1. THE THEORY OF RELATIVITY

1-1 The Galilean Transformation; the Principle of Relativity, 1.

1-2 The Postulates of Special Relativity, 5.

1-3 The Lorentz Transformation, 8.

1-4 Relativistic Kinematics, 9.

1-5 Review of Tensor Analysis, 16.

1-6 The 4-vector System of Space Time, £7.

1-7 Relativistic Mechanics, 30.

1-8 Relativistic Electrodynamics, 40.

1-9 Energy Units, 48.

1-10 The Classical Electron, 50.

1-11 The General Theory of Relativity, 52.

2. QUANTUM MECHANICS 57

2-1 Introductory Background, 58.

2-2 Primary Requisites of Quantum Mechanics, 80.

2-3 Postulatory Basis of Quantum Mechanics, 91.

2-4 Some Elementary Properties of Quantum Mechanics, 104.

2-5 Some Useful General Theorems, 114.

2-6 Conclusion, 126.

3. THE ONE-DIMENSIONAL HARMONIC OSCILLATOR 128

3-1 The Hamiltonian Function; the Schroedinger Equation, 128.

3-2 Solution of the Schroedinger Equation, 130.

3-3 The Energy Levels and Wave Functions, 133.

3-4 Parity, 138.

4. THE FREE PARTICLE 141

4-1 The Schroedinger Equation One Dimension, 141.

4-2 Boundary Conditions and Normalization, 142.

4-3 Superposition of Wave Trains, 143.

4-4 Wave Packets; Motion of a Free Particle, 144.

4-5 Eigenvalues of Energy and Momentum for a Free Particle, 147.

4-6 Transmission and Reflection at a Barrier, 148.

4-7 The Rectangular Potential Well, 152.

4-8 Transmission through a Barrier, 155.

4-9 The Free Particle in Three Dimensions, 157.

4-10 The Particle in a Box; Periodic Boundary Condition, 159.

5. THE ONE-ELECTRON ATOM 163

5-1 Hamiltonian Function and Operator for the Simple Model, 164.

5-2 The Schroedinger Equation, 165.

5-3 Solution of Time-independent Schroedinger Equation, 166.

5-4 Some Properties of the One-electron-atom Wave Functions, 176.

5-5 Electron Spin, 184.

5-6 Spin-Orbit Forces, 191.

5-7 The Quantization of Angular Momentum, 195.

5-8 Spin-Orbit Fine Structure, 199.

5-9 Relativistic Corrections, 200.

5-10 Hydrogen Fine Structure, 201.

5-11 Spectroscopic Term Classification; Selection Rules, 204.

5-12 Nuclear Spin; Hyperfine Structure, 206.

6. RADIATION AND RADIATIVE TRANSITIONS 211

6-1 Normal Coordinates and Hamiltonian Representation of a Continuous Elastic System, 212.

6-2 Energy Eigenfunctions a for Normal Coordinates, 214.

6-3 Quantization of the Radiation Field, 216.

6-4 Selection Rules and Transition Probabilities for a Harmonic Oscillator with a Linear Perturbation, 218.

6-5 Some General Properties of Radiative Transitions, 224.

6-6 Electric-dipole Selection Rules for a One-electron Atom, 229.

6-7 Summary of the Properties of Radiative Transitions, 231.

7. THE PAULA PRINCIPLE, ATOMIC SHELL STRUCTURE, AND THE PERIODIC SYSTEM 288

7-1 Introductory Sketch, 233.

7-2 Exchange Symmetry of Wave Functions, 236.

7-3 The Many-electron Atom in the Schroedinger Theory, 246.

7-4 Conclusion, 252.

8. ATOMIC SPECTROSCOPY 254

8-1 General Considerations, 255.

8-2 The Hamiltonian Function of a Complicated Atom, 256.

8-3 Russell-Saunders, or LS, Coupling, 259.

8-4 j-j Coupling, 268.

8-5 Selection Rules, 270.

8-6 Energy-level Diagrams for Complex Atoms, 272.

8-7 Regularities in Complex Spectra, 274.

8-8 The Zeeman Effect, 276.

8-9 The Excitation of Atoms, 280.

8-10 The Breadth of Spectral Lines, 282.

8-11 Conclusion, 285.

9. MOLECULAR BINDING AND MOLECULAR SPECTRA 287

9-1 The Hydrogen Molecule Ion, 288.

9-2 The Neutral Hydrogen Molecule, 294.

9-3 Further Properties of Chemical Binding, 295.

9-4 Energy States of Diatomic Molecules, 298.

