58619.6.2 Diffraction gratings 58719.6.3 Dispersion of a diffraction grating 58819.6.4 Resolving power of a diffraction grating 58819.6.5 Free spectral range 58919.6.6 Optimum slit width 58919.6.7 Grating blaze 58919.6.8 Rowland circle 58919.6.9 Michelson interferometer 58919.6.10 Fabry-Perot interferometer 590

19.7 Spectra 59319.7.1 Important spectral lines 59319.7.2 Common laser wavelengths 596

19.8 References 596

20. Particle Accelerators and Storage Rings 597Kai Desler and Donald A. Edwards20.1 Introduction 59820.2 Single-Particle Motion 598

20.2.1 Linear transverse motion 59920.2.2 Longitudinal motion 60420.2.3 Transverse coupling 60620.2.4 Nonlinear effects 60820.2.5 Synchrotron radiation 611

20.3 Multiparticle Dynamics 61520.3.1 Space charge 61520.3.2 Collective instabilities 61720.3.3 Beam cooling 61920.3.4 Luminosity 622

20.4 References 623

21. Plasma Physics 625David L. Book21.1 Fundamental Plasma Parameters 626

21.1.1 Frequencies 62621.1.2 Lengths 62721.1.3 Velocities 628

CONTENTS XXV

21.1.4 Dimensionless 62821.1.5 Miscellaneous 628

21.2 Plasma Dispersion Function 62921.2.1 Definition 62921.2.2 Differential equation 63121.2.3 Series expansions 63121.2.4 Symmetry properties 63121.2.5 Two-pole approximations 631

21.3 Collisions and Transport 63221.3.1 Relaxation rates 63221.3.2 Temperature isotropization 63421.3.3 Thermal equilibration 63421.3.4 Coulomb logarithm 63521.3.5 Fokker-Planck equation 63521.3.6 B-G-K collision operator 63621.3.7 Transport coefficients 63721.3.8 Weakly ionized plasmas 639

21.4 Solar and Ionospheric Physics 64021.5 Thermonuclear Fusion 642

21.5.1 Basic data and relationships 64221.5.2 Fusion reactions 642

21.6 Electron and Ion Beams 64421.7 Laser-Plasma Interactions 648

21.7.1 System parameters 64821.7.2 Formulas 648

21.8 Atomic Physics and Radiation 64921.8.1 Excitation and decay 65021.8.2 Ionization and recombination 65021.8.3 Ionization equilibrium models 65121.8.4 Radiation 652

21.9 References 654

22. Polymer Physics 656Stephen Z. D. Cheng22.1 Introduction 65822.2 Polymer Molecules . . 65822.3 Molecular-Mass Averages # 658

22.3.1 fcth moment of a molecular-mass distribution P(M) 65822.3.2 Molecular-mass averages 658

22.4 Single-Chain Dimensions 65922.5 0 Solvents and Temperatures 66022.6 Molecular-Weight Characterization 662

22.6.1 Solution viscosity 66222.6.2 Osmotic pressure TT 66222.6.3 Ultracentrifugation 663

XXVi CONTENTS

22.6.4 Static light scattering 66322.6.5 Dynamic (quasielastic) light scattering 663

22.7 Characterization by Spectroscopic Techniques 66422.7.1 Nuclear magnetic resonance 66422.7.2 Vibrational spectroscopy 664

22.8 Crystal Structures 66422.9 Bond Lengths and Angles of Polymers 66722.10 Melting and Crystallization 669

22.10.1 Variation of melting point of thin crystals with thickness . . . 66922.10.2 Spherulitic growth rate controlled by secondary (surface)

nucleation 66922.10.3 Avrami equation to describe overall kinetics of phase changes 670

22.11 Liquid Crystalline Transitions 67022.12 Heat Capacity and Thermodynamic Functions 671

22.12.1 Heat capacity in solid and liquid states of semicrystallinepolymers 671

22.12.2 General features of the heat capacity 67222.12.3 Residual entropies at absolute zero for glass polymers

and other properties 67322.13 Glass Transition 67322.14 Thermal Expansion 67522.15 Optical Properties of Polymers 676

