The nuclear many-body problem

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Hauptverfasser: Ring, Peter 1941- (VerfasserIn), Schuck, Peter (VerfasserIn)
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Sprache:English
Veröffentlicht: Berlin Springer 2004
Ausgabe:1. ed., 3. printing, study ed.
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adam_text PETER RING PETER SCHUCK THE NUCLEAR MANY-BODY PROBLEM WITH 171 FIGURES SPRINGER CONTENTS THE LIQUID DROP MODEL 1.1 INTRODUCTION 1 1.2 THE SEMI-EMPIRICAL MASS FORMULA 2 1.3 DEFORMATION PARAMETERS 5 1.4 SURFACE OSCILLATIONS ABOUT A SPHERICAL SHAPE 9 1.5 ROTATIONS AND VIBRATIONS FOR DEFORMED SHAPES 17 1.5.1 THE BOHR HAMILTONIAN 17 1.5.2 THE AXIALLY SYMMETRIC CASE 22 1.5.3 THE ASYMMETRIC ROTOR 26 1.6 NUCLEAR FISSION 28 1.7 STABILITY OF ROTATING LIQUID DROPS 32 THE SHELL MODEL 36 2.1 INTRODUCTION AND GENERAL CONSIDERATIONS 36 2.2 EXPERIMENTAL EVIDENCE FOR SHELL EFFECTS 37 2.3 THE AVERAGE POTENTIAL OF THE NUCLEUS 38 2.4 SPIN ORBIT COUPLING 42 2.5 THE SHELL MODEL APPROACH TO THE MANY-BODY PROBLEM 45 2.6 SYMMETRY PROPERTIES 50 2.6.1 TRANSLATIONAL SYMMETRY 50 X CONTENTS 2.6.2 ROTATIONAL SYMMETRY 51 2.6.3 THE ISOTOPIC SPIN 53 2.7 COMPARISON WITH EXPERIMENT 56 2.7.1 EXPERIMENTAL EVIDENCE FOR SINGLE-PARTICLE (HOLE) STATES 56 2.7.2 ELECTROMAGNETIC MOMENTS AND TRANSITIONS 60 2.8 DEFORMED SHELL MODEL 65 2.8.1 EXPERIMENTAL EVIDENCE 65 2.8.2 GENERAL DEFORMED POTENTIAL 67 2.8.3 THE ANISOTROPIC HARMONIC OSCILLATOR 68 2.8.4 NILSSON HAMILTONIAN 70 2.8.5 QUANTUM NUMBERS OF THE GROUND STATE IN ODD NUCLEI 78 2.8.6 CALCULATION OF DEFORMATION ENERGIES 79 2.9 SHELL CORRECTIONS TO THE LIQUID DROP MODEL AND THE STRUTINSKI METHOD 83 2.9.1 INTRODUCTION 83 2.9.2 BASIC IDEAS OF THE STRUTINSKI AVERAGING METHOD 84 2.9.3 DETERMINATION OF THE AVERAGE LEVEL DENSITY 86 2.9.4 STRUTINSKI S SHELL CORRECTION ENERGY 89 2.9.5 SHELL CORRECTIONS AND THE HARTREE-FOCK METHOD 92 2.9.6 SOME APPLICATIONS 95 ROTATION AND SINGLE-PARTICLE MOTION % 3.1 INTRODUCTION 96 3.2 GENERAL SURVEY 97 3.2.1 EXPERIMENTAL OBSERVATION OF HIGH SPIN STATES 97 3.2.2 THE STRUCTURE OF THE YRAST LINE 99 3.2.3 PHENOMENOLOGICAL CLASSIFICATION OF THE YRAST BAND 103 3.2.4 THE BACKBENDING PHENOMENON 104 3.3 THE PARTICLE-PLUS-ROTOR MODEL 107 3.3.1 THE CASE OF AXIAL SYMMETRY 109 3.3.2 SOME APPLICATIONS OF THE PARTICLE-PLUS-ROTOR MODEL 119 3.3.3 THE TRIAXIAL PARTICLE-PLUS-ROTOR MODEL 122 3.3.4 ELECTROMAGNETIC PROPERTIES 125 3.4 THE CRANKING MODEL 126 3.4.1 SEMICLASSICAL DERIVATION OF THE CRANKING MODEL 127 3.4.2 THE CRANKING FORMULA 130 3.4.3 THE ROTATING ANISOTROPIC HARMONIC OSCILLATOR 133 3.4.4 THE ROTATING NILSSON SCHEME 137 3.4.5 THE DEFORMATION ENERGY SURFACE AT HIGH ANGULAR MOMENTA 139 CONTENTS XI 3.4.6 ROTATION ABOUT A SYMMETRY AXIS 142 3.4.7 YRAST TRAPS 143 NUCLEAR FORCES 147 4.1 