9-5 Spectroscopy of Diatomic Molecules, 305.

9-6 Effects of Nuclear Spin; Ortho- and Para-Hydrogen, 318.

9-7 Van der Waals’ Forces, 323.

9-8 Conclusion, 325.

10. QUANTUM STATISTICS 327

10-1 Derivation of the Three Quantum Distribution Laws, 328.

10-2 Applications of the Quantum Distribution Laws: General Considerations, 339.

10-3 Applications of the Maxwell-Boltzmann Distribution Law, 345.

10-4 Applications of the Fermi-Dirac Distribution Law, 350.

10-5 Applications of the Einstein-Bose Distribution Law, 365.

11. THE BAND THEORY OF SOLIDS 377

11-1 The Band Structure of the Electronic Energy States of a Crystal, 378.

11-2 Periodicity Properties of Electronic Wave Functions, 391.

12. X-RAYS 405

12-1 Historical Introduction, 405.

12-2 The Production of X-rays, 408.

12-3 The Interactions of X-rays with Matter, 421.

12-4 X-ray Diffraction, 435.

12-5 Atomic and Crystal Structure Factors, 451.

12-6 Refraction and Reflection of X-rays, 454.

13. BASIC PROPERTIES OF NUCLEI 458

13-1 Charge and Mass, 463.

13-2 Nuclear Angular Momentum, 467.

13-3 Magnetic Moments of Nuclei; Nuclear Magnetic Resonance, 468.

13-4 Electricquadripole Moments, 470.

13-5 Radioactivity, 475.

13-6 The Constituents of Nuclei; 476.

13-7 Symbols and Nomenclature for Nuclear Structure, 478.

13-8 Excited States of Nuclei; Nuclear Reactions, 479. 13-9 Particles, 483.

13-10 Conclusion, 483.

14. PARTICLE SCATTERING 486

14-1 The Classical Theory of Rutherford Scattering, 485.

14-2 Transformation from CM to Laboratory Coordinates, 492.

14-3 Multiple Coulomb Scattering and Energy Loss by Ionization, 494.

14-4 Primary and Secondary Ionization; Knock-on Electrons; Delta Rays, 801.

14-5 Range; Straggling, 501.

14-6 Some General Properties of Particle Scattering, 504,

15. RADIOACTIVITY 512

15-1 The Four Radioactive Series, 612.

15-2 The Growth and Decay of Radioactivity, 513.

15-3 The Ages of Minerals and of the Earth, 520.

15-4 Other Naturally Occurring Radionuclides, 523.

15-5 Artificial Radioactivity, 523.

15-7 Beta Decay; the Neutrino Hypothesis, 529.

15-9 Electron Capture, 544.

16. SYSTEMATICS OF NUCLEAR STABILITY 546

16-1 Binding Energy of Nuclei, 547.

16-2 The Sizes of Nuclei, 549.

16-3 The Semiempirical Mass Formula of Weizsacker, 551.

16-4 The Stability of Nuclei; Stability Rules, 554.

17. DYNAMICS OF NUCLEAR REACTIONS 562

17-1 Kinds of Nuclear Reactions, 562.

17-2 Common Modes of Formation of Excited Nuclei, 565.

17-3 Conservation Laws, 567.

17-4 Cross Section, 577.

17-5 Some Properties of Specific Types of Nuclear Reactions, 583.

17-6 Experimentally Observed Properties of Nuclear Excited States, 589.

18. NUCLEAR MODELS 595

18-2 The Liquid-drop Model; Fission, 597.

18-3 The Fermi Gas Model, 599.

18-4 The Shell Model, 600.

18-5 The Liquid-rotator Model, 607.

18-6 The Complex-potential Model, 608.

18-7 Conclusion, 610.

19. NUCLEAR FORCES 611

19-1 Bound States of the Two-nucleon System, 611.

19-2 Scattering Experiments, 614.

19-3 The Meson Theory of Nuclear Forces, 616.

20. PARTICLES 623

20-1 Electrons and Positrons, 624.

20-2 Photons, 627.

20-3 Protons, 627.

20-4 Neutrons, 628.

20-5 Neutrinos, 630.

20-8 K-mesons (Thetons and Tauons), 641.

20-9 Hyperons, 649.

20-10 Theoretical Interpretation of Particle Properties, 651.

20-11 The Dirac Theory of the Electron, 661.

20-12 Quantum Electrodynamics, 669.

21. MODERN PHYSICS IN NATURE 680’

21-1 Cosmic Rays, 680.

21-2 Stellar Energy, 708.

21-3 The Formation of the Elements, 710.

