Nuclear superfluidity: pairing in finite systems

Cover......Page 1
Half-Title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
1.1 Pairing in nuclei, superconductors, liquid He and neutrons stars......Page 17
1.2 Macroscopic wavefunction and phase rigidity......Page 19
1.3 Broken symmetry and collective modes......Page 22
1.4 Superfluid He (He II)......Page 24
1.5 Critical velocity for superconductors......Page 29
1.6 Pairing in nuclei......Page 30
1.7 Superconductivity......Page 35
1.8 Superfluidity of liquid He......Page 41
1.9 Comparison of pairing in nuclei with superconductivity......Page 42
1.10 Neutron stars......Page 46
2.1 Evidence for pairing correlations......Page 49
2.2 The pairing interaction......Page 52
2.3 The delta -function nucleon–nucleon potential......Page 55
2.4 The degenerate model and quasi-spin......Page 58
2.5 Pairing binding energy formula......Page 60
2.6 Quasi-spin wavefunctions......Page 61
2.7 Pairing rotations......Page 63
2.8 Exact solution of the pairing Hamiltonian......Page 64
3.1 The BCS wavefunction......Page 68
3.2 The energy......Page 71
3.3 Excited states and quasiparticles......Page 73
3.4 The mean-field Hamiltonian......Page 76
3.5 The correlation energy......Page 77
3.6 Pairing correlations in the wavefunction......Page 80
3.7 The degenerate model in the BCS approximation......Page 81
3.8 Gauge invariance......Page 82
3.9 Matrix elements of one-body operators......Page 83
3.10 Pairing and isospin......Page 85
4.1 General background......Page 88
4.1.1 Infinite systems and finite systems......Page 90
4.2 Pairing in atomic nuclei (0D systems…......Page 91
4.2.1 Deformation in gauge space: mean-field approximation......Page 92
4.2.2 Solution of the RPA equations......Page 96
4.2.3 The zero-frequency mode......Page 98
4.2.4 Two-particle transfer reaction......Page 100
4.2.5 A schematic model......Page 101
4.2.6 Comparison with experiment......Page 103
4.3 Infinite 3D neutral superconductors…......Page 104
4.3.1 Neutral superconductor......Page 105
5.1 The two-level model......Page 108
5.1.1 Collective treatment of pairing vibrations; normal systems (x < 1)......Page 111
5.1.2 Collective treatment of pairing vibrations; superfluid systems (x > 1)......Page 113
5.1.3 Pairing phase transitions......Page 116
5.2.1 Normal systems (Pb isotopes)......Page 118
5.2.2 Superfluid systems (Sn isotopes)......Page 122
5.3.1 Normal systems (Pb isotopes)......Page 124
5.3.2 Superfluid systems (heavy deformed nuclei)......Page 126
6 Phase transitions......Page 133
6.1 The experimental situation......Page 135
6.2 Static pairing correlations: the BCS theory of pairing phase transitions in strongly rotating nuclei......Page 138
6.2.1 Estimate of crossing frequency: gapless superconductivity......Page 140
6.2.2 Pairing in D-states......Page 144
6.2.3 Time-reversal violation due to rotation (the i model)......Page 148
6.2.4 Detailed numerical calculations......Page 152
6.3 Pairing fluctuations......Page 154
6.4 Moments of inertia......Page 157
6.5 Condensation-induced tunnelling......Page 160
6.6 Response function technique to calculate RPA fluctuations......Page 161
7 Plastic behaviour of nuclei and other finite systems......Page 170
7.1 Exotic decay......Page 171
7.1.1 Inertia......Page 174
7.1.2 Potential energy......Page 175
7.1.3 Formation probability......Page 176
7.1.6 Tunnelling probability......Page 177
7.1.7 Comparison to experiment......Page 178
7.2 A variety of applications......Page 179
7.3 Low-lying surface vibrations......Page 181
7.4 Fission in metal clusters......Page 184
8 Sources of pairing in nuclei......Page 186
8.1 The bare nucleon–nucleon potential and the pairing interaction......Page 187
8.1.1 Calculation of the pairing properties of Sn......Page 189
8.2 Mean-field theory......Page 193
8.2.1 Effective mass (k-mass)......Page 196
8.3 Random phase approximation......Page 200
8.3.1 RPA dispersion relation......Page 203
8.3.2 Sum rules......Page 207
8.3.3 Frequency of the giant quadrupole resonance......Page 209
8.3.4 Damping of giant vibrations......Page 211
8.4 Correlation energy contribution to nuclear masses......Page 215
9.1 Doorway states......Page 220
9.1.1 The dynamical shell model......Page 221
9.1.2 Motion of a particle in a complex potential......Page 224
9.2 Effective mass (omega-mass)......Page 227
9.3 The omega-mass and the induced interaction......Page 231
10.1 Simple estimates......Page 235
10.2 Microscopic calculations......Page 239
10.3 Slab model......Page 247
10.4.1 Solution of the Dyson equation for normal and abnormal densities......Page 255
10.5 Superfluidity in the inner crust of neutron stars......Page 260
10.5.1 Interplay between density and magnetic modes......Page 264
11 Pairing in exotic nuclei......Page 273
11.1 The halo nucleus Li......Page 274
11.1.1 Single-particle states in Li: effective mass processes......Page 278
11.1.2 Li and the Cooper pair problem......Page 282
11.1.3 Spatial structure of the Cooper pair......Page 287
11.1.4 Transfer reactions......Page 289
11.2 The halo nucleus Be......Page 291
A.1 Fermions......Page 296
A.2 Particles and holes......Page 302
A.3 Bosons......Page 304
A.4 Quasi-bosons......Page 306
Appendix B Single particle in a non-local potential......Page 308
B.1 Single particle in a non-local, omega-dependent potential......Page 310
C.2 The relation between…......Page 313
Appendix D Particle-vibration coupling......Page 315
D.1 Estimate of…......Page 317
D.2 Asimple estimate of…......Page 319
Appendix E Model of the single-particle strength function......Page 321
Appendix F Simple model of Pauli principle corrections......Page 324
G.1 Solution of the pairing Hamiltonian......Page 326
G.2 Two-quasiparticle excitations......Page 331
G.3 Minimization......Page 333
G.4 BCS wavefunction......Page 334
H.1 BCS solution......Page 336
H.2 Cranking moment of inertia......Page 338
H.3 Two-particle transfer......Page 339
H.4 Polarization effects......Page 340
I.1 Conjugate variables......Page 343
I.2 Rotation about an axis......Page 344
I.3 Rotations in gauge space......Page 345
I.4 Symmetry restoring fluctuations and pairing rotations......Page 346
I.4.1 Demonstration that…......Page 348
Appendix J RPA solution of the pairing Hamiltonian......Page 351
J.1 Diagonalization of the…......Page 352
J.2 Diagonalization of the…......Page 355
J.3 Diagonalization of the full Hamiltonian…......Page 359
K.1 Simple estimates......Page 365
K.2 Critical velocity for the excitation of rotons......Page 370
K.3 Critical velocity for superfluidity......Page 371
Appendix L Josephson effect......Page 372
References......Page 377
Index......Page 390