Verfügbarkeit: The physics of warm nuclei | Technische Universität München

The physics of warm nuclei: with analogies to mesoscopic systems

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Bibliographische Detailangaben
Beteilige Person:	Hofmann, Helmut (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Oxford [u.a.] Oxford Univ. Press 2008
Ausgabe:	1. publ.
Schriftenreihe:	Oxford studies in nuclear physics 25
Schlagwörter:	Mesoscopic phenomena (Physics) Nuclear physics Modell Kernphysik Mesoskopisches System Nichtgleichgewichtsstatistik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016391008&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XIX, 623 S.
ISBN:	9780198504016 0198504012

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Datensatz im Suchindex

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adam_text	CONTENTS I BASIC ELEMENTS AND MODELS Elementary concepts of nuclear physics 3 1.1 The force between two nucléons 3 1.1.1 Possible forms of the interaction 4 1.1.2 The radial dependence of the interaction 5 1.1.3 The role of sub-nuclear degrees of freedom 6 1.2 The model of the Fermi gas 7 1.2.1 Many-body properties in the ground state 9 1.2.2 Two-body correlations in a homogeneous system 11 1.3 Basic properties of finite nuclei 14 1.3.1 The interaction of nucléons with nuclei 14 1.3.2 The optical model 19 1.3.3 The liquid drop model 23 Nuclear matter as a Fermi liquid 30 2.1 A first, qualitative survey 30 2.1.1 The inadequacy of Hartree-Fock with bare interactions 30 2.1.2 Short-range correlations 32 2.1.3 Properties of nuclear matter in chiral dynamics 34 2.1.4 How dense is nuclear matter? 35 2.2 The independent pair approximation 36 2.2.1 The equation for the one-body wave functions 36 2.2.2 The total energy in terms of two-body wave functions 37 2.2.3 The Bethe-Goldstone equation 38 2.2.4 The G-matrix 42 2.3 Brueckner-Hartree-Fock approximation (BHF) 44 2.3.1 BHF at finite temperature 48 2.4 A variational approach based on generalized Jastrow func¬ tions 48 2.4.1 Extension to finite temperature 50 2.5 Effective interactions of Skyrme type 52 2.5.1 Expansion to small relative momenta 52 2.6 The nuclear equation of state (EOS) 55 2.6.1 An energy functional with three-body forces 55 2.6.2 The EOS with Skyrme interactions 56 2.6.3 Applications in astrophysics 59 2.7 Transport phenomena in the Fermi liquid 61 2.7.1 Semi-classical transport equations 62 Contents Independent particles and quasiparticles in finite nuclei 67 3.1 Hartree-Fock with effective forces 67 3.1.1 Н -F with the Skyrme interaction 67 3.1.2 Constrained Hartree-Fock 68 3.1.3 Other effective interactions 69 3.2 Phenomenological single particle potentials 70 3.2.1 The spherical case 70 3.2.2 The deformed single particle model 73 3.3 Excitations of the many-body system 78 3.3.1 The concept of particle-hole excitations 78 3.3.2 Pair correlations 79 From the shell model to the compound nucleus 85 4.1 Shell model with residual interactions 85 4.1.1 Nearest level spacing 86 4.2 Random Matrix Model 87 4.2.1 Gaussian ensembles of real symmetric matrices 87 4.2.2 Eigenvalues, level spacings and eigenvectors 89 4.2.3 Comments on the RMM 91 4.3 The spreading of states into more complicated configurations 93 4.3.1 A schematic model 94 4.3.2 Strength functions 95 4.3.3 Time-dependent description 98 4.3.4 Spectral functions for single particle motion 99 Shell effects and Strutinsky renormalization 104 5.1 Physical background 106 5.1.1 The independent particle picture, once more 107 5.1.2 The Strutinsky energy theorem 108 5.2 The Strutinsky procedure 109 5.2.1 Formal aspects of smoothing 109 5.2.2 Shell correction to level density and ground state en¬ ergy 110 5.2.3 Further averaging procedures 113 5.3 The static energy of finite nuclei 115 5.4 An excursion into periodic-orbit theory (POT) 119 5.5 The total energy at finite temperature 122 5.5.1 The smooth part of the energy at small excitations 123 5.5.2 Contributions from the oscillating level density 124 Average collective motion of small amplitude 128 6.1 Equation of motion from energy conservation 129 6.1.1 Induced forces for harmonic motion 129 6.1.2 Equation of motion 131 6.1.3 One-particle one-hole excitations 133 Contents xiii 6.2 The collective response function 134 6.2.1 Collective response