APPENDIXES 721

A. A Table of Physical Constants, 721.

B. Black-body Distribution Function (Graph), 724.

C. Some Electronic Properties of Atoms, 727.

D. Constants of Some Diatomic Molecules, 730.

F. Plots of Range versus Energy and Momentum, 733.

G. Table of Nuclear Species, 736,

Index 785

Page references in boldface type indicate main discussions of topics

Aberration, 4, 38

Absorption, X-ray, 421

coefficients, 422

photoelectric, 424

Acceptor atom, 387

Activity, 518

Adiabatic approximation, 289

Age, of carbonaceous materials, 698

of the earth, 520

of minerals, 520

Alpha-particle model of nucleus, 596

Alpha-particle radioactivity theory, 52.

Alternation of multiplicities (law), 268, 276

Angular momentum, addition, 198

eigenvalues, 177

of nuclei, 467

orbital, 177

operators for, 102

commutation properties, 102, 195

in rectangular coordinates, 102

in spherical coordinates, 177

quantization, 195

experimental observation, 89

in Bohr theory, 72

in Stern-Gerlach experiment, 89

quantum numbers, 177

rotational, of molecules, 299, 310

spin, 185, 667

Antineutrino, 630

Antineutron, 629

Antiparticle, 624

Antiproton, 628

Atmosphere, properties (table), 732

Atomic energy-level diagrams, 77, 91

Atomic energy states, 76

Atomic mass units, 464

Atomic masses (table), 736-783

Atomic number, 478

Atomic structure, 69

nuclear theory, 71

Rutherford theory, 71

Thomson theory, 70

Atomic structure factors, 451

Atomic transitions, 77, 90

forbidden, 90

selection rules for, 271

Auger effect, 427

in nuclei, 480

Autoionization, 427

Balmer formula, 75

Balmer series, 74

Band structure (solids), 378

Band system (spectroscopy), 454

Band theory of solids, 377

Barrier penetration (see Potential barrier)

Baryon, 652

electron spectrum for, 535

inverse, 532

lifetimes for, 538

neutrino hypothesis, 531

selection rules, 538, 542

statistical factor, 535

theory, 532

transitions in, allowed, 540

forbidden, 541, 542

(See also Electron capture)

Black-body radiation, 60

classical interpretation, 61

laws for, distribution (graph), 725

Planck, 64

from quantum statistics, 349, 366

Rayleigh-Jeans, 64

Stefan-Boltzmann, 62

Wien displacement, 62

(See also Photon gas)

Bloch function, 394, 401

Bohr correspondence principle, 88, 105

Bohr magneton, 185

Bohr theory of hydrogen atom, 72

Boltzmann factor, 342

Bose particle, 239

Bragg condition, 437, 447

Bragg reflection, 402, 437

Bragg spectrometer, 449

Bremsstrahlung, 408, 674

distribution, angular, 408, 410

spectral, 413

atomic mechanism, 415

polarization, 415

role in electron showers, 690

Brillouin zones, 400

influence on electrical properties, 402

Canonical equations (Hamilton), 48, 92, 106-107

Canonical momenta, 92

Carbon cycle, 709

Center-of-mass system, defined, 39

in nuclear reactions, 492, 493

speed, 39, 49

Characteristic radiation

(see X rays)

Charge, continuity equation for, 43

Charge-current 4-vector, 43

Charge density, defined, 41

transformation law for, 42, 46

Chemical binding, directional character, 298

Chemical binding, homopolar, 288

ionic (heteropolar), 288, 295

measure of character, 296

saturation properties, 297

CM system

(see Center-of-mass system)

Collision broadening (spectra), 285

Collision excitation of atoms, 281

Complex atoms, energy-level diagrams, 272

Hamiltonian function for, 256

Complex potential

(see Nuclear models)

Compound nucleus, 563, 610

excitation energy, 573

Compton collision, 40, 432

Compton cross section, 433

Compton scattering, 432

viewed in space time, 674

Conduction band, 386

Conservation, energy, 37

in radiative transitions, 227

mass-energy, 37

momentum, 34, 37, 568

momentum-energy, 37, 568

parity, 569

probability, 112

Conservation laws in nuclear reactions, 567

(See also specific quantities)

