Collective motion and phase transitions in nuclear systems : proceedings of the Predeal International Summer School in Nuclear Physics, Predeal, Romania, 28 August-9 September 2006

CONTENTS......Page 12
Preface......Page 6
Organising Committee and List of Participants......Page 8
I.1 Phenomenological Approaches......Page 18
1. Introduction......Page 20
2. The basis of the Bohr model......Page 22
3. The Bohr model with Quadrupole and Octupole......Page 23
4. Intrinsic amplitudes for quadrupole and octupole......Page 24
5. Quantization of the quadrupole - octupole Hamiltonian......Page 26
6. The third component of the angular momentum......Page 27
7. Axial octupole mode with stable quadrupole deformation......Page 30
8. Going close to the quadrupole critical point......Page 31
9. Specific models for quadrupole-octupole oscillations......Page 32
10. Critical-point behaviour for 224Ra and 224Th ?......Page 35
References......Page 37
1. Introduction......Page 38
2. Brief review of CSM......Page 40
3. CSM extension to the negative parity states......Page 42
4. Extension to the K" = I* bands......Page 44
5. Numerical results......Page 46
References......Page 60
1. Introduction......Page 61
2. Minimization of deformation energy......Page 64
3. Saddle point shapes with reflection symmetry......Page 68
4. Qualitative explanation of the mass asymmetry in fission......Page 69
5. Ternary Fission......Page 70
6. Quaternary and multicluster fission......Page 72
References......Page 75
1. Introduction......Page 79
2. Ternary configuration shapes......Page 80
3. Three center potential......Page 81
4. The Hamiltonian......Page 83
5. The spin-orbit and Z2 - terms......Page 86
6. Results......Page 90
7. Conclusions......Page 92
References......Page 93
1. Introduction......Page 95
2.1. IGISOL......Page 98
2.2. Linear Paul trap: RFQ cooler and buncher at IGISOL......Page 99
3. Atomic Masses measurements at JYFLTRAP......Page 100
3.1. Binding energies and nuclear stmcture......Page 101
3.2. Pail-ing and shell gap energies......Page 103
3.3. Atomic Masses and the Nucleosynthesis......Page 106
4. Precision QEC Determination for Superallowed Beta Decay......Page 107
5. Summary......Page 109
References......Page 110
1. Introduction......Page 111
2. The IBA Hamiltonian and symmetry triangle......Page 113
3. Comparison of X(3), X(5)-P2, and X(5)-p4 predictions to the IBA......Page 115
4. Comparison of X(3), X(5)-p2, and X(5)-P4 predictions to experiment......Page 122
5. Discussion......Page 125
References......Page 127
1. Introduction......Page 129
2. The X(3) model......Page 130
3. Numerical results and comparison to experiment......Page 135
References......Page 137
Chaotic Behavior of Nuclear Systems J.M.G. Gdmez, L. M U ~ O Z , J. Retamosa, R.A. Molina, A. Rela6o and E. Faleiro......Page 139
1. Introduction......Page 140
2. Chaos in nuclei......Page 141
3. Chaoticity of Ca, Sc and Ti isotopes......Page 142
4. Time series, chaos and l / f noise......Page 147
5.1. Atomic nuclei......Page 149
5.2. RMT ensembles......Page 150
6. The power spectrum conjecture......Page 152
7. RMT derivation of the l/f noise in quantum chaos......Page 153
8. Conclusions......Page 155
References......Page 156
1. Introduction......Page 158
2. Introduction, some vocabulary......Page 159
2.1. The 7Be(p,y)sB reaction in the Sun......Page 160
3. Indirect methods in nuclear astrophysics......Page 161
3.1. The Coulomb dissociation......Page 162
3.2. The ANC method......Page 163
3.3. Breakup of loosely bound nuclei at intermediate energies......Page 166
4. Other spectroscopic methods......Page 170
References......Page 171
I.2 Microscopic Formalisms......Page 174
1. Introduction......Page 175
2.1. Direct diagonalixation: Lancxos method......Page 176
2.2. Shell Model Monte Carlo......Page 177
2.3. Quantum Monte Carlo Diagonalization......Page 179
3.1. The algorithm......Page 180
3.2. Importance sampling......Page 182
3.4. Selective numerical tests......Page 183
3.5. Remarks......Page 185