22.15.1 Orientation birefringence An in amorphous polymers 67622.15.2 Stress optical coefficient C 67622.15.3 Form birefringence A n / i n two-phase systems 67622.15.4 Birefringence An of oriented crystalline polymers 67622.15.5 Birefringence of spherulites Ansph 676

22.16 Stress cr,j and Displacement M;-at Crack Tips 67722.17 Internal Friction Peaks in Semicrystalline Polymers 67822.18 Representative Mechanical Properties of Some Common Structural

Polymers 67922.19 Rheology 680

22.19.1 Introduction 68022.19.2 Linear viscoelasticity 680

22.20 Electrical Properties 68422.20.1 Dipole moments '. . . 68422.20.2 Typical electrical properties 684

22.21 Diffusion and Permeation 68522.21.1 Diffusion into plane sheet 68522.21.2 Diffusion data 68622.21.3 Gas transmission 686

22.22 Nonlinear Optical Properties 68622.23 References 690

CONTENTS XXVii

23. Quantum Theory 693M. P. Silverman and R. L. MallettPart I. Quantum Mechanics 69423.1 Basic Formalisms 69423.2 Operator Representations and Relationships 695

23.2.1 Operator algebra 69523.2.2 Coordinate and linear momentum operators 69523.2.3 Angular momentum 69723.2.4 Hamiltonian 70123.2.5 Commutation and uncertainty relations 701

23.3 Quantum Dynamics 70323.3.1 Time-displacement operator 70323.3.2 Single-particle wave equations 70323.3.3 Operator equations of motion 705

23.4 Approximate Methods: Stationary States 70623.4.1 Perturbation theory (bound states) 70623.4.2 Variational Method 70823.4.3 Wentzel-Kramers-Brillouin (WKB) theory 70823.4.4 Scattering theory (stationary state) 710

23.5 Time-Dependent Perturbation Theory 71123.5.1 First-order transitions 71123.5.2 Second-order transitions 71123.5.3 Fermi Golden Rule 71123.5.4 Density of states 71223.5.5 Exponential decay 712

23.6 Radiation Theory 71223.6.1 Interaction Hamiltonian 71223.6.2 Absorption and emission 71323.6.3 Multipole transitions 71323.6.4 Sum rules 714

23.7 Additional Links to Quantum Systems in other Chapters 71523.7.1 Coulomb potential 71523.7.2 Quantum rotator 71523.7.3 Anharmonic oscillator 715

Part II. Quantum Field Theory 71523.8 Brief History 71523.9 Feynman Rules for Gauge Theories 715

23.9.1 The S matrix 71523.9.2 Cross sections 71623.9.3 Decay rates 71623.9.4 Diagrammatic construction of amplitudes 71623.9.5 Fermion spin sums 72023.9.6 Polarization sums 72123.9.7 Contraction and trace relations 721

XXViii CONTENTS

23.10 Quantum Chromodynamics 72123.11 Standard Electroweak Model 722

23.11.1 Coupling constants and fields 72223.11.2 Example: Elastic neutrino-electron scattering 723

23.12 References 724

24. Solid State Physics 725Costas M. Soukoulis and Eleftherios N. Economou24.1 Introduction 72724.2 Classification of Solids According to Their Bonding Character 727

24.2.1 Simple metals 72724.2.2 Transition and rare-earth metals 72724.2.3 Covalent solids 72824.2.4 Ionic solids 72824.2.5 Van der Waals solids 72824.2.6 Crystals with hydrogen bonding 728

24.3 Approximations 72824.4 Electrons in Periodic Solids 729

24.4.1 Bloch's theorem; reciprocal lattice; Brillouin zone 72924.4.2 Density of states 73024.4.3 Jellium model 732

24.5 Methods for band-structure calculations 73424.5.1 General computational framework 73424.5.2 Linear combination of atomic orbitals 73624.5.3 Plane wave method 73624.5.4 Other methods 737

24.6 Ionic vibrations 73724.7 Thermodynamic Quantities 73924.8 Linear Response to Perturbations 741

24.8.1 Dielectric function and conductivity 74124.8.2 Temperature dependence of the DC conductivity 74424.8.3 Thermal conductivity and thermoelectric power 74624.8.4 Hall effect and magnetoresistance 74624.8.5 Cyclotron resonance, ESR, and NMR 747

