The Nuclear Many-Body Problem

By: Peter Ring, Peter Schuck

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Paperback | 25 March 2004

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This long-standing introductory text thoroughly describes nuclear many-body theory, with an emphasis on methodology and the technical aspects of the theories that have been used to describe the nucleus. Now available in a more affordable softcover edition, the original contents of The Nuclear Many-Body Problem presented here is intended for students with basic knowledge of quantum mechanics and some understanding of nuclear phenomena.

From the reviews:
"Its scope and complexity are suitable for easy reading by beginning students of nuclear theory. With a crisp and concise style, the authors quickly develop the shell-model approach to the nuclear many-body problem and subsequently devote more than a third of the text to Hartree-Fock and related models..." Physics Today

Industry Reviews

From the reviews: "The monography by Peter Ring and Peter Schuck covers the techniques used to solve the nuclear many-body problem ! . is recognized as a reference by the nuclear physics community. Theoretical developments are explained pedagogically, with a constant rigour, are well documented and are illustrated with suitably chosen examples. The book contains a lot of references ! . It is served by a concise style. By its scope and rigour, it has no real rival and will expectedly remain a familiar introductory text in nuclear structure theory for many years." (Joseph Cugnon, Physicalia, Vol. 57 (3), 2005) "In many ways, the 1950s through to the 1970s may be seen as a golden period for the development of nuclear physics, both experimental and theoretical. ! The book contains an excellent description of many basic theoretical methods, which continue to be relevant today, it is still of value to specialist students of nuclear theory." (J. P. Elliott, Contemporary Physics, Vol. 46 (6), 2005)

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Non-Fiction Science Physics Nuclear Physics Family & Health Quantum Physics & Quantum Mechanics & Quantum Field Theory Atomic & Molecular Physics Politics & Government Classical Mathematics Wave Mechanics including Vibration & Acoustics

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Published: 1st November 2008

