Nuclear Physics in a Nutshell

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  • Format: Hardcover
  • Copyright: 2007-04-03
  • Publisher: Princeton Univ Pr

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Nuclear Physics in a Nutshellprovides a clear, concise, and up-to-date overview of the atomic nucleus and the theories that seek to explain it. Bringing together a systematic explanation of hadrons, nuclei, and stars for the first time in one volume, Carlos A. Bertulani provides the core material needed by graduate and advanced undergraduate students of physics to acquire a solid understanding of nuclear and particle science.Nuclear Physics in a Nutshellis the definitive new resource for anyone considering a career in this dynamic field. The book opens by setting nuclear physics in the context of elementary particle physics and then shows how simple models can provide an understanding of the properties of nuclei, both in their ground states and excited states, and also of the nature of nuclear reactions. It then describes: nuclear constituents and their characteristics; nuclear interactions; nuclear structure, including the liquid-drop model approach, and the nuclear shell model; and recent developments such as the nuclear mean-field and the nuclear physics of very light nuclei, nuclear reactions with unstable nuclear beams, and the role of nuclear physics in energy production and nucleosynthesis in stars. Throughout, discussions of theory are reinforced with examples that provide applications, thus aiding students in their reading and analysis of current literature. Each chapter closes with problems, and appendixes address supporting technical topics.

Author Biography

Carlos A. Bertulani is Research Professor of Physics at the University of Tennessee and the Oak Ridge National Laboratory.