INTRODUCTION 147 4.2 THE BARE NUCLEON-NUCLEON FORCE 149 4.2.1 GENERAL PROPERTIES OF A TWO-BODY FORCE 149 4.2.2 THE STRUCTURE OF THE NUCLEON-NUCLEON INTERACTION 153 4.3 MICROSCOPIC EFFECTIVE INTERACTIONS 156 4.3.1 BRUCKNER S G-MATRIX AND BE THE GOLDSTONE EQUATION 156 4.3.2 EFFECTIVE INTERACTIONS BETWEEN VALENCE NUCLEONS 164 4.3.3 EFFECTIVE INTERACTIONS BETWEEN PARTICLES AND HOLES 170 4.4 PHENOMENOLOGICAL EFFECTIVE INTERACTIONS 172 4.4.1 GENERAL REMARKS 172 4.4.2 SIMPLE CENTRAL FORCES 174 4.4.3 THE SKYRME INTERACTION 175 4.4.4 THE GOGNY INTERACTION 176 4.4.5 THE MIGDAL FORCE 177 4.4.6 THE SURFACE-DELTA INTERACTION (SDI) 179 4.4.7 SEPARABLE FORCES AND MULTIPOLE EXPANSIONS 180 4.4.8 EXPERIMENTALLY DETERMINED EFFECTIVE INTERACTIONS 185 4.5 CONCLUDING REMARKS 187 THE HARTREE-FOCK METHOD 189 5.1 INTRODUCTION 189 5.2 THE GENERAL VARIATIONAL PRINCIPLE 190 5.3 THE DERIVATION OF THE HARTREE-FOCK EQUATION 192 5.3.1 THE CHOICE OF THE SET OF TRIAL WAVE FUNCTIONS 192 5.3.2 THE HARTREE-FOCK ENERGY 194 5.3.3 VARIATION OF THE ENERGY 194 5.3.4 THE HARTREE-FOCK EQUATIONS IN COORDINATE SPACE 1% 5.4 THE HARTREE-FOCK METHOD IN A SIMPLE SOLVABLE MODEL 197 5.5 THE HARTREE-FOCK METHOD AND SYMMETRIES 201 5.6 HARTREE-FOCK WITH DENSITY DEPENDENT FORCES 203 5.6.1 APPROACH WITH MICROSCOPIC EFFECTIVE INTERACTIONS 203 5.6.2 HARTREE-FOCK CALCULATIONS WITH THE SKYRME FORCE 208 5.7 CONCLUDING REMARKS 215 XII CONTENTS 6 PAIRING CORRELATIONS AND SUPERFLUID NUCLEI 217 6.1 INTRODUCTION AND EXPERIMENTAL SURVEY 217 6.2 THE SENIORITY SCHEME 221 6.3 THE BCS MODEL 228 6.3.1 THE WAVE FUNCTION 228 6.3.2 THE BCS EQUATIONS 230 6.3.3 THE SPECIAL CASE OF A PURE PAIRING FORCE 232 6.3.4 BOGOLIUBOV QUASI-PARTICLES*EXCITED STATES AND BLOCKING 234 6.3.5 DISCUSSION OF THE GAP EQUATION 238 6.3.6 SCHEMATIC SOLUTION OF THE GAP EQUATION 240 7 THE GENERALIZED SINGLE-PARTICLE MODEL (HFB THEORY) 244 7.1 INTRODUCTION 244 7.2 THE GENERAL BOGOLIUBOV TRANSFORMATION 245 7.2.1 QUASI-PARTICLE OPERATORS 245 7.2.2 THE QUASI-PARTICLE VACUUM 249 7.2.3 THE DENSITY MATRIX AND THE PAIRING TENSOR 251 7.3 THE HARTREE-FOCK-BOGOLIUBOV EQUATIONS 252 7.3.1 DERIVATION OF THE HFB EQUATION 252 7.3.2 PROPERTIES OF THE HFB EQUATIONS 255 7.3.3 THE GRADIENT METHOD 258 7.4 THE PAIRING-PLUS-QUADRUPOLE MODEL 259 7.5 APPLICATIONS OF THE HFB THEORY FOR GROUND STATE PROPERTIES 262 7.6 CONSTRAINED HARTREE-FOCK THEORY (CHF) 266 7.7 HFB THEORY IN THE ROTATING FRAME (SCC) 271 8 HARMONIC VIBRATIONS 280 8.1 INTRODUCTION 280 8.2 TAMM-DANCOFF METHOD 282 8.2.1 TAMM-DANCOFF SECULAR EQUATION 282 8.2.2 THE SCHEMATIC MODEL 285 8.2.3 PARTICLE-PARTICLE (HOLE-HOLE) TAMM-DANCOFF METHOD 288 8.3 GENERAL CONSIDERATIONS FOR COLLECTIVE MODES 289 8.3.1 VIBRATIONS IN QUANTUM MECHANICS 289 8.3.2 CLASSIFICATION OF COLLECTIVE MODES 290 8.3.3 DISCUSSION OF SOME COLLECTIVE PH- VIBRATIONS 293 8.3.4 