Correspondence principle, 88, 105

Cosmic radiation, composition, 681

discovery and gross properties, 680, 689

energy spectrum, 682

nuclear collisions by, 682, 684, 687

origin, 699

primary, 681

production of ¹⁴C and ³H by, 523, 697

radioactivity induced by, 697

secondary, 688

electron showers, 689, 690

general features, 688

nucleonic cascades, 688

"soft" component, 697

Coulomb barrier, 524, 567, 583, 584

Coulomb excitation, 562, 563, 566

Covariance, of Maxwell’s equations, 6

of physical laws, 12, 28

Critical energy, 691

Cross section, definitions, 577

differential, 579

Cross section, geometric, 580

lab vs. CM, 579

partial, 578

resonance, 577

Thomson, 429

total interaction, 578

Crystal lattice, direct, 445

one-dimensional, 392

Periodicity Properties of Electronic Wave Functions

primitive vectors, 440

reciprocal, 445

reciprocal vectors, 445

spacing of atoms in, 438

types, 438, 439

unit cell, 438

Crystal planes, Miller indices, 448

Crystal structure factors, 451

Crystals, electron energy states in, 378

periodicity properties, 391

Curie (unit of radioactivity), 518

Current density, defined, 41

4-vector, 43

transformation, 46

D’Alembertian operator, 43

de Broglie wavelength, 81

Degeneracy, 116

removal, 116, 118

and statistical weight, 116

Delta, Kronecker, 21

Delta function, 109

Delta rays, 501

Deuteron, 611

ground-state wave function, 613

Diatomic molecules

(see Molecules)

Diffraction (X-ray), 435

Bragg conditions, 437, 447

Laue equations, 444

Dineutron, 611

Dirac equation, 664

Dirac theory for electrons, 661

Disintegration constant, 515

Displacement law, 276

Donor atoms, 387

Doppler broadening, 284

Doppler effect (relativistic), 14, 38

Effective mass, 400

Eigenfunction, of a coordinate, 108

definition, 108

Eigenfunction, degenerate, 116

of energy, for independent systems, 122

of momentum, nonquantized, 109

quantized, 110

orthogonal, 114

expansion in terms of, 115, 122

permissible (conditions), 108

of two or more quantities, 110, 111

Eigenstates (stationary), 111

transitions between, 120

Eigenvalues, equation for, 108

as only possible result of exact measurement, 115

Einstein condensation, 373

Einstein frequency condition, 73

Einstein photoelectric equation, 68

Einstein-Bose statistics, applications, liquid helium, 368

photon gas, 365

distribution law for, 335, 339

general properties, 342

Elastic system, classical treatment, 212- 214

quantum treatment, 214

Electric dipole, selection rules, 206

(See also Moments)

Electrodynamics, quantum, 669

relativistic (classical), 40

field equations, 40, 44

Electromagnetic charge density, 41

Electromagnetic current density, 41

Electromagnetic equations, 40, 44

Electromagnetic field tensor, 44

Electromagnetic force, 40

Electromagnetic potentials, 41, 46

Electron, 624

Dirac theory, 661

equivalent, 264, 267

magnetic moment, 185

anomalous, 677

radius (classical), 50

Electron capture, 544

Electron configuration (notation), 236

Electron gas (energy distribution), 351

Electron showers (cosmic ray), 690

Electron spin

(see Spin)

Electrostatic effect, 550, 553

Elements, formation of, 710

Emission, induced, 223

spontaneous, 223, 228

Energy, relativistic, 36

conservation, 37

critical, 691

kinetic, 37

self- (rest), 37

total, 36, 37

stellar, 708

Energy loss (ionization), 494

primary, 501

secondary, 501

Energy units, 48

Equivalent electrons, 264

LS terms for, 267

Ether hypothesis, 3

Event (relativity), 10

Exchange correlation, 258

Exchange forces, 244

in nuclei, 616

Exchange invariance of Hamiltonian, 237

Exchange operator, properties, 238

Exchange symmetry of wave functions, 236

observable effects, 239

rules for, 236

Excitation, of atoms, mechanisms, 280

of nuclei, 479

Exclusion principle, early form, 236

exchange symmetry rules, 236

Expectation value, change with time, 106, 111

defined, 95

Fermi energy, 341

Fermi gas, 350

energy distribution for, 351

nuclear model, 599

etc.