Table of Contents

Introductionp. 1
What is Nuclear Physics?p. 1
This Bookp. 3
Hadronsp. 4
Nucleonsp. 4
Nuclear Forcesp. 5
Pionsp. 7
Antiparticlesp. 8
Inversion and Parityp. 8
Isospin and Baryonic Numberp. 10
Isospin Invariancep. 13
Magnetic Moment of the Nucleonsp. 14
Strangeness and Hyperchargep. 15
Quantum Chromodynamicsp. 21
Exercisesp. 29
The Two-Nucleon Systemp. 31
Introductionp. 31
Electrostatic Multipolesp. 32
Magnetic Moment with Spin-orbit Couplingp. 34
Experimental Data for the Deuteronp. 36
A Square-well Model for the Deuteronp. 38
The Deuteron Wavefunctionp. 41
Angular momentum couplingp. 41
Two particles of spin [fraction12]p. 42
Total wavefunctionp. 43
Particles in the Continuum: Scatteringp. 46
Partial Wave Expansionp. 49
Low Energy Scatteringp. 53
Effective Range Theoryp. 59
Proton-Proton Scatteringp. 61
Neutron-Neutron Scatteringp. 64
High Energy Scatteringp. 65
Laboratory and Center of Mass Systemsp. 65
Exercisesp. 68
The Nucleon-Nucleon Interactionp. 71
Introductionp. 71
Phenomenological Potentialsp. 72
Local Potentialsp. 72
Nonlocal potentialp. 78
Meson Exchange Potentialsp. 80
Yukawa and Van der Waals potentialsp. 80
Field theory picturep. 84
Short range part of the NN interactionp. 86
Chiral symmetryp. 87
Generalized boson exchangep. 89
Beyond boson exchangep. 91
Effective Field Theoriesp. 95
Exercisesp. 96
General Properties of Nucleip. 98
Introductionp. 98
Nuclear Radiip. 98
Binding Energiesp. 101
Total Angular Momentum of the Nucleusp. 104
Multipole Momentsp. 104
Magnetic Dipole Momentp. 106
Electric Quadrupole Momentp. 109
Excited States of Nucleip. 111
Nuclear Stabilityp. 114
Exercisesp. 116
Nuclear Modelsp. 119
Introductionp. 119
The Liquid Drop Modelp. 119
The Fermi Gas Modelp. 124
The Shell Modelp. 128
Residual Interactionp. 142
Nuclear Vibrationsp. 144
Nuclear Deformationp. 149
The Nilsson Modelp. 150
The Rotational Modelp. 153
Microscopic Theoriesp. 160
Hartree-Fock theoryp. 160
The Skyrme interactionp. 162
Relativistic mean field theoryp. 164
Exercisesp. 166
Radioactivityp. 170
Introductionp. 170
Multiple Decays-Decay Chainp. 171
Preparation of a Radioactive Samplep. 173
Secular Equilibriump. 174
Natural Radioactive Seriesp. 174
Radiation Unitsp. 176
Radioactive Datingp. 177
Properties of Unstable States-Level Widthp. 179
Transition Probability-Golden Rulep. 181
Exercisesp. 183
Alpha-Decayp. 185
Introductionp. 185
Theory of [alpha]-Decayp. 185
Angular Momentum and Parity in [alpha]-Decayp. 191
Exercisesp. 194
Beta-Decayp. 195
Introductionp. 195
Energy Released in [Beta]-Decayp. 196
Fermi Theoryp. 197
The Decay Constant-The Log ft Valuep. 202
Gamow-Teller Transitionsp. 204
Selection Rulesp. 206
Parity Nonconservation in [Beta]-Decayp. 206
Double [Beta]-Decayp. 211
Electron Capturep. 213
Exercisesp. 215
Gamma-Decayp. 218
Introductionp. 218
Quantization of Electromagnetic Fieldsp. 218
Fields and gauge invariancep. 218
Normal modesp. 220
Photonsp. 221
Interaction of Radiation with Matterp. 224
Radiation probabilityp. 227
Long wavelength approximationp. 228
Quantum and Classical Transition Ratesp. 235
Selection Rulesp. 240
Estimate of the Disintegration Constantsp. 241
Isomeric Statesp. 243
Internal Conversionp. 244
Resonant Absorption-The Mossbauer Effectp. 249
Exercisesp. 255
Nuclear Reactions-Ip. 258
Introductionp. 258
Conservation Lawsp. 260
Kinematics of Nuclear Reactionsp. 261
Scattering and Reaction Cross Sectionsp. 265
Resonancesp. 270
Compound Nucleusp. 273
Mean Free Path of a Nucleon in Nucleip. 276
Empirical Optical Potentialp. 277
Compound Nucleus Formationp. 282
Compound Nucleus Decayp. 290
Exercisesp. 294
Nuclear Reactions-IIp. 298
Direct Reactionsp. 298
Theory of direct reactionsp. 301
Validation of the Shell Modelp. 303
Photonuclear Reactionsp. 306
Cross sectionsp. 307
Sum rulesp. 308
Giant resonancesp. 312
Coulomb Excitationp. 315
Fissionp. 319
Mass Distribution of Fission Fragmentsp. 321
Neutrons Emitted in Fissionp. 324
Cross Sections for Fissionp. 325
Energy Distribution in Fissionp. 327
Isomeric Fissionp. 328
Exercisesp. 331
Nuclear Astrophysicsp. 334
Introductionp. 334
Astronomical Observationsp. 335
The Milky Wayp. 335
Dark matterp. 336
Luminosity and Hubble's lawp. 337
The Big Bangp. 338
Stellar Evolutionp. 341
Stars burn slowlyp. 341
Gamow peak and astrophysical S-factorp. 342
The Sunp. 347
Deuterium formationp. 348
Deuterium burningp. 350
[superscript 3]He burningp. 351
Reactions involving [superscript 7]Bep. 352
The CNO Cyclep. 354
Hot CNO and rp processp. 355
Helium Burningp. 357
Red Giantsp. 360
Advanced Burning Stagesp. 362
Carbon burningp. 362
Neon burningp. 364
Oxygen burningp. 365
Silicon burningp. 365
Synthesis of Heaviest Elementsp. 367
White Dwarfs and Neutron Starsp. 368
Supernova Explosionsp. 370
Nuclear Reaction Modelsp. 375
Microscopic modelsp. 375
Potential and DWBA modelsp. 376
Parameter fitp. 377
Statistical modelsp. 377
Exercisesp. 379
Rare Nuclear Isotopesp. 385
Introductionp. 385
Light Exotic Nucleip. 388
Halo nucleip. 390
Bonomean nucleip. 393
Superheavy Elementsp. 395
Exercisesp. 400
Angular Momentump. 401
Orbital Momentump. 401
Spherical Functionsp. 402
Generation of Rotationsp. 402
Orbital Rotationsp. 403
Spinp. 404
Ladder Operatorsp. 406
Angular Momentum Multipletsp. 409
Multiplets as Irreducible Representationsp. 412
SU(2) Group and Spin [fraction12]p. 413
Properties of Spherical Harmonicsp. 414
Explicit derivationp. 414
Legendre polynomialsp. 415
Completenessp. 416
Spherical functions as matrix elements of finite rotationsp. 417
Addition theoremp. 417
Angular Momentum Couplingp. 419
Tensor Operatorsp. 419
Transformation of operatorsp. 419
Scalars and vectorsp. 420
Tensors of rank 2p. 421
Introduction to selection rulesp. 422
Angular Momentum Couplingp. 423
Two subsystemsp. 423
Decomposition of reducible representationsp. 424
Tensor operators and section rules revisitedp. 426
Vector coupling of angular momentap. 427
Wigner-Eckart theoremp. 428
Vector Modelp. 429
Symmetriesp. 432
Time Reversalp. 432
Spin Transformation and Kramer's Theoremp. 433
Time-conjugate Orbitsp. 435
Two-component Neutrino and Fundamental Symmetriesp. 436
Charge Conjugationp. 437
Electric Dipole Momentp. 438
CPT-Invariancep. 439
Relativistic Quantum Mechanicsp. 440
Lagrangiansp. 440
Covariancep. 441
Electromagnetic Fieldp. 442
Relativistic Equationsp. 444
Particle at restp. 446
Covariant form: [gamma] matricesp. 446
Probability and Currentp. 448
Wavefunction Transformationp. 448
Bilinear Covariantsp. 450
Parityp. 451
Plane Wavesp. 451
Summary of plane wave spinor propertiesp. 453
Projection operatorsp. 454
Plane Wave Expansionp. 454
Electromagnetic Interactionp. 455
Pauli Equationp. 455
Spin-orbit and Darwin termsp. 457
Useful Constants and Conversion Factorsp. 459
Constantsp. 459
Massesp. 460
Conversion Factorsp. 460
Referencesp. 461
Indexp. 469
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