4. Collective modes and anharmonicities in nuclei......Page 187
4.1. An equations of motion approach for generating a multiphonon basis......Page 188
4.2. Redundancy-free multiphonon basis......Page 189
4.3. A numerical illustrative application of the method: l6 0......Page 191
5. Concluding remarks......Page 195
References......Page 196
1. Single j Shell Calculations--f7/2......Page 198
1.2. Orthogonulizing T-gmuter states with T-lower states......Page 201
1.4. Other single j symmetries......Page 203
2. Partial Dynamical Symmetry When T = 0 Two-Body Matrix Elements are Set Equal to Zero......Page 204
3. A Brief Discussion of the g g / 2 Shell......Page 209
4.1. The even-even Ca isotopes......Page 213
4.2. Isoscalar moments......Page 214
References......Page 215
1. Introduction......Page 216
2. The nucleon-nucleon potential......Page 218
3. The shell-model effective interaction......Page 222
4. The low-momentum nucleon-nucleon potential K0w-k......Page 223
5. Review of selected results......Page 226
References......Page 231
1. Introduction......Page 234
2.1. Continuum-HFB approach......Page 235
2.2. Resonant states in the BCS approach......Page 236
2.3. Linear response theory with pair correlations and continuum coupling......Page 237
2.4. Quasiparticle excitations and two-neutron tmnsfer in neutron-rich nuclei......Page 240
3.1. Superfiuid properties of the inner crust matter......Page 242
3.2. Specific heat of the inner crust baryonic matter......Page 244
3.3. Collective modes in the inner crust matter......Page 246
3.4. Cooling time of the inner crust......Page 248
4. Conclusions......Page 249
References......Page 250
1. Introduction......Page 251
2. Theoretical Framework......Page 252
3. Shape Coexistence Effects in 78Kr......Page 255
4. Coulomb-Induced Isospin-Mixing Effects on the Superallowed Fermi Beta Decay......Page 261
5. Magnetic Bands in ”Rb......Page 265
References......Page 268
1. Introduction......Page 269
2.1. HFB theory......Page 271
2.2. MHFB theory......Page 274
2.3. MBCS theory......Page 279
3. Phonon-damping model in quasiparticle representation......Page 280
4.1. Temperature dependence of pairing gap......Page 283
4.2. Ternpemtum dependence of GDR width......Page 284
References......Page 286
1. Introduction......Page 287
2.1. QRPA......Page 288
2.2. MAVA......Page 289
2.3. MAVA-2......Page 290
3. Numerical application......Page 291
4.1. Cadmium isotopes......Page 292
4.2. Ruthenium isotopes......Page 294
4.3. Molybdenum isotopes......Page 296
References......Page 298
I.3 Relativistic Nuclear Structure......Page 302
1. Introduction......Page 304
2. The relativistic Hartree-Bogoliubov model......Page 305
2.1. Covariant density functional theory with pairing......Page 307
3.1. Shape coesistence in the deformed N = 28 region......Page 311
3.2. Neutron halo in light nuclei......Page 316
4. Proton-rich nuclei and the proton drip-line......Page 319
5. Relativistic Random Phase Approximation......Page 325
5.1. Isovector dipole response in nuclei with a large neutron excess......Page 326
References......Page 333
1. Introduction......Page 336
2. The framework......Page 337
3. Parameter adjustment and predictive power......Page 344
4. Superheavy nuclei......Page 349
References......Page 352
II. NUCLEAR MULTIFRAGMENTATION AND EQUATION OF STATE......Page 354
1. Introduction......Page 356
2. Isospin effects on Deep-Inelastic Collisions......Page 357
3. Isospin Dynamics in Neck Fragmentation at Fermi Energies......Page 359
4. Effective Mass Splitting and Collective Flows......Page 360
5. Relativistic Collisions......Page 363
6. Isospin effects on sub-threshold kaon production at intermediate energies......Page 364
7. Testing Deconfinement at High Isospin Density......Page 368
References......Page 371
1.1. What is (nuclear) multifragmentation?......Page 374
2. Microcanonical Multifragmentation Model (MMM)......Page 375
3.2. Liquid-gas phase transitions in nuclear matter......Page 376
4.1. Preliminaries......Page 379
4.2. Method......Page 381
4.4. Consistency checking......Page 384