and sum rules for stable systems 137 6.2.2 Generalization to several dimensions 139 6.2.3 Mean field approximation for an effective two-body in¬ teraction 141 6.2.4 Isovector modes 143 6.3 Rotations as degenerate vibrations 143 6.4 Microscopic origin of macroscopic damping 145 6.4.1 Irreversibility through energy smearing 146 6.4.2 Relaxation in a Random Matrix Model 150 6.4.3 The effects of collisions on nucleonic motion 150 6.5 Damped collective motion at thermal excitations 154 6.5.1 The equation of motion at finite thermal excitations 154 6.5.2 The strict Markov limit 157 6.5.3 The collective response for quasi-static processes 160 6.5.4 An analytically solvable model 164 6.6 Temperature dependence of nuclear transport 166 6.6.1 The collective strength distribution at finite Τ 166 6.6.2 Diabatic models 171 6.6.3 Т -dependence of transport coefficients 177 6.7 Rotations at finite thermal excitations 185 Transport theory of nuclear collective motion 190 7.1 The locally harmonic approximation 191 7.2 Equilibrium fluctuations of the local oscillator 194 7.3 Fluctuations of the local propagators 196 7.3.1 Quantal diffusion coefficients from the FDT 200 7.4 Fokker-Planck equations for the damped harmonic oscillator 203 7.4.1 Stationary solutions for oscillators 203 7.4.2 Dynamics of fluctuations for stable modes 206 7.4.3 The time-dependent solutions for unstable modes and their physical interpretation 207 7.5 Quantum features of collective transport from the microscopic point of view 209 7.5.1 Quantized Hamiltonians for collective motion 210 7.5.2 A non-perturbative Nakajima-Zwanzig approach 217 II COMPLEX NUCLEAR SYSTEMS The statistical model for the decay of excited nuclei 225 8.1 Decay of the compound nucleus by particle emission 225 8.1.1 Transition rates 225 8.1.2 Evaporation rates for light particles 228 8.2 Fission 229 8.2.1 The Bohr-Wheeler formula 229 xiv Contents 8.2.2 Stability conditions in the macroscopic limit 232 9 Pre-equilibrium reactions 235 9.1 An illustrative, realistic prototype 236 9.2 A sketch of existing theories 242 9.2.1 Comments 244 10 Level densities and nuclear thermometry 246 10.1 Darwin-Fowler approach for theoretical models 246 10.1.1 Level densities and Strutinsky renormalization 247 10.1.2 Dependence on angular momentum 251 10.1.3 Microscopic models with residual interactions 252 10.2 Empirical level densities 254 10.3 Nuclear thermometry 257 11 Large-scale collective motion at finite thermal excitations 262 11.1 Global transport equations 262 11.1.1 Fokker-Planck equations 262 11.1.2 Over-damped motion 265 11.1.3 Langevin equations 267 11.1.4 Probability distribution for collective variables 269 11.2 Transport coefficients for large-scale motion 270 11.2.1 The LHA at level crossings and avoided crossings 275 11.2.2 Thermal aspects of global motion 278 12 Dynamics of fission at finite temperature 280 12.1 Transitions between potential wells 280 12.1.1 Transition rate for over-damped motion 281 12.2 The rate formulas of Kramers and Langer 283 12.3 Escape time for strongly damped motion 288 12.4 A critical discussion of timescales 291 12.4.1 Transient-and saddle-scission times 293 12.4.2 Implications from the concept of the MFPT 296 12.5 Inclusion of quantum effects 299 12.5.1 Quantum decay rates within the LHA 300 12.5.2 Rate formulas for motion treated self-consistently 302 12.5.3 Quantum effects in collective transport, a true chal¬ lenge 307 13 Heavy-ion collisions at low energies 308 13.1 Transport models for heavy-ion collisions 309 13.1.1 Commonly used inputs for transport equations 313 13.2 Differential cross sections 317 13.3 Fusion reactions 319 13.3.1 Micro- and macroscopic formation probabilities 321 Contents xv 13.4 Critical remarks on theoretical approaches and their assump¬ tions 326 14 Giant dipole excitations 330 14.1 Absorption and radiation of the classical dipole 330 14.2 Nuclear dipole modes 332 14.2.1 Extension to quantum mechanics 333 14.2.2 Damping of giant dipole modes 333 III MESOSCOPIC SYSTEMS 15 Metals and quantum wires 341 15.1 Electronic transport in metals 341 15.1.1 The Drude model and basic definitions 341 15.1.2 The transport equation and electronic conductance 342 15.2 Quantum wires 344 15.2.1 Mesoscopic systems in semiconductor heterostructures 344 15.2.2 Two-dimensional