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The Liquid Drop Model	p. 1
Introduction	p. 1
The Semi-empirical Mass Formula	p. 2
Deformation Parameters	p. 5
Surface Oscillations About a Spherical Shape	p. 9
Rotations and Vibrations for Deformed Shapes	p. 17
The Bohr Hamiltonian	p. 17
The Axially Symmetric Case	p. 22
The Asymmetric Rotor	p. 26
Nuclear Fission	p. 28
Stability of Rotating Liquid Drops	p. 32
The Shell Model	p. 36
Introduction and General Considerations	p. 36
Experimental Evidence for Shell Effects	p. 37
The Average Potential of the Nucleus	p. 38
Spin Orbit Coupling	p. 42
The Shell Model Approach to the Many-Body Problem	p. 45
Symmetry Properties	p. 50
Translational Symmetry	p. 50
Rotational Symmetry	p. 51
The Isotopic Spin	p. 53
Comparison with Experiment	p. 56
Experimental Evidence for Single-Particle (Hole) States	p. 56
Electromagnetic Moments and Transitions	p. 60
Deformed Shell Model	p. 65
Experimental Evidence	p. 65
General Deformed Potential	p. 67
The Anisotropic Harmonic Oscillator	p. 68
Nilsson Hamiltonian	p. 70
Quantum Numbers of the Ground State in Odd Nuclei	p. 78
Calculation of Deformation Energies	p. 79
Shell Corrections to the Liquid Drop Model and the Strutinski Method	p. 83
Introduction	p. 83
Basic Ideas of the Strutinski Averaging Method	p. 84
Determination of the Average Level Density	p. 86
Strutinski's Shell Correction Energy	p. 89
Shell Corrections and the Hartree-Fock Method	p. 92
Some Applications	p. 95
Rotation and Single-Particle Motion	p. 96
Introduction	p. 96
General Survey	p. 97
Experimental Observation of High Spin States	p. 97
The Structure of the Yrast Line	p. 99
Phenomenological Classification of the Yrast Band	p. 103
The Backbending Phenomenon	p. 104
The Particle-plus-Rotor Model	p. 107
The Case of Axial Symmetry	p. 109
Some Applications of the Particle-plus-Rotor Model	p. 119
The triaxial Particle-plus-Rotor Model	p. 122
Electromagnetic Properties	p. 125
The Cranking Model	p. 126
Semiclassical Derivation of the Cranking Model	p. 127
The Cranking Formula	p. 130
The Rotating Anisotropic Harmonic Oscillator	p. 133
The Rotating Nilsson Scheme	p. 137
The Deformation Energy Surface at High Angular Momenta	p. 139
Rotation about a Symmetry Axis	p. 142
Yrast Traps	p. 143
Nuclear Forces	p. 147
Introduction	p. 147
The Bare Nucleon-Nucleon Force	p. 149
General Properties of a Two-Body Force	p. 149
The Structure of the Nucleon-Nucleon Interaction	p. 153
Microscopic Effective Interactions	p. 156
Bruckner's G-Matrix and Bethe Goldstone Equation	p. 156
Effective Interactions between Valence Nucleons	p. 164
Effective Interactions between Particles and Holes	p. 170
Phenomenological Effective Interactions	p. 172
General Remarks	p. 172
Simple Central Forces	p. 174
The Skyrme Interaction	p. 175
The Gogny Interaction	p. 176
The Migdal Force	p. 177
The Surface-Delta Interaction (SDI)	p. 179
Separable Forces and Multipole Expansions	p. 180
Experimentally Determined Effective Interactions	p. 185
Concluding Remarks	p. 187
The Hartree-Fock Method	p. 189
Introduction	p. 189
The General Variational Principle	p. 190
The Derivation of the Hartree-Fock Equation	p. 192
The Choice of the Set of Trial Wave Functions	p. 192
The Hartree-Fock Energy	p. 194
Variation of the Energy	p. 194
The Hartree-Fock Equations in Coordinate Space	p. 196
The Hartree-Fock Method in a Simple Solvable Model	p. 197
The Hartree-Fock Method and Symmetries	p. 201
Hartree-Fock with Density Dependent Forces	p. 203
Approach with Microscopic Effective Interactions	p. 203
Hartree-Fock Calculations with the Skyrme Force	p. 208
Concluding Remarks	p. 215
Pairing Correlations and Superfluid Nuclei	p. 217
Introduction and Experimental Survey	p. 217
The Seniority Scheme	p. 221
The BCS Model	p. 228
The Wave Function	p. 228
The BCS Equations	p. 230
The Special Case of a Pure Pairing Force	p. 232
Bogoliubov Quasi-particles-Excited States and Blocking	p. 234