ANALOG RESONANCES 297 8.3.5 PAIRING VIBRATIONS 299 8.4 PARTICLE-HOLE THEORY WITH GROUND STATE CORRELATIONS (RPA) 301 CONTENTS XIII 8.4.1 DERIVATION OF THE RPA EQUATIONS 301 8.4.2 STABILITY OF THE RPA 305 8.4.3 NORMALIZATION AND CLOSURE RELATIONS 305 8.4.4 NUMERICAL SOLUTION OF THE RPA EQUATIONS 306 8.4.5 REPRESENTATION BY BOSON OPERATORS 307 8.4.6 CONSTRUCTION OF THE RPA GROUND STATE 310 8.4.7 INVARIANCES AND SPURIOUS SOLUTIONS 311 8.5 LINEAR RESPONSE THEORY 314 8.5.1 DERIVATION OF THE LINEAR RESPONSE EQUATIONS 315 8.5.2 CALCULATION OF EXCITATION PROBABILITIES AND SCHEMATIC MODEL 319 8.5.3 THE STATIC POLARIZABILITY AND THE MOMENT OF INERTIA 321 8.5.4 RPA EQUATIONS IN THE CONTINUUM 322 8.6 APPLICATIONS AND COMPARISON WITH EXPERIMENT 325 8.6.1 PARTICLE-HOLE CALCULATIONS IN A PHENOMENOLOGICAL BASIS 325 8.6.2 PARTICLE-HOLE CALCULATIONS IN A SELF-CONSISTENT BASIS 328 8.7 SUM RULES 330 8.7.1 SUM RULES AS ENERGY WEIGHTED MOMENTS OF THE STRENGTH FUNCTIONS 330 8.7.2 THE 5,-SUM RULE AND THE RPA APPROACH 331 8.7.3 EVALUATION OF THE SUM RULES S,, 5_,, AND S 3 332 8.7.4 SUM RULES AND POLARIZABILITIES 335 8.7.5 CALCULATION OF TRANSITION CURRENTS AND DENSITIES 335 8.8 PARTICLE-PARTICLE RPA 339 8.8.1 THE FORMALISM 339 8.8.2 GROUND STATE CORRELATIONS INDUCED BY PAIRING VIBRATIONS 341 8.9 QUASI-PARTICLE RPA 343 BOSON EXPANSION METHODS 346 9.1 INTRODUCTION 346 9.2 BOSON REPRESENTATIONS IN EVEN-EVEN NUCLEI 348 9.2.1 BOSON REPRESENTATIONS OF THE ANGULAR MOMENTUM OPERATORS 348 9.2.2 CONCEPTS FOR BOSON EXPANSIONS 351 9.2.3 THE BOSON EXPANSION OF BELYAEV AND ZELEVINSKI 354 9.2.4 THE BOSON EXPANSION OF MARUMORI 362 9.2.5 THE BOSON EXPANSION OF DYSON 367 9.2.6 THE MATHEMATICAL BACKGROUND 368 9.2.7 METHODS BASED ON PP-BOSONS 372 XIV CONTENTS. 9.2.8 APPLICATIONS 375 9.3 ODD MASS NUCLEI AND PARTICLE VIBRATION COUPLING 381 9.3.1 BOSON EXPANSION FOR ODD MASS SYSTEMS 382 9.3.2 DERIVATION OF THE PARTICLE VIBRATION COUPLING (BOHR) HAMILTONIAN 383 9.3.3 PARTICLE VIBRATION COUPLING (PERTURBATION THEORY) 385 9.3.4 THE NATURE OF THE PARTICLE VIBRATION COUPLING VERTEX 387 9.3.5 EFFECTIVE CHARGES 389 9.3.6 INTERMEDIATE COUPLING AND DYSON S BOSON EXPANSION 390 9.3.7 OTHER PARTICLE VIBRATION COUPLING CALCULATIONS 395 9.3.8 WEAK COUPLING IN EVEN SYSTEMS 397 10 THE GENERATOR COORDINATE METHOD 398 10.1 INTRODUCTION 398 10.2 THE GENERAL CONCEPT 399 10.2.1 THE GCM ANSATZ FOR THE WAVE FUNCTION 399 10.2.2 THE DETERMINATION OF THE WEIGHT FUNCTION/(A 401 10.2.3 METHODS OF NUMERICAL SOLUTION OF THE HW EQUATION 404 10.3 THE LIPKIN MODEL AS AN EXAMPLE 405 10.4 THE GENERATOR COORDINATE METHOD AND BOSON EXPANSIONS 406 10.5 THE ONE-DIMENSIONAL HARMONIC OSCILLATOR 409 10.6 COMPLEX GENERATOR COORDINATES 411 10.6.1 THE BARGMAN SPACE 411 10.6.2 THE SCHRODINGER EQUATION 413 10.6.3 GAUSSIAN WAVE PACKETS IN THE HARMONIC OSCILLATOR 414 