Few Body Problem (eBook)

Front Cover 2
The Few Body Problem 6
Copyright Page 7
Table of Contents 12
PREFACE 10
ORGANIZATION 8
LIST OF PARTICIPANTS 14
PART I: THE NUCLEON-NUCLEON INTERACTION 22
CHAPTER 1. NUCLEON-NUCLEON INTERACTION IN APPLICATIONS 24
1. Introduction 24
2, Nuclear many-body problem: accuracy of its solution and results 24
3. Derivation of the nucleon-nucleon potential 30
4. Beyond classic nuclear structure 32
5. Conclusion 36
References 36
CHAPTER 2. NN AND NN INTERACTIONS 38
1 . Introduction 38
2. Nucleon-nucleon elastic scattering 38
3. Nucleon-nucleon interaction – theory 40
4. Nucleon-nucleon interactions – experiment 41
5. Deuteron properties 45
6. NN bound states and resonances 46
References 47
PART II: THREE AND FOUR NUCLEON SYSTEMS 50
CHAPTER 3. THREE- AND FOUR-NUCLEON SYSTEMS (EXPERIMENT) 52
1. Introduction 52
2. Experimental results of the three-nucleon system 52
3. Faddeev calculations 54
4. Polarisation transfer coefficient measurements 57
5. Coulomb effects in p-d scattering 59
6. Determination of the asympototic D- to S-state normalization of the deuteron and triton wave function 60
7. Charge symmetry 62
References 65
CHAPTER 4. THE THREE AND FOUR NUCLEON SYSTEMS (THEORY) 68
1. Introduction 68
2. The three nucleon system 68
3. The Four Nucleon System 77
References 80
CHAPTER 5. GRAPHS OF THREE-BODY WAVE FUNCTIONS 82
1. Introduction 82
2. Faddeev Equations in Configuration Space 83
3. Bound State Wave Functions 85
4. Scattering Wave Functions 90
5. Summary 93
References 93
CHAPTER 6. K-MESON EXPERIMENTS 96
1. Introduction 96
2. K+-Nucleon Amplitudes 96
3. K-Nucleus Scattering 97
4. Hypernuclear Physics 100
5. Summary 104
References 104
CHAPTER 7. ELECTROMAGNETIC DISINTEGRATION OF THE A=3 and A=4 NUCLEI 106
1. Introduction 106
2. The Low Energy Photodisintegration Operator 108
3. El Photodisintegration of 3H(3He) 109
4. A View of 4He Photodisintegration 115
5. Summary 118
References 119
CHAPTER 8. NON-MESONIC FEW-NUCLEON PHENOMENA 120
1. Introduction 120
2. Tests of Invariance Principles 120
3. Properties of Nuclei 124
4. Dynamics 125
5. New Calculations 131
6. Summary and Conclusion 131
References 132
CHAPTER 9. MESONIC FEW-NUCLEON PHENOMENA 134
1. Introduction 134
2. .....p theories 134
3. p-d elastic scattering 135
4. The p-d atom 136
5. The ...dp+ reaction 136
6. Dibaryon resonances 138
7. Elastic p- 3He scattering and p-. scattering lengths 139
8. The reactions pd.t.+, pd.3 He. , pd.Hey and pt.tp Frascaria in ref.36 ) calculates the reactions pd+tp+ (..=180°) and 140
9. Stopped . in 3He, 3H and ai 4He and 4He (n±, .±p) 3H 142
10. The effect of retardation on the binding energy and CFF of A=3 nuclei 143
11. Additional topics 144
References 145
PART III: COULOMB AND n-PARTICLE COLLISION PROBLEMS 148
CHAPTER 10. THE COULOMB PROBLEM A SELECTIVE REVIEW 150
1. Introduction 150
2. Bound states 150
3. Resonances 151
4. Scattering 152
5. Acknowledgment 161
CHAPTER 11. SOME RECENT DEVELOPMENTS IN n-PARTICLE SCATTERING THEORY 164
1. Introduction 164
2. Theoretical Summary 164
3. Interdisciplinary Applications 165
4. Formal and Technical Developments 169
5. Controversies 171
6. Open Questions 173
7. Acknowledgements 173
References 174
CHAPTER 12. THE (p,2p) AND (.,..) REACTIONS 178
1. Introduction 178
2. Recent results 178
3. The DWIA calculations 181
4. Refinements in the DWIA 
184 
5. Peering inside the calculation 186
References 190
CHAPTER 13. COULOMB AND n-PARTICLE PROBLEMS 192
1. Introduction 192
2. Long-range effects in two-body systems 192
3. The Efimov effect for n = 4 195
4. The half-shell Coulomb T matrix half-shell effects
5. The three-body problem and the Coulomb interaction 198
6. The n-body problem 201
7. Conclusion 204
8. Acknowledgments 204
References 204
CHAPTER 14. ATOMIC, MOLECULAR AND NUCLEAR COLLISIONS 206
1. Introduction 206
2. Methods for rearrangement collisions 206
3. Applications of few-body methods in chemistry 210
4. Scattering and reaction experiments in atomic and nuclear physics 211