Discussion of the Gap Equation	p. 238
Schematic Solution of the Gap Equation	p. 240
The Generalized Single-Particle Model (HFB Theory)	p. 244
Introduction	p. 244
The General Bogoliubov Transformation	p. 245
Quasi-particle Operators	p. 245
The Quasi-particle Vacuum	p. 249
The Density Matrix and the Pairing Tensor	p. 251
The Hartree-Fock-Bogoliubov Equations	p. 252
Derivation of the HFB Equation	p. 252
Properties of the HFB Equations	p. 255
The Gradient Method	p. 258
The Pairing-plus-Quadrupole Model	p. 259
Applications of the HFB Theory for Ground State Properties	p. 262
Constrained Hartree-Fock Theory (CHF)	p. 266
HFB Theory in the Rotating Frame (SCC)	p. 271
Harmonic Vibrations	p. 280
Introduction	p. 280
Tamm-Dancoff Method	p. 282
Tamm-Dancoff Secular Equation	p. 282
The Schematic Model	p. 285
Particle-Particle (Hole-Hole) Tamm-Dancoff Method	p. 288
General Considerations for Collective Modes	p. 289
Vibrations in Quantum Mechanics	p. 289
Classification of Collective Modes	p. 290
Discussion of Some Collective /(/(-Vibrations	p. 293
Analog Resonances	p. 297
Pairing Vibrations	p. 299
Particle-Hole Theory with Ground State Correlations (RPA)	p. 301
Derivation of the RPA Equations	p. 301
Stability of the RPA	p. 305
Normalization and Closure Relations	p. 305
Numerical Solution of the RPA Equations	p. 306
Representation by Boson Operators	p. 307
Construction of the RPA Ground State	p. 310
Invariances and Spurious Solutions	p. 311
Linear Response Theory	p. 314
Derivation of the Linear Response Equations	p. 315
Calculation of Excitation Probabilities and Schematic Model	p. 319
The Static Polarizability and the Moment of Inertia	p. 321
RPA Equations in the Continuum	p. 322
Applications and Comparison with Experiment	p. 325
Particle-Hole Calculations in a Phenomenological Basis	p. 325
Particle-Hole Calculations in a Self-Consistent Basis	p. 328
Sum Rules	p. 330
Sum Rules as Energy Weighted Moments of the Strength Functions	p. 330
The 5,-Sum Rule and the RPA Approach	p. 331
Evaluation of the Sum Rules 5, 5, and 53	p. 332
Sum Rules and Polarizabilities	p. 335
Calculation of Transition Currents and Densities	p. 335
Particle-Particle RPA	p. 339
The Formalism	p. 339
Ground State Correlations Induced by Pairing Vibrations	p. 341
Quasi-particle RPA	p. 343
Boson Expansion Methods	p. 346
Introduction	p. 346
Boson Representations in Even-Even Nuclei	p. 348
Boson Representations of the Angular Momentum Operators	p. 348
Concepts for Boson Expansions	p. 351
The Boson Expansion of Belyaev and Zelevinski	p. 354
The Boson Expansion of Marumori	p. 362
The Boson Expansion of Dyson	p. 367
The Mathematical Background	p. 368
Methods Based on pp-Bosons	p. 372
Applications	p. 375
Odd Mass Nuclei and Particle Vibration Coupling	p. 381
Boson Expansion for Odd Mass Systems	p. 382
Derivation of the Particle Vibration Coupling (Bohr) Hamiltonian	p. 383
Particle Vibration Coupling (Perturbation Theory)	p. 385
The Nature of the Particle Vibration Coupling Vertex	p. 387
Effective Charges	p. 389
Intermediate Coupling and Dyson's Boson Expansion	p. 390
Other Particle Vibration Coupling Calculations	p. 395
Weak Coupling in Even Systems	p. 397
The Generator Coordinate Method	p. 398
Introduction	p. 398
The General Concept	p. 399
The GCM Ansatz for the Wave Function	p. 399
The Determination of the Weight Function f(a)	p. 401
Methods of Numerical Solution of the HW Equation	p. 404
The Lipkin Model as an Example	p. 405
The Generator Coordinate Method and Boson Expansions	p. 406
The One-Dimensional Harmonic Oscillator	p. 409
Complex Generator Coordinates	p. 411
The Bargman Space	p. 411
The Schrodinger Equation	p. 413
Gaussian Wave Packets in the Harmonic Oscillator	p. 414
Double Projection	p. 418
Derivation of a Collective Hamiltonian	p. 419
General Considerations	p. 419
The Symmetric Moment Expansion (SME)	p. 420