Fermi level, 341

Fermi particles, 239

of cosmic-ray acceleration, 704

Fermi-Dirac statistics, applications, 350

contact potential, 354

electronic-energy distribut.ion, 351

electronic specific heat, 360

thermionic emission, 355

theory of metals, 350

Thomas-Fermi atomic model, 362

distribution law for, 335, 339

general character, 340

Feynman diagram, 672

Field, electromagnetic, equations, 40

transformation, 46

of moving charge, 46

tensor, 44

Field oscillators, 216

Field tensor, 44

Fine-structure constant, 200

Fission, 597

stability against, 555

Force, 4-vector, 34

Minkowski, 34

ordinary, 35

spin-orbit, 191

transformation law for, 35

Fortrat parabola, 318

Fountain effect, 370, 371

Fourier inversion, as extension of Fourier series, 96

formulas, 97

Free particle

(see Particle)

Galilean transformation, 2

Geiger-Nuttall law, 529

Gravitation constant, 54

Gravitation theory, 53

Ground state (atomic), spectroscopic character, 268, 727-729

Hamiltonian function, of complex atom, 256

formation from Lagrangian, 92

of harmonic oscillator, 92

of particle in electromagnetic field, 47,219, 661

Hamiltonian operator, for conservative system, 102

invariance properties, 567

(See also Parity)

Harmonic oscillator, 128

and black-body radiation, 64

energy levels, 65, 133

Hamiltonian function for, 128

Hamiltonian operator for, 129

motion compared with classical oscillator, 136, 137

Schroedinger equation for, 129

series solution, 130, 131

time-dependent, 129

time-independent, 129

Harmonic oscillator, wave functions for, 133

equations, 133

graphs, 134, 135

Hartley law (doublet separation), 275

Heisenberg formulation of quantum mechanics, 81

Heisenberg uncertainty principle, 86, 105

Helium, liquid, 368

superfluid condensation, 374

Hermite differential equation, 131

Hermite polynomials, 132

formulas, .132

generating function, 132

normalizing factor, 133

recurrence relations, 133

Hermitian adjoint, 664

Hermitian operator, definition, 101

properties, conservation of probability, 113

real-expectation values, 101

Hydrogen atom, Bohr theory, 72

energy-level formula, 74, 175

fine structure, 79, 201, 202

Schroedinger theory, 163

Sommerfeld theory, 78

spectral series, 77, 78

Hydrogen molecule, neutral, 428

parity of ground state, 430

similarities with ion, 428

spin correlation in, 429

Hydrogen molecule ion, 421

binding energy, 427

electronic energy, 425

separation distance, 427

wave functions, 425

Hyperfine structure, 206

selection rules, 208

Hyperons, 483, 649

Identical particles, noninteracting, 240

probability density for, 245

wave function symmetry for, 236

Impact parameter, 486

Insulators, energy-band structure, 383

Interaction, between charge and radiation, 218-220

classification of various types, 652

self-, 677

Interaction, weak (strangeness theory), 653

Internal conversion, 480

Intersystem transition, 273

Inverted multiplets, 263

Ionic binding, 288, 295

compared with homopolar, 296

Isobars, stability, 555-559

Isoelectronic sequence, 276

Isomer, 479

Isotone, 479

Isotopes, 460, 476, 479

stability, 559, 560

Isotopic abundances, 521, 711, 712, 736-783

Isotopic constitution (of lead), 521, 522

Isotopic number, 478

Isotopic spin, 569

multiplets, 570, 590

in nuclear reactions, 569

in strangeness theory, 654

j-j coupling, 268

Klein-Gordon equation, 620, 662

Klein-Nishina formula, 433, 674

Knock-on electron, 501

Kronecker delta, 21

Kurie plot, 536, 537, 543

Lab system, 492

transformation from CM system, 493

Lagrangian function, nonrelativistic, 92

relativistic, 47, 662

Laguerre functions, associated, 174

Laguerre polynomials, 174

Lamb shift, 678

Landé g-factor, 279

for deuteron, 613

Landé interval rule, in LS coupling, 261

in molecular spectra, 438

Lattice

(see Crystal lattice)