4.5. Remarks......Page 387
References......Page 388
1. Introduction......Page 390
2.1. Thermodynamical approach......Page 391
2.2. Asymmetric nuclear matter case......Page 395
3.1. The linear response......Page 397
3.2. Spinodal decomposition: Numerical simulations......Page 399
4.1. Multifrrrgmentation......Page 400
4.2. Neck frcrgrnentation......Page 402
5. Conclusions......Page 405
References......Page 406
1. Phase properties of supernovae and neutron stars......Page 408
1.1. Nuclear matter versus stellar matter......Page 409
1.2. Instabilities in stellar matter......Page 410
1.2.1. Finite wavelength fluctuations......Page 411
1.2.2. Beta-equilibrium and phase structure......Page 412
1.3.2. Ising analogue to stellar matter......Page 413
2. Thermodynamics of finite nuclei......Page 416
2.1. An information theory approach......Page 417
2.2. Ensemble inequivalence......Page 418
2.3. Continuum states and boundary conditions......Page 419
2.4. Time dependent statistical ensembles......Page 420
2.5. The dynamics of the expansion......Page 421
3. Phase transitions in finite systems and applications in nuclear physics......Page 424
3.2. Bimodalities and the Yang-Lee theorem......Page 425
3.3. Phase transition versus channel opening......Page 426
3.4. Bimodalities in fragmentation distributions......Page 427
3.5. TJae efleet of constraints......Page 428
3.6. Getting rid of the effect of constraints......Page 430
4. Conclusion......Page 432
References......Page 433
1. Light-ion induced reactions......Page 435
1.1. ISiS Experimental program......Page 436
1.2. Charge Distributions......Page 437
1.3. Timescale of fragment emission......Page 439
1.4. Indications of a Phase Transition......Page 440
1.5. Breakup density......Page 441
2. Symmetry Energy of the Nuclear Equation-of-State.......Page 443
2.1. Isoscaling......Page 444
2.2. Experimental Details of NiFe data......Page 445
2.3. Tsoscaling of Intermediate Mass Fragments......Page 446
2.4. Production of Neutron-rich Nuclei by DIC Collisions......Page 449
4. Acknowledgements:......Page 451
References......Page 452
1. Introduction......Page 453
2. The Nuclear Equation-of-State......Page 455
3. Transport Descriptions of Heavy Ion Collisions......Page 459
4. The EOS at High Density......Page 464
5. Low Density EOS and Dynamical Fragmentation......Page 467
6. Summary......Page 472
References......Page 473
1. Introduction......Page 475
2. The EOS from ab inito calculations......Page 476
2.1. EOS in symmetric and asymmetric nuclear matter......Page 479
2.1.1. Effective nucleon masses......Page 482
2.1.3. Optical potentials......Page 484
2.2. Probing the EOS by kaon production in heavy ion reactions......Page 486
2.3. Constmints from neutron stars......Page 488
3. Summary......Page 489
References......Page 490
III. ALPHA DECAY, NUCLEAR REACTIONS, COLD FISSION AND NUCLEAR FUSION......Page 494
1. Introduction......Page 496
2. The dinuclear system model......Page 497
3. Normal- and superdeformed bands......Page 498
4. Hyperdeformed states in heavy ion collisions......Page 500
5. Rotation modes in the dinuclear model......Page 502
6. Rotation modes and the structure of 238U......Page 503
7. Dynamics of fusion in the dinuclear system model......Page 506
7.1. Models with adiabatic and diabatic potentials......Page 507
7.2. Evapomtion residue cross section......Page 508
7.3. Isotopic dependence of production cross section......Page 509
8. Quasifission as signature for mass transfer......Page 510
Acknowledgements......Page 512
References......Page 513
1. Introduction......Page 514
2. Theoretical background......Page 515
3. Numerical application......Page 517
4. Conclusions......Page 529
References......Page 531
Hindrance in Deep Sub-Barrier Fusion Reactions 8. Migicu and H. Esbensen......Page 532
1. Introduction......Page 533
2. Coupled-Channels Approach......Page 534
3.1. Cross-Sections......Page 538
3.2. S-factors......Page 540
3.4. Average spin for fusion......Page 541
4.1. Anti-resonance......Page 544