The Local Approximation (LA)	p. 423
The Gaussian Overlap Approximation (GOAL)	p. 424
The Lipkin Model	p. 428
The Multidimensional Case	p. 430
The Choice of the Collective Coordinate	p. 430
Application of the Generator Coordinate Method for Bound States	p. 433
Giant Resonances	p. 433
Pairing Vibrations	p. 435
Restoration of Broken Symmetries	p. 438
Introduction	p. 438
Symmetry Violation in the Mean Field Theory	p. 441
Transformation to an Intrinsic System	p. 451
General Concepts	p. 451
Translational Motion	p. 454
Rotational Motion	p. 457
Projection Methods	p. 458
Projection Operators	p. 458
Projection Before and After the Variation	p. 460
Particle Number Projection	p. 463
Approximate Projection for Large Deformations	p. 466
The Inertial Parameters	p. 470
Angular Momentum Projection	p. 473
The Structure of the Intrinsic Wave Functions	p. 482
The Time Dependent Hartree-Fock Method (TDHF)	p. 485
Introduction	p. 485
The Full Time-Dependent Hartree-Fock Theory	p. 486
Derivation of the TDHF Equation	p. 486
Properties of the TDHF Equation	p. 489
Quasi-static Solutions	p. 492
General Discussion of the TDHF Method	p. 493
An Exactly Soluble Model	p. 499
Applications of the TDHF Theory	p. 500
Adiabatic Time-Dependent Hartree-Fock Theory (ATDHF)	p. 505
The ATDHF Equations	p. 505
The Collective Hamiltonian	p. 510
Reduction to a Few Collective Coordinates	p. 513
The Choice of the Collective Coordinates	p. 516
General Discussion of the Atdhf Methods	p. 519
Applications of the ATDHF Method	p. 521
Adiabatic Perturbation Theory and the Cranking Formula	p. 523
Semiclassical Methods in Nuclear Physics	p. 527
Introduction	p. 527
The Static Case	p. 528
The Thomas-Fermi Theory	p. 528
Wigner-Kirkwood ħ-Expansion	p. 534
Partial Resummation of the ħ-Expansion	p. 545
The Saddle Point Method	p. 547
Application to a Sperical Woods-Saxon Potential	p. 549
Semiclassical Treatment of Pairing Properties	p. 550
The Dynamic Case	p. 552
The Boltzmann Equation	p. 553
Fluid Dynamic Equations from the Boltzmann Equation	p. 555
Application of Ordinary Fluid Dynamics to Nuclei	p. 558
Variational Derivation of Fluid Dynamics	p. 562
Momentum Distribution of the Density ₀	p. 564
Imposed Fluid Dynamic Motion	p. 568
An Illustrative Example	p. 573
Appendices
Angular Momentum Algebra in the Laboratory and the Body-Fixed System	p. 575
Electromagnetic Moments and Transitions	p. 580
The General Form of the Hamiltonian	p. 580
Static Multipole Moments	p. 581
The Multipole Expansion of the Radiation Field	p. 584
Multipole Transitions	p. 587
Single-Particle Matrix Elements in a Spherical Basis	p. 591
Translational Invariance and Electromagnetic Transitions	p. 592
The Cross Section for the Absorption of Dipole Radiation	p. 593
Second Quantization	p. 595
Creation and Annihilation Operators	p. 595
Field Operators in the Coordinate Space	p. 598
Representation of Operators	p. 599
Wick's Theorem	p. 601
Density Matrices	p. 603
Normal Densities	p. 603
Densities of Slater Determinants	p. 605
Densities of BCS and HFB States	p. 608
The Wigner Transformation of the Density Matrix	p. 609
Theorems Concerning Product Wave Functions	p. 611
The Bloch-Messiah Theorem [BM 62]	p. 611
Operators in the Quasi-particle Space	p. 613
Thouless' Theore*n	p. 615
The Onishi Formula	p. 618
Bogoliubov Transformations for Bosons	p. 620
Many-Body Green's Functions	p. 623
Single-Particle Green's Function and Dyson's Equation	p. 623
Perturbation Theory	p. 628
Skeleton Expansion	p. 631
Factorization and Briickner-Hartree-Fock	p. 632
Hartree-Fock-Bogoliubov Equations	p. 634
The Bethe-Salpeter Equation and Effective Forces	p. 640
Bibliography	p. 643
Author Index	p. 681
Subject Index	p. 699
Table of Contents provided by Publisher. All Rights Reserved.

The Nuclear Many-Body Problem

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Paperback

Industry Reviews

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