electron gas 345 15.2.3 Quantization of conductivity for ballistic transport 346 15.2.4 Physical interpretation and discussion 348 16 Metal clusters 350 16.1 Structure of metal clusters 350 16.2 Optical properties 351 16.2.1 Cross sections for scattering of light 353 16.2.2 Optical properties for the jellium model 354 16.2.3 The infinitely deep square well 355 17 Energy transfer to a system of independent fermions 361 17.1 Forced energy transfer within the wall picture 361 17.1.1 Energy transfer at finite frequency 363 17.1.2 Fermions inside billiards 365 17.2 Wall friction by Strutinsky smoothing 366 IV THEORETICAL TOOLS 18 Elements of reaction theory 373 18.1 Potential scattering 373 18.1.1 The T-matrix 373 18.1.2 Phase shifts for central potentials 379 18.1.3 Inelastic processes 380 18.2 Generalization to nuclear reactions 382 18.2.1 Reaction channels 382 18.2.2 Cross section 383 18.2.3 The Т -matrix for nuclear reactions 384 18.2.4 Isolated resonances 385 xvi Contents 18.2.5 Overlapping resonances 389 18.2.6 Т -matrix with angular momentum coupling 389 18.3 Energy averaged amplitudes 390 18.3.1 The optical model 390 18.3.2 Intermediate structure through doorway resonances 392 18.4 Statistical theory 395 18.4.1 Porter-Thomas distribution for widths 396 18.4.2 Smooth and fluctuating parts of the cross section 396 18.4.3 Hauser-Feshbach theory 401 18.4.4 Critique of the statistical model 403 19 Density operators and Wigner functions 406 19.1 The many-body system 406 19.1.1 Hubert states of the many-body system 406 19.1.2 Density operators and matrices 406 19.1.3 Reduction to one- and two-body densities 408 19.2 Many-body functions from one-body functions 410 19.2.1 One- and two-body densities 411 19.3 The Wigner transformation 412 19.3.1 The Wigner transform in three dimensions 412 19.3.2 Many-body systems of indistinguishable particles 414 19.3.3 Propagation of wave packets 415 19.3.4 Correspondence rules 416 19.3.5 The equilibrium distribution of the oscillator 417 20 The Hartree-Fock approximation 420 20.1 Hartree-Fock with density operators 420 20.1.1 The Hartree-Fock equations 422 20.1.2 The ground state energy in HF-approximation 423 20.2 Hartree-Fock at finite temperature 424 20.2.1 TDHF at finite Τ 425 21 Transport equations for the one-body density 426 21.1 The Wigner transform of the von Neumann equation 426 21.2 Collision terms in semi-classical approximations 428 21.2.1 The collision term in the Born approximation 430 21.2.2 The BUU and the Landau-Vlasov equation 431 21.3 Relaxation to equilibrium 432 21.3.1 Relaxation time approximation to the collision term 434 21.3.2 A few remarks on the concept of self-energies 435 22 Nuclear thermostatics 437 22.1 Elements of statistical mechanics 437 22.1.1 Thermostatics for deformed nuclei 438 22.1.2 Generalized ensembles 443 22.1.3 Extremal properties 448 Contents xvii 22.2 Level densities and energy distributions 450 22.2.1 Composite systems 452 22.2.2 A Gaussian approximation 454 22.2.3 Darwin-Fowler method for the level density 457 22.3 Uncertainty of temperature for isolated systems 461 22.3.1 The physical background 461 22.3.2 The thermal uncertainty relation 463 22.4 The lack of extensivity and negative specific heats 464 22.5 Thermostatics of independent particles 466 22.5.1 Sommerfeld expansion for smooth level densities 469 22.5.2 Thermostatics for oscillating level densities 470 22.5.3 Influence of angular momentum 472 23 Linear response theory 475 23.1 The model of the damped oscillator 475 23.2 A brief reminder of perturbation theory 478 23.2.1 Transition rate in lowest order 480 23.3 General properties of response functions 482 23.3.1 Basic definitions 482 23.3.2 Basic properties 484 23.3.3 Dissipation of energy 486 23.3.4 Spectral representations 487 23.4 Correlation functions and the fluctuation dissipation theorem 489 23.4.1 Basic definitions 489 23.4.2 The fluctuation dissipation theorem 491 23.4.3 Strength functions for periodic perturbations 492 23.4.4 Linear response for a Random Matrix Model 493 23.5 Linear response at complex frequencies 496 23.5.1 Relation to thermal Green functions 497 23.5.2 Response functions for unstable modes 498 23.5.3 Equilibrium fluctuations of the oscillator 499 23.6 Susceptibilities and the static response 501 23.6.1 Static perturbations