This book offers a comprehensive survey of basic elements of nuclear dynamics at low energies and discusses similarities to mesoscopic systems. It addresses systems with finite excitations of their internal degrees of freedom, so that their collective motion exhibits features typical for transport processes in small and isolated systems. The importance of quantum aspects is examined with respect to both the microscopic damping mechanism and the nature of the transport equations. The latter must account for the fact that the collective motion is self-sustained. This implies highly nonlinear couplings between internal and collective degrees of freedom --- different to assumptions made in treatments known in the literature. A critical discussion of the use of thermal concepts is presented. The book can be considered self-contained. It presents existing models, theories and theoretical tools, both from nuclear physics and other fields, which are relevant to an understanding of the observed physical phenomena.
Author(s): Helmut Hofmann
Year: 2008
Language: English
Pages: 644
Contents......Page 12
I: BASIC ELEMENTS AND MODELS......Page 22
1.1 The force between two nucleons......Page 24
1.2 The model of the Fermi gas......Page 28
1.3 Basic properties of finite nuclei......Page 35
2.1 A first, qualitative survey......Page 51
2.2 The independent pair approximation......Page 57
2.3 Brueckner–Hartree–Fock approximation (BHF)......Page 65
2.4 A variational approach based on generalized Jastrow functions......Page 69
2.5 Effective interactions of Skyrme type......Page 73
2.6 The nuclear equation of state (EOS)......Page 76
2.7 Transport phenomena in the Fermi liquid......Page 82
3.1 Hartree–Fock with effective forces......Page 88
3.2 Phenomenological single particle potentials......Page 91
3.3 Excitations of the many-body system......Page 99
4.1 Shell model with residual interactions......Page 106
4.2 Random Matrix Model......Page 108
4.3 The spreading of states into more complicated configurations......Page 114
5 Shell effects and Strutinsky renormalization......Page 125
5.1 Physical background......Page 127
5.2 The Strutinsky procedure......Page 130
5.3 The static energy of finite nuclei......Page 136
5.4 An excursion into periodic-orbit theory (POT)......Page 140
5.5 The total energy at finite temperature......Page 143
6 Average collective motion of small amplitude......Page 149
6.1 Equation of motion from energy conservation......Page 150
6.2 The collective response function......Page 155
6.3 Rotations as degenerate vibrations......Page 164
6.4 Microscopic origin of macroscopic damping......Page 166
6.5 Damped collective motion at thermal excitations......Page 175
6.6 Temperature dependence of nuclear transport......Page 187
6.7 Rotations at finite thermal excitations......Page 206
7 Transport theory of nuclear collective motion......Page 211
7.1 The locally harmonic approximation......Page 212
7.2 Equilibrium fluctuations of the local oscillator......Page 215
7.3 Fluctuations of the local propagators......Page 217
7.4 Fokker–Planck equations for the damped harmonic oscillator......Page 224
7.5 Quantum features of collective transport from the microscopic point of view......Page 230
II: COMPLEX NUCLEAR SYSTEMS......Page 244
8.1 Decay of the compound nucleus by particle emission......Page 246
8.2 Fission......Page 250
9 Pre-equilibrium reactions......Page 256
9.1 An illustrative, realistic prototype......Page 257
9.2 A sketch of existing theories......Page 263
10.1 Darwin–Fowler approach for theoretical models......Page 267
10.2 Empirical level densities......Page 275
10.3 Nuclear thermometry......Page 278
11.1 Global transport equations......Page 283
11.2 Transport coefficients for large-scale motion......Page 291
12.1 Transitions between potential wells......Page 301
12.2 The rate formulas of Kramers and Langer......Page 304
12.3 Escape time for strongly damped motion......Page 309
12.4 A critical discussion of timescales......Page 312
12.5 Inclusion of quantum effects......Page 320
13 Heavy-ion collisions at low energies......Page 329
13.1 Transport models for heavy-ion collisions......Page 330
13.2 Differential cross sections......Page 338
13.3 Fusion reactions......Page 340
13.4 Critical remarks on theoretical approaches and their assumptions......Page 347
14.1 Absorption and radiation of the classical dipole......Page 351
14.2 Nuclear dipole modes......Page 353
III: MESOSCOPIC SYSTEMS......Page 360
15.1 Electronic transport in metals......Page 362
15.2 Quantum wires......Page 365
16.1 Structure of metal clusters......Page 371
16.2 Optical properties......Page 372
17.1 Forced energy transfer within the wall picture......Page 382
17.2 Wall friction by Strutinsky smoothing......Page 387
IV: THEORETICAL TOOLS......Page 392
18.1 Potential scattering......Page 394
18.2 Generalization to nuclear reactions......Page 403
18.3 Energy averaged amplitudes......Page 411
18.4 Statistical theory......Page 416
19.1 The many-body system......Page 427
19.2 Many-body functions from one-body functions......Page 431
19.3 The Wigner transformation......Page 433
20.1 Hartree–Fock with density operators......Page 441
20.2 Hartree–Fock at finite temperature......Page 445
21.1 The Wigner transform of the von Neumann equation......Page 447
21.2 Collision terms in semi-classical approximations......Page 449
21.3 Relaxation to equilibrium......Page 453
22.1 Elements of statistical mechanics......Page 458
22.2 Level densities and energy distributions......Page 471
22.3 Uncertainty of temperature for isolated systems......Page 482
22.4 The lack of extensivity and negative specific heats......Page 485
22.5 Thermostatics of independent particles......Page 487
23.1 The model of the damped oscillator......Page 496
23.2 A brief reminder of perturbation theory......Page 499
23.3 General properties of response functions......Page 503
23.4 Correlation functions and the fluctuation dissipation theorem......Page 510
23.5 Linear response at complex frequencies......Page 517
23.6 Susceptibilities and the static response......Page 522
23.7 Linear irreversible processes......Page 528
23.8 Kubo formula for transport coefficients......Page 539
24.1 Path integrals in quantum mechanics......Page 543
24.2 Path integrals for statistical mechanics......Page 553
24.3 Green functions and level densities......Page 560
24.4 Functional integrals for many-body systems......Page 564
25.1 The Brownian particle, a heuristic approach......Page 575
25.2 General properties of stochastic processes......Page 581
25.3 Non-linear equations in one dimension......Page 591
25.4 The mean first passage time......Page 594
25.5 The multidimensional Kramers equation......Page 596
25.6 Microscopic approach to transport problems......Page 601
V: AUXILIARY INFORMATION......Page 608
26.1 Gaussian integrals......Page 610
26.2 Stationary phase and steepest decent......Page 611
26.4 Fourier and Laplace transformations......Page 612
26.6 The Mori product......Page 613
26.7 Spin and isospin......Page 614
26.8 Second quantization for fermions......Page 615
27 Natural units in nuclear physics......Page 617
References......Page 618
C......Page 636
E......Page 637
H......Page 638
L......Page 639
P......Page 640
R......Page 641
S......Page 642
V......Page 643
Z......Page 644
