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The Nuclear Many-Body Problem : Texts and Monographs in Physics - Peter Ring

The Nuclear Many-Body Problem

Texts and Monographs in Physics

Paperback Published: 1st October 2004
ISBN: 9783540212065
Number Of Pages: 718

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It is the aim of this book to describe in concise form our present theoretical understanding of the nuclear many-body problem. The presen- tation of the enormous amount of material that has accumulated in this field over the last few decades may be divided into two broad categories: One can either concentrate on the physical phenomena, such as the single-particle excitations, rotations, vibrations, or large-amplitude collec- tive motion, and treat each of them using a variety of theoretical methods; or one may stress the methodology and technical aspects of the different theories that have been used to describe the nucleus. We have chosen the second avenue. The structure of this book is thus dictated by the different methods used-Hartree-Fock theory, time-dependent Hartree-Fock the- ory, generator coordinates, boson expansions, etc. -rather than by the physical subjects. Many of the present theories have, of course, already been presented in other textbooks. In order to be able to give a more rounded picture, we shall either briefly review such topics (as in the case of the liquid drop or the shell model) or try to give more updated versions (as in the cases of rotations or the random phase approximation). Our essential aim, however, is to present the more modern theories-such as boson expansions, genera- tor coordinates, time-dependent Hartree-Fock, semiclassical theories, etc. -which have either never been seen, or at best had little detailed treat- ment in, book form.

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)