5. Acknowledgements 217
References 217
PART IV: RELATIVISTIC AND PARTICLE PHYSICS 220
CHAPTER 15. MUON CAPTURE IN HYDROGEN ISOTOPES 222
1. Introduction 222
2. Atomic and molecular processes 222
3. The relevance of the population of hyperfine states 226
4. Recent experimental,investigations 227
References 234
CHAPTER 16. QUARKS IN THE CONTEXT OF FEW BODY PHYSICS 236
1. Introduction 236
2. The simplest baryonic and mesonic configurations 237
3. The (1s)2q ( . s ) -2q configurations 242
4. The (Is)4q ( Is ) q configurations 245
5. heavy quarks in the MIT bag 246
6. The q6 configurations and the baryon-baryon interaction 248
7. Subquarks? 251
References 253
CHAPTER 17. RELATIVISTIC EFFECTS IN THE ATOMIC AND NUCLEAR FEW-BODY PROBLEMS 254
1. Introduction 254
2. Calculational methods 259
3. Experiment 260
References 265
CHAPTER 18. THE SYNTHESIS OF QUANTUM CHROMODYNAMICS AND NUCLEAR PHYSICS 268
1. Introduction 268
2. Short distance processes in QCD 269
3. Nuclear applications of quantum chromodynamics 272
4. QCD and the nucleon – nucleon interaction 274
5. The continuity of nuclear physics and quantum chromodynamics 275
Acknowledgements 276
References 276
CHAPTER 19. RELATIVITY, FIELD THEORY, QUARKS, BAGS, ETC 278
Introduction 278
1. Relativistic wave equations 278
2. Quarks and nucleons and the nuclear force 283
3. Existence 284
4. Confinement and the Coulomb problem 285
References 286
CHAPTER 20. PHOTON-PHOTON INTERACTIONS 288
1. Introduction 288
2. Testing Quantum Electrodynamics 289
3. Two photon production of hadrons 289
4. Conclusion 290
Acknowledgment 290
References 291
PART V: ATOMIC AND MOLECULAR FEW BODY PROBLEMS 292
CHAPTER 21. REARRANGEMENT AND ENERGY TRANSFER COLLISIONS OF FEW-BODY MOLECULAR SYSTEMS: EXPERIMENTAL 294
1. Introduction 294
2. Energy Transfer Collisions 295
3. Rearrangement Collisions 300
ACKNOWLEDGMENTS 306
REFERENCES 306
CHAPTER 22. FEW BODY MOLECULAR COLLISIONS: THEORETICAL 308
I. Introduction 308
2. Electronically adiabatic expansion 308
3. The mapping of potential energy surfaces for triatomic systems 310
4. Scattering formalism in body-fixed coordinates 312
5. Approximate methods 313
6. Calculations for systems leading to changes in electronic state 314
REFERENCES 314
CHAPTER 23. RECENT FORMULATIONS OF e±-., e~-He+, e -He SCATTERING: MULTICHANNEL THEORY AND COMPARISON WITH EXPERIMENT 316
1. Introduction 316
2. Theory 317
3. Computational Results and Experiment 323
4. Impact Ionization 327
Acknowledgments 328
References 328
CHAPTER 24. FEW-BODY PROCESSES IN ATOM-DIATOM COLLISIONS 330
1. Introduction 330
2. Electronic potential energies 331
3. Wavemechanical methods and results 333
4. Transition-operator methods 338
Acknowledgements 343
References 343
CHAPTER 25. (e,2e) THEORY AND EXPERIMENT 348
1. Introduction 348
2. Experimental Methods 349
3. The Differential Cross Section 350
4. The Overlap Amplitude 352
5. The Cross Section for Atomic Targets 354
6. Molecules 357
7. Summary 360
8. Acknowledgment 361
CHAPTER 26. WAVEPACKET THEORY OF COLLISIONAL DISSOCIATION IN MOLECULES 
362 
1. Introduction 362
2. Calculations 363
3, Results 364
4. Conclusions 371
References 371
PART VI: MATHEMATICAL ASPECTS 372
CHAPTER 27. THE NONLINEAR DYNAMICS OF THE CLASSICAL FEW BODY PROBLEM 374
1. Introduction 374
2. Integrable and Nonintegrable systems,2,3) 374
3. The Semiclassical Limit of Quantum Mechanics 378
4. Fluid Dynamics 380
5. References 383
CHAPTER 28. MATHEMATICAL AND COMPUTATIONAL METHODS 386
1. Introduction 386
2. Numerical methods 386
3. Mathematics 389
4. Physically motivated methods 390
5. Other comments 392
References 394
PART VII: STATISTICAL MECHANICS 396
CHAPTER 29. APPLICATION OF FEW-BODY METHODS TO STATISTICAL MECHANICS 398
1. Introduction 398
2. Many-body time delay 399
3. A time delay approach to statistical mechanics 401
4. Arrangement channel quantum mechanics and the kinetic theory of reacting mixtures 406
REFERENCES 409
CONTENTS OF CONTRIBUTED PAPERS VOLUME 412
AUTHOR INDEX 422