Laue equations, 444

Legendre functions, associated, 167-171

normalizing factor for, 169

Legendre polynomials, 168, 169

graphs, 170, 171

normalized, 169

Lorentz condition, 42, 43

Lorentz transformation, 8

as space-time rotation, 27, 29

Lorentz-FitzGerald contraction, 5, 11

LS coupling, 259

fine structure due to, 261

Magnetic field transformation, 46

Magnetic moment, anomalous, 677

of electron, 185, 723

of nuclei, 207, 736-783

orientation energy, 277

of proton, 207, 723

Many-electron atom, 246

absence of i-degeneracy for, 253

central-field approximation for, 246

Mass, of particles (table), 49, 624-650, 736-783

reduced, 164; 299, 487

relativistic, 35

rest, 36

variation with speed, 35

of residual nucleus, 574

Mass-energy conservation, 37

Mass excess, 548

Mass number, 478

Mass renormalization, 677

Mass spectrometer, 464

Matrix, Pauli (spin operators), 188

rotation, three dimensions, 19

four dimensions, 29

defined, 124

for electric dipole transitions, 225-230

and line intensity, 125

and selection rules, 125, 220-230

Matrix multiplication, 189

Maxwell distribution law of molecular speeds, 284, 349

Maxwell’s equations, 40

in 4-tensor form, 44

Maxwell-Boltzmann distribution law, 335, 339

general properties, 340

as limit of Fermi-Dirac or Einstein-Bose statistics, 342

Maxwell-Boltzmann statistics, applications, 342, 345

to black-body radiation, 349

to specific heats of solids, 346

Mechanics, relativistic, 30-40

Mesic atoms, 184, 550

Meson, K-, 641

O-, 641

Meson theory of nuclear forces, 616

Mesotron

(see Meson)

Metals, contact potential, 354

electrical conductivity, 360

electronic specific heat, 360

energy-band structure, 381

free-electron theory, 350

paramagnetism, 361

Michelson-Moreley experiment, 4

Miller indices, 448

Mirror nuclides, 540

as isotopic spin multiplets, 590

Molecules, diatomic, centrifugal potential, 300

constants, 730

effects of nuclear spin in, 318

electronic transitions, 311

energy states, 298

rotational angular momentum, 299, 311

rotational spectrum, 306

rotational states, 302

spectroscopy, 305

selection rules, 306, 307, 312

vibration-rotation transitions, 302, 308

homonuclear, 319

nuclear spin effects for, 318

ortho- and para- forms, 321

Moments, of charge distribution, 471

nuclear

(see Nuclei)

Momentum, conservation, 34, 37, 568

4-vector, 34

ordinary, 34

Momentum-energy conservation, 37, 568

Momentum-energy 4-vector, 34

transformation law for, 34

Moseley law (X-ray wavelengths), 407, 419

Multiplicity, 204

Neutrino, 529, 531, 630

Neutrino hypothesis, 529, 531

Neutron number, 478

Neutrons, delayed, 599

properties, 628

Normal coordinates, 212

Nuclear forces, 611

Nuclear magnetic induction, 469

Nuclear magnetic resonance, 468

Nuclear magneton, 207

Nuclear mass units, 464

Nuclear models, 595

complex-potential, 608

Fermi-gas, 599

liquid-drop, 597

liquid-rotator, 607

shell, 600

Nuclear reactions, 479, 562

compound nucleus in, 563

conservation laws in, 567

dynamics, 562

endoergic, 482

energy balance in, 482

exoergic, 482

specific properties, 583

types, 562

Nuclear species, table, 736-783

Nuclear spin, 206

Nuclei, angular momentum, 467

basic properties, 458

binding energy, 467, 547, 736-783

charge, 463

constituents, 476

electric quadripole moments, 470, 736-783

excitation, 479, 565

magnetic moments, 468, 736-783

masses, 463, 736-783

radioactivity (see Radioactivity)

sizes, 549

stability, 546, 554

surface-tension effects in, 552

Nucleon, 478

Nucleonic cascade, 688

Nuclide, 479

radioactive, artificial, 523

natural, 512

Occupation index, definition, 340

for Fermi-Dirac statistics, 341

Odd-even effect, 553

One-electron atom, 163

angular momentum states, 177

electric dipole selection rules for, 229, 232

energy levels, 74, 175

fine structure, 201, 202

relativistic shifts, 200, 207

spin-orbit shifts, 199

Hamiltonian function for, 164

Hamiltonian operator for, 164

Schroedinger equation for, 165

wave functions for, 166-176

parity, 184

properties, 176

table, 183

Operator, commutator, 101, 105

Hamiltonian, 102

Hermitian, 101

linear, 101

quantum-mechanical, 98

Ortho- and para-hydrogen, 322

Oscillator

(see Harmonic oscillator)

Oscillator strength, 229, 231

Packing fraction, 548

Pair production, 625, 666, 676

role in electron showers, 690

Parity, conservation, 569

definition, 139

of hydrogenic wave functions, 184

in molecular binding, 422

nonconservation, 631, 659

in nuclear reactions, 569

operator (one dimension), 139

eigenfunctions, 139

eigenvalues, 139

Particle, in box, 159

distribution of energy states for, 161

equation of motion, 46

fields due to, 46

free, one dimension, 141

energy eigenvalues, 147

momentum eigenvalues, 147

motion (wave packets), 144

Schroedinger equation, 141

wave functions, 141

boundary conditions on, 142

normalization, 142

three dimensions, 157

Hamiltonian for (relativistic), 47, 661

Particle, Lagrangian for (relativistic), 47, 662

motion, in electromagnetic field, 46

in magnetic field, 46

Particles, 483, 623

hyperons, 483, 649

identical (see Identical particles)

mesons, 483, 616, 633-641

scattering, 485, 504

method of partial waves, 505

Rutherford, 485

(See also specific types)