The Liquid Drop Modelp. 1
Introductionp. 1
The Semi-empirical Mass Formulap. 2
Deformation Parametersp. 5
Surface Oscillations About a Spherical Shapep. 9
Rotations and Vibrations for Deformed Shapesp. 17
The Bohr Hamiltonianp. 17
The Axially Symmetric Casep. 22
The Asymmetric Rotorp. 26
Nuclear Fissionp. 28
Stability of Rotating Liquid Dropsp. 32
The Shell Modelp. 36
Introduction and General Considerationsp. 36
Experimental Evidence for Shell Effectsp. 37
The Average Potential of the Nucleusp. 38
Spin Orbit Couplingp. 42
The Shell Model Approach to the Many-Body Problemp. 45
Symmetry Propertiesp. 50
Translational Symmetryp. 50
Rotational Symmetryp. 51
The Isotopic Spinp. 53
Comparison with Experimentp. 56
Experimental Evidence for Single-Particle (Hole) Statesp. 56
Electromagnetic Moments and Transitionsp. 60
Deformed Shell Modelp. 65
Experimental Evidencep. 65
General Deformed Potentialp. 67
The Anisotropic Harmonic Oscillatorp. 68
Nilsson Hamiltonianp. 70
Quantum Numbers of the Ground State in Odd Nucleip. 78
Calculation of Deformation Energiesp. 79
Shell Corrections to the Liquid Drop Model and the Strutinski Methodp. 83
Introductionp. 83
Basic Ideas of the Strutinski Averaging Methodp. 84
Determination of the Average Level Densityp. 86
Strutinski's Shell Correction Energyp. 89
Shell Corrections and the Hartree-Fock Methodp. 92
Some Applicationsp. 95
Rotation and Single-Particle Motionp. 96
Introductionp. 96
General Surveyp. 97
Experimental Observation of High Spin Statesp. 97
The Structure of the Yrast Linep. 99
Phenomenological Classification of the Yrast Bandp. 103
The Backbending Phenomenonp. 104
The Particle-plus-Rotor Modelp. 107
The Case of Axial Symmetryp. 109
Some Applications of the Particle-plus-Rotor Modelp. 119
The triaxial Particle-plus-Rotor Modelp. 122
Electromagnetic Propertiesp. 125
The Cranking Modelp. 126
Semiclassical Derivation of the Cranking Modelp. 127
The Cranking Formulap. 130
The Rotating Anisotropic Harmonic Oscillatorp. 133
The Rotating Nilsson Schemep. 137
The Deformation Energy Surface at High Angular Momentap. 139
Rotation about a Symmetry Axisp. 142
Yrast Trapsp. 143
Nuclear Forcesp. 147
Introductionp. 147
The Bare Nucleon-Nucleon Forcep. 149
General Properties of a Two-Body Forcep. 149
The Structure of the Nucleon-Nucleon Interactionp. 153
Microscopic Effective Interactionsp. 156
Bruckner's G-Matrix and Bethe Goldstone Equationp. 156
Effective Interactions between Valence Nucleonsp. 164
Effective Interactions between Particles and Holesp. 170
Phenomenological Effective Interactionsp. 172
General Remarksp. 172
Simple Central Forcesp. 174
The Skyrme Interactionp. 175
The Gogny Interactionp. 176
The Migdal Forcep. 177
The Surface-Delta Interaction (SDI)p. 179
Separable Forces and Multipole Expansionsp. 180
Experimentally Determined Effective Interactionsp. 185
Concluding Remarksp. 187
The Hartree-Fock Methodp. 189
Introductionp. 189
The General Variational Principlep. 190
The Derivation of the Hartree-Fock Equationp. 192
The Choice of the Set of Trial Wave Functionsp. 192
The Hartree-Fock Energyp. 194
Variation of the Energyp. 194
The Hartree-Fock Equations in Coordinate Spacep. 196
The Hartree-Fock Method in a Simple Solvable Modelp. 197
The Hartree-Fock Method and Symmetriesp. 201
Hartree-Fock with Density Dependent Forcesp. 203
Approach with Microscopic Effective Interactionsp. 203
Hartree-Fock Calculations with the Skyrme Forcep. 208
Concluding Remarksp. 215
Pairing Correlations and Superfluid Nucleip. 217
Introduction and Experimental Surveyp. 217
The Seniority Schemep. 221
The BCS Modelp. 228
The Wave Functionp. 228
The BCS Equationsp. 230
The Special Case of a Pure Pairing Forcep. 232
Bogoliubov Quasi-particles-Excited States and Blockingp. 234
Discussion of the Gap Equationp. 238
Schematic Solution of the Gap Equationp. 240
The Generalized Single-Particle Model (HFB Theory)p. 244
Introductionp. 244
The General Bogoliubov Transformationp. 245
Quasi-particle Operatorsp. 245
The Quasi-particle Vacuump. 249
The Density Matrix and the Pairing Tensorp. 251
The Hartree-Fock-Bogoliubov Equationsp. 252
Derivation of the HFB Equationp. 252
Properties of the HFB Equationsp. 255
The Gradient Methodp. 258
The Pairing-plus-Quadrupole Modelp. 259
Applications of the HFB Theory for Ground State Propertiesp. 262
Constrained Hartree-Fock Theory (CHF)p. 266
HFB Theory in the Rotating Frame (SCC)p. 271
Harmonic Vibrationsp. 280
Introductionp. 280
Tamm-Dancoff Methodp. 282
Tamm-Dancoff Secular Equationp. 282
The Schematic Modelp. 285
Particle-Particle (Hole-Hole) Tamm-Dancoff Methodp. 288
General Considerations for Collective Modesp. 289
Vibrations in Quantum Mechanicsp. 289
Classification of Collective Modesp. 290
Discussion of Some Collective /(/(-Vibrationsp. 293
Analog Resonancesp. 297
Pairing Vibrationsp. 299
Particle-Hole Theory with Ground State Correlations (RPA)p. 301
Derivation of the RPA Equationsp. 301
Stability of the RPAp. 305
Normalization and Closure Relationsp. 305
Numerical Solution of the RPA Equationsp. 306
Representation by Boson Operatorsp. 307
Construction of the RPA Ground Statep. 310
Invariances and Spurious Solutionsp. 311
Linear Response Theoryp. 314
Derivation of the Linear Response Equationsp. 315
Calculation of Excitation Probabilities and Schematic Modelp. 319
The Static Polarizability and the Moment of Inertiap. 321
RPA Equations in the Continuump. 322
Applications and Comparison with Experimentp. 325
Particle-Hole Calculations in a Phenomenological Basisp. 325
Particle-Hole Calculations in a Self-Consistent Basisp. 328
Sum Rulesp. 330
Sum Rules as Energy Weighted Moments of the Strength Functionsp. 330
The 5,-Sum Rule and the RPA Approachp. 331