4.2. Correlation between the pocket energy and E,......Page 546
5. Conclusions......Page 547
Acknowledgements......Page 548
References......Page 549
1. Introduction......Page 550
2.1. Double-Folding real potential......Page 553
2.2. The semi-microscopic and regional optical potentials......Page 557
3. (a,ao) semi-microscopic and phenomenological analyses......Page 558
4. Total a-reaction and (a,n) cross sections......Page 560
5. a-particle emission cross section analysis......Page 561
References......Page 565
1. Introduction......Page 568
2. Nuclear surface localization of the first N N collision......Page 570
3. The average energy-dependent partial-level density......Page 575
4. Systematic analysis of PE surface effects......Page 578
5. Conclusions......Page 582
References......Page 583
1. Introduction......Page 586
2.1. Single channel. Spherical system......Page 587
2.2 . Coupled channels. Deformed system......Page 588
3. Model estimates for the a- cluster formation amplitude......Page 590
5. The Element 118 and its a-descendants......Page 591
6. Concluding remarks......Page 593
References......Page 595
IV. DARK MATTER, DOUBLE BETA DECAY, AND POSSIBLE MECHANISMS FOR DILEPTON PRODUCTION......Page 596
1. Introduction......Page 598
2.1.1. The Z-exchange contribution......Page 602
2.1.3. The Intermediate Higgs Contribution......Page 603
2.2.1. The Kaluza-Klein Boson as a dark matter candidate......Page 604
3. Going from the Quark to the Nucleon Level......Page 606
4. The allowed SUSY Parameter Space......Page 607
5. Event rates......Page 608
6. The WIMP velocity distribution......Page 609
7. The Direct detection rate......Page 610
8. Bounds on the scalar proton cross section......Page 611
9. Transitions to excited states......Page 612
10. Other non recoil experiments......Page 613
References......Page 614
1. Introduction......Page 617
2. Nuclear Matrix Elements for Double Beta Decay......Page 618
3. Beta Decay as a Probe of Virtual Transitions......Page 622
4. Muon Capture as a Probe of Virtual Transitions......Page 623
5. Nuclear Matrix Elements for Dark-Matter Detection......Page 626
6. Summary and conclusions......Page 630
References......Page 631
1. Introduction......Page 633
2.1. Radiation damping......Page 634
2.3. Collision broadening......Page 635
3 . Nucleon resonances in nuclei......Page 638
4. In-medium properties of vector mesons: Theoretical models......Page 640
5. In-medium properties of vector mesons: Experiments on dilepton production......Page 641
6.1. Dilepton modes in decays of light unflavored mesons......Page 642
6.2. Dilepton modes in decays of nucleon resonances......Page 643
7. Microscopic eVMD model......Page 644
8. How to keep photon massless with po - w - y mixing?......Page 645
9.1. A constraint to w-meson collision width from DLS and HADES data......Page 646
9.2. Evidence for decoherence in transition form factors of nucleon resonances from DLS and HADES data......Page 647
10. Conclusions......Page 648
References......Page 649
1. Introduction......Page 651
2. Preliminaries......Page 652
3. The SU(n) @ U(1) gauge models with mHm......Page 654
4. Three-generation SU(3) @ U(1), model......Page 659
5. Concluding remarks......Page 662
References......Page 663
V. THEORETICAL AND EXPERIMENTAL RESULTS ON THE PROTON STRUCTURE......Page 666
1. Introduction......Page 668
2. The observables of lepton-hadron scattering......Page 669
3. Elastic lepton-hadron scattering......Page 670
4. Deep inelastic scattering and the naive parton model......Page 671
5. Quantum Chromodynamics and the improved quark-parton model......Page 672
6. The HERA project......Page 675
7. Proton structure measurements at HERA......Page 677
8. Structure functions measurements: F2, FL and zF3......Page 680
9. Parton distribution functions and electroweak effects......Page 682
10. Exclusive measurements at HERA......Page 684
11. e*p collision with a polarised lepton beam......Page 685
12. Study of the nucleon spin in polarised ep collisions......Page 686
13. Outlook......Page 687
References......Page 688