of the local equilibrium 501 23.6.2 Isothermal and adiabatic susceptibilities 504 23.6.3 Relations to the static response 505 23.7 Linear irreversible processes 507 23.7.1 Relaxation functions 507 23.7.2 Variation of entropy in time 510 23.7.3 Time variation of the density operator 512 23.7.4 Onsager relations for macroscopic motion 515 23.8 Kubo formula for transport coefficients 518 24 Functional integrals 522 24.1 Path integrals in quantum mechanics 522 24.1.1 Time propagation in quantum mechanics 522 Contents 24.1.2 Semi-classical approximation to the propagator 525 24.1.3 The path integral as a functional 531 24.2 Path integrals for statistical mechanics 532 24.2.1 The classical limit of statistical mechanics 535 24.2.2 Quantum corrections 536 24.3 Green functions and level densities 539 24.3.1 Periodic orbit theory 540 24.3.2 The level density for regular and chaotic motion 542 24.4 Functional integrals for many-body systems 543 24.4.1 The Hubbard-Stratonovich transformation 543 24.4.2 The high temperature limit and quantum corrections 546 24.4.3 The perturbed static path approximation (PSPA) 548 25 Properties of Langevin and Fokker-Planck equations 554 25.1 The Brownian particle, a heuristic approach 554 25.1.1 Langevin equation 554 25.1.2 Fokker-Planck equations 557 25.1.3 Cumulant expansion and Gaussian distributions 559 25.2 General properties of stochastic processes 560 25.2.1 Basic concepts 561 25.2.2 Markov processes and the Chapman-Kolmogorov equa¬ tion 562 25.2.3 Fokker-Planck equations from the Kramers Moyal ex¬ pansion 564 25.2.4 The master equation 568 25.3 Non-linear equations in one dimension 570 25.3.1 Transport equations for multiplicative noise 570 25.3.2 Properties of the general Fokker-Planck equation 572 25.4 The mean first passage time 573 25.4.1 Differential equation for the MFPT 574 25.5 The multidimensional Kramers equation 575 25.5.1 Gaussian solutions in curvilinear coordinates 576 25.5.2 Time dependence of first and second moments for the harmonic oscillator 578 25.6 Microscopic approach to transport problems 580 25.6.1 The Nakajima- Zwanzig projection technique 580 25.6.2 Perturbative approach for factorized coupling 582 V AUXILIARY INFORMATION 26 Formal means 589 26.1 Gaussian integrals 589 26.2 Stationary phase and steepest decent 590 26.3 The 5-function 591 26.4 Fourier and Laplace transformations 591 Contents xix 26.5 Derivative of exponential operators 592 26.6 The Mori product 592 26.7 Spin and isospin 593 26.8 Second quantization for fermions 594 27 Natural units in nuclear physics 596 References 597 Index 615
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spellingShingle	Hofmann, Helmut The physics of warm nuclei with analogies to mesoscopic systems Oxford studies in nuclear physics Mesoscopic phenomena (Physics) Nuclear physics Modell (DE-588)4039798-1 gnd Kernphysik (DE-588)4030340-8 gnd Mesoskopisches System (DE-588)4280799-2 gnd Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd
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title	The physics of warm nuclei with analogies to mesoscopic systems
title_auth	The physics of warm nuclei with analogies to mesoscopic systems
title_exact_search	The physics of warm nuclei with analogies to mesoscopic systems
title_full	The physics of warm nuclei with analogies to mesoscopic systems Helmut Hofmann
title_fullStr	The physics of warm nuclei with analogies to mesoscopic systems Helmut Hofmann
title_full_unstemmed	The physics of warm nuclei with analogies to mesoscopic systems Helmut Hofmann
title_short	The physics of warm nuclei
title_sort	the physics of warm nuclei with analogies to mesoscopic systems
title_sub	with analogies to mesoscopic systems
topic	Mesoscopic phenomena (Physics) Nuclear physics Modell (DE-588)4039798-1 gnd Kernphysik (DE-588)4030340-8 gnd Mesoskopisches System (DE-588)4280799-2 gnd Nichtgleichgewichtsstatistik (DE-588)4136220-2 gnd
topic_facet	Mesoscopic phenomena (Physics) Nuclear physics Modell Kernphysik Mesoskopisches System Nichtgleichgewichtsstatistik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016391008&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV001898310
work_keys_str_mv	AT hofmannhelmut thephysicsofwarmnucleiwithanalogiestomesoscopicsystems

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