Evaluation of the Sum Rules 5, 5, and 53p. 332
Sum Rules and Polarizabilitiesp. 335
Calculation of Transition Currents and Densitiesp. 335
Particle-Particle RPAp. 339
The Formalismp. 339
Ground State Correlations Induced by Pairing Vibrationsp. 341
Quasi-particle RPAp. 343
Boson Expansion Methodsp. 346
Introductionp. 346
Boson Representations in Even-Even Nucleip. 348
Boson Representations of the Angular Momentum Operatorsp. 348
Concepts for Boson Expansionsp. 351
The Boson Expansion of Belyaev and Zelevinskip. 354
The Boson Expansion of Marumorip. 362
The Boson Expansion of Dysonp. 367
The Mathematical Backgroundp. 368
Methods Based on pp-Bosonsp. 372
Applicationsp. 375
Odd Mass Nuclei and Particle Vibration Couplingp. 381
Boson Expansion for Odd Mass Systemsp. 382
Derivation of the Particle Vibration Coupling (Bohr) Hamiltonianp. 383
Particle Vibration Coupling (Perturbation Theory)p. 385
The Nature of the Particle Vibration Coupling Vertexp. 387
Effective Chargesp. 389
Intermediate Coupling and Dyson's Boson Expansionp. 390
Other Particle Vibration Coupling Calculationsp. 395
Weak Coupling in Even Systemsp. 397
The Generator Coordinate Methodp. 398
Introductionp. 398
The General Conceptp. 399
The GCM Ansatz for the Wave Functionp. 399
The Determination of the Weight Function f(a)p. 401
Methods of Numerical Solution of the HW Equationp. 404
The Lipkin Model as an Examplep. 405
The Generator Coordinate Method and Boson Expansionsp. 406
The One-Dimensional Harmonic Oscillatorp. 409
Complex Generator Coordinatesp. 411
The Bargman Spacep. 411
The Schrodinger Equationp. 413
Gaussian Wave Packets in the Harmonic Oscillatorp. 414
Double Projectionp. 418
Derivation of a Collective Hamiltonianp. 419
General Considerationsp. 419
The Symmetric Moment Expansion (SME)p. 420
The Local Approximation (LA)p. 423
The Gaussian Overlap Approximation (GOAL)p. 424
The Lipkin Modelp. 428
The Multidimensional Casep. 430
The Choice of the Collective Coordinatep. 430
Application of the Generator Coordinate Method for Bound Statesp. 433
Giant Resonancesp. 433
Pairing Vibrationsp. 435
Restoration of Broken Symmetriesp. 438
Introductionp. 438
Symmetry Violation in the Mean Field Theoryp. 441
Transformation to an Intrinsic Systemp. 451
General Conceptsp. 451
Translational Motionp. 454
Rotational Motionp. 457
Projection Methodsp. 458
Projection Operatorsp. 458
Projection Before and After the Variationp. 460
Particle Number Projectionp. 463
Approximate Projection for Large Deformationsp. 466
The Inertial Parametersp. 470
Angular Momentum Projectionp. 473
The Structure of the Intrinsic Wave Functionsp. 482
The Time Dependent Hartree-Fock Method (TDHF)p. 485
Introductionp. 485
The Full Time-Dependent Hartree-Fock Theoryp. 486
Derivation of the TDHF Equationp. 486
Properties of the TDHF Equationp. 489
Quasi-static Solutionsp. 492
General Discussion of the TDHF Methodp. 493
An Exactly Soluble Modelp. 499
Applications of the TDHF Theoryp. 500
Adiabatic Time-Dependent Hartree-Fock Theory (ATDHF)p. 505
The ATDHF Equationsp. 505
The Collective Hamiltonianp. 510
Reduction to a Few Collective Coordinatesp. 513
The Choice of the Collective Coordinatesp. 516
General Discussion of the Atdhf Methodsp. 519
Applications of the ATDHF Methodp. 521
Adiabatic Perturbation Theory and the Cranking Formulap. 523
Semiclassical Methods in Nuclear Physicsp. 527
Introductionp. 527
The Static Casep. 528
The Thomas-Fermi Theoryp. 528
Wigner-Kirkwood ħ-Expansionp. 534
Partial Resummation of the ħ-Expansionp. 545
The Saddle Point Methodp. 547
Application to a Sperical Woods-Saxon Potentialp. 549
Semiclassical Treatment of Pairing Propertiesp. 550
The Dynamic Casep. 552
The Boltzmann Equationp. 553
Fluid Dynamic Equations from the Boltzmann Equationp. 555
Application of Ordinary Fluid Dynamics to Nucleip. 558
Variational Derivation of Fluid Dynamicsp. 562
Momentum Distribution of the Density 0p. 564
Imposed Fluid Dynamic Motionp. 568
An Illustrative Examplep. 573
Appendices
Angular Momentum Algebra in the Laboratory and the Body-Fixed Systemp. 575
Electromagnetic Moments and Transitionsp. 580
The General Form of the Hamiltonianp. 580
Static Multipole Momentsp. 581
The Multipole Expansion of the Radiation Fieldp. 584
Multipole Transitionsp. 587
Single-Particle Matrix Elements in a Spherical Basisp. 591
Translational Invariance and Electromagnetic Transitionsp. 592
The Cross Section for the Absorption of Dipole Radiationp. 593
Second Quantizationp. 595
Creation and Annihilation Operatorsp. 595
Field Operators in the Coordinate Spacep. 598
Representation of Operatorsp. 599
Wick's Theoremp. 601
Density Matricesp. 603
Normal Densitiesp. 603
Densities of Slater Determinantsp. 605
Densities of BCS and HFB Statesp. 608
The Wigner Transformation of the Density Matrixp. 609
Theorems Concerning Product Wave Functionsp. 611
The Bloch-Messiah Theorem [BM 62]p. 611
Operators in the Quasi-particle Spacep. 613
Thouless' Theore*np. 615
The Onishi Formulap. 618
Bogoliubov Transformations for Bosonsp. 620
Many-Body Green's Functionsp. 623
Single-Particle Green's Function and Dyson's Equationp. 623
Perturbation Theoryp. 628
Skeleton Expansionp. 631
Factorization and Briickner-Hartree-Fockp. 632
Hartree-Fock-Bogoliubov Equationsp. 634
The Bethe-Salpeter Equation and Effective Forcesp. 640
Bibliographyp. 643
Author Indexp. 681
Subject Indexp. 699
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540212065
ISBN-10: 354021206X
Series: Texts and Monographs in Physics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 718
Published: 1st October 2004
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 23.67 x 15.49  x 4.12
Weight (kg): 1.08