Pauli exclusion principle, 236

Pauli neutrino hypothesis, 531

Periodic boundary condition, 159

Periodic system of elements and electron configuration, 251

empirical form, 233

Schroedinger theory, 246

Perturbation analysis, for energy-level

shifts, 118

first-order effect, 119

for transitions, 120

first-order effect, 124, 125

Phase shifts, 507

Phase space, 92

Phonon, 367

Photoelectric effect, 67

Einstein equation for, 68

in X-ray absorption, 424

Photon, 627

Photon gas, 365

Pickup reactions, 564

Planck constant, 65

Planck distribution, 64, 349, 366

Polarization of bremsstrahlung, 415

Positron, in Dirac theory, 666

properties, 624

Positronium, 624

Postulates, exchange-symmetry, 239

of quantum mechanics, 93-103

of quantum statistics, 330

of special relativity, 5

Potential, centrifugal, 436

4-vector (electromagnetic), 43

transformation, 46

wave equation, 43

Morse, 440

Potential barrier, finite, 155

semi-infinite, 148

Potential scattering, 504, 563

Potential well, one dimension, 152

energy eigenvalues for, 153, 154

scattering by, 155, 505

wave functions for, 154

spherical (scattering by), 504

three dimensions, square (box), 159

Precession, Larmor, 192

Thomas, 192

Probability, conservation, 112

physical, 245

Probability amplitude, 93

Probability current, 113

Probability density, 93

Probability distribution, 95

Progressions (molecular spectra), 453

Propagation vector, 158, 216

Proper time, 31

Proton, properties, 627

Proton-proton cycle, 709

Pseudoscalar, definition, 25

Pseudoscalar mesons, 621

Quantum of action, 65

Quantum electrodynamics, 669

Quantum states, of atoms, experimental observation, 88

role in quantum theory, 88

in Schroedinger theory, 107

of hydrogen, in Bohr theory, 72

in Schroedinger theory, 163, 176

in Sommerfeld theory, 79

Quantum statistics, macroscopic distribution, 330

microscopic distribution, 330

postulate for, 330

three distribution laws, 335, 339

Quantum theory, historical sketch, 60

Radiation, from accelerated charge, non-relativistic, 409

relativistic, 412

cosmic (see Cosmic radiation)