24.9 Disordered Systems 74724.9.1 Localization and metal-insulator transition 74724.9.2 Metal-insulator transition in 2D disordered systems . . . . . . 749

24.10 Magnetism 74924.11 Superconductivity 75124.12 Elementary Excitations 753

24.12.1 Excitons 75324.12.2 Polarons and bipolarons 75324.12.3 Spin waves 754

24.13 Artificial Solid Structures and Photonic Crystals 75424.14 References 755

CONTENTS XXix

25. Surfaces and Films 756Roland Resch and Bruce E. Koel25.1 Introduction 75725.2 Surface Analysis: Probing Surfaces and Films 758

25.2.1 Electron spectroscopy 75825.2.2 Ion spectroscopy 75925.2.3 Electron diffraction 76125.2.4 Field emission 76225.2.5 Electron microscopy 76225.2.6 Scanning probe microscopy 762

25.3 Structure and Composition of Surfaces 76425.3.1 Thermodynamics of one-component surfaces 76425.3.2 Surface morphology, defects, and dislocations 76525.3.3 Surface lattices and superstructures 76525.3.4 Atomistic structure: relaxation and reconstruction 76725.3.5 Surfaces of compounds and metal alloys 767

25.4 Electronic Structure at Surfaces 76725.5 The Gas-Solid Interface 769

25.5.1 Solid-gas interactions 76925.5.2 Energy accommodation and adsorption 77025.5.3 Desorption 77225.5.4 Surface diffusion 77225.5.5 Chemical reactions at solid surfaces 773

25.6 Solid-Liquid and Liquid-Liquid Interfaces 77425.6.1 Electrochemical processes and the double layer 77425.6.2 Solid-liquid interactions 77625.6.3 Solid-liquid reactions 777

25.7 Film Formation and Structure 77825.7.1 Nucleation and growth modes 77825.7.2 Structure and properties of thin films 78125.7.3 Film growth from the gaseous phase 78125.1.4 Film growth from the liquid phase 78425.7.5 Film growth at the gas-liquid interface 785

25.8 Mechanical Properties of Surfaces and Thin Films 78525.8.1 Friction 78525.8.2 Lubrication 78725.8.3 Wear , 78725.8.4 Adhesion 787

25.9 References 788

26. Thermodynamics and Thermophysics 791J. P. Martin Trusler and William A. Wakeham26.1 Introduction 79226.2 Classical Thermodynamics 792

26.2.1 The laws of thermodynamics 792

XXX CONTENTS

26.2.2 Consequences of the first and second laws 79526.2.3 Dependence of the thermodynamic properties on temperature,

pressure, and composition 79726.2.4 Phase equilibria 80026.2.5 Chemical equilibria 801

26.3 Statistical Thermodynamics 80126.3.1 Postulates of statistical thermodynamics 80226.3.2 The perfect gas 80426.3.3 Real gases 806

26.4 Transport Properties 80726.4.1 Fluxes and gradients 80726.4.2 Definitions of transport coefficients 80926.4.3 Measurement of transport properties 810

26.5 Kinetic Theory 81226.5.1 The Boltzmann equation 81226.5.2 The transport properties 81326.5.3 Monatomic gases 81426.5.4 Dense fluids 815

26.6 References 816

27. Practical Laboratory Data 817David R. Lide27.1 Introduction 81727.2 Table: Periodic Table 81927.3 Table: Physical Constants of Elements and Compounds 82027.4 Table: Thermal and Electrical Properties of Metals 82627.5 Table: Dielectric Constant (Relative Permittivity) of Liquids 82827.6 Table: Viscosity of Liquids and Gases 83027.7 Table: Vapor Pressure of the Elements and Selected Compounds . . . . 83127.8 Table: Vapor Pressure of Cryogenic Fluids 83527.9 Table: Aqueous Solubility of Solids and Liquids 83627.10 Table: Solubility of Gases in Water 83827.11 Table: Properties of Miscellaneous Solid Materials 83827.12 Table: Densities Known to High Accuracy 84027.13 Fixed Points on the International Temperature Scale of 1990 84127.14 Table: Properties of Liquid Helium 84227.15 Table: Properties of Water and Ice ,. . . 84327.16 Table: Vapor Pressure of Water on the ITS-90 Temperature Scale . . . 843

Index 845