quantum theory, 211

rate of, classical vs. quantum-mechanical, 228-229

Radiation field, interaction of charges with, 211, 218-220

Radiation length (shower theory), 691

Radioactive-decay law, 513, 516

Radioactive equilibrium, secular, 519

transient, 519

Radioactive mean life, 518

Radioactive nuclides, artificial, 523

natural, 512

Radioactive series, 512

artificial, 523

discovery and early history, 459

growth and decay, 513

induced by cosmic radiation, 697

kinds, 460

positron, 524

Range, of nuclear forces, 618

of stopping particle, 501

Range-energy curves, 733-735

Rare earths (shell structure), 252

Rayleigh-Jeans law, 64

Rectification theory, 388

Reduced mass, 164, 299, 487

Relativistic electrodynamics, 40

Relativistic energy, 36-37

Relativistic kinematics, 9

Relativistic mass, 36

Relativistic mechanics, 30-40

Relativity, general theory, 52

principle, 1

special theory, 1

Renormalization, of charge, 677

of mass, 677

Residual nucleus, 483

mass, 574

Resonance, nuclear magnetic, 468

Richardson-Dushman equation, 356

Rigid rotator, 302, 311, 312

Rotation spectrum, 306

Russell-Saunders coupling, 259

Rutherford scattering, experiments, 71

law, 71, 485, 490

theory, 485

Rutherford theory of atomic structure, 71

Rydberg series, 275

Rydberg unit, 75

Saturation properties, chemical forces, 297

nuclear forces, 551

Scattering, multiple Coulomb, 494

n-p, 614

Scattering, partial wave analysis, 505

phase shifts for, 504, 507

p-p, 614

P-wave, 509

Rutherford, 71, 485

S-wave, 509

as second-order process, 231

surface, 563

of X-rays, modified (Compton), 432

unmodified (Thomson), 428

Schmidt lines, 605

Schroedinger equation, introduced (postulate), 103

time-independent, 112

Schroedinger formulation of quantum mechanics, 81

postulates for, 91-103

Second sound, 370

Selection rules, 77

electric dipole, 224, 226

for j-j coupling, 271

for LS coupling, 271

for one-electron atom, 229

for harmonic oscillator, 218, 222

and line intensities, 90

and matrix elements, 125

for strangeness, 657

Self-consistent field, 247

Semiconductors, energy-band structure, 384

impurity, 386

intrinsic, 386

n-type, 387

p-type, 387

as rectifiers, 391

Shell notation, for atoms, 235

in X-ray spectra, 418

Shell structure, atomic, 235

and Bohr orbits, 235

notation, 235

order of subshell states, 249

Schroedinger theory, 246

nuclear, 600

Simultaneity, 12, 14

Solid-angle transformation equations, 412, 493

Solids, band theory, 377

Sommerfeld theory of hydrogen, 78

Space time, 27

Spallation reactions, 565

Spectra, regularities in, 274

Spectral lines, breadth, 282-283

Spectroscopic fine structure, 202

Spectroscopic hyperfine structure, 206

Spectroscopic notation, 204, 205

Spectroscopic selection rules, 206, 270, 443, 446, 454

Spectroscopic series, 76

Spectroscopic term classification, 204

Spectroscopic terms, 76

for equivalent electrons, 264-267

Spectroscopy, atomic, 254

j-j coupling, 268

LS coupling, 259

regularities in, 274

selection rules, 206, 270

Zeeman effect, 276

molecular, 305

electronic,. 311

band systems, 314

selection rules, 312

rotational, 305

selection rules, 306

vibration-rotation, 307

selection rules, 307

Spin, electron, 184

Dirac theory, 667

eigenfunctions, 187, 188

operators, 187, 188

Pauli theory, 188

nuclear, 206

Spin-orbit effects in nuclei, 616

Spin-orbit fine structure, 199

Spin-orbit forces, 191

Stark broadening, 285

State, of classical system, 93

degenerate, 116

quantized, 107

of quantum-mechanical system, 93

State function defined, 93

Statistical weight, 116, 328, 343

for homonuclear molecules, 322

Statistics, quantum

(see Quantum statistics)

Stefan constant, 62

Stefan-Boltzmann law, 62

Stern-Gerlach experiment, 89

Straggling, 501, 503

Strange particles, hyperons, 483, 649

K mesons, 641

Strangeness theory, 653

Stripping reactions, 564

Superfluid (see Helium)

Supernovae, element formation, 714, 716, 718

Surface scattering, 563

Surface-tension effects in nuclei, 552

Surface transmutation, 563

Target nucleus, 482

Temperature in quantum statistics, 339

Tensor fields, 25

Tensors, addition, 22

contraction, 23

curl, 26

definition, 22

divergence, 26

four-dimensional, 27

notation, 29

gradient, 25

multiplication, 23

notation, 18

summation convention, 20

symmetry, 24

transformation law, 22

Terms, spectroscopic, 76, 264-267

Thermionic emission, 355

Thomas-Fermi atomic model, 362

Time, proper, 31

Time dilation, 5, 11, 12

Top, symmetrical, energy states, 312

Transitions, first-order theory, 120

forbidden, 125

matrix element for, 124

radiative, 211

summary of properties, 231

Tunnel effect, 157

Uncertainty principle, 86, 93, 105

Undetermined multipliers, 335

evaluation, 336

for dilute gas, 338

Vacuum polarization, 677

Valence band, 386

Valence and shell structure, 250

Variance (measure of uncertainty), 95

Van der Waals’ forces, 297, 323

Vector potential, electromagnetic, 43

Vectors, four-dimensional, 27

transformation law, 17

Velocity, addition, 14

four-dimensional, 32

transformation, 14

Vibrational progressions, 313

Virtual process, 673

Wave amplitude, 85

Wave functions, defined, 93

four-component, 664

Wave packet, free-particle, 144

group velocity, 147

phase velocity, 147

Wave-particle duality, 367

Wave properties of particles, 81, 104

Wave trains, as representation of particle beam, 142

Wavelength, de Broglie, 81

Weizsacker mass formula, 551

Wien displacement law, 62, 66

Wilson-Sommerfeld quantization rules, 77

X-ray fluorescence, 424

X-rays, 405

absorption, 421

Auger effect, 424, 427

characteristic radiation, 407, 417

Bohr-theory interpretation, 407, 419

diffraction, 435

interaction with matter, 421

polarization, 428

production, 408

reflection, 454

refraction, 454

scattering, 428, 432

series (notation), 419

Yukawa meson hypothesis, 616

Yukawa potential, 620

Zeeman effect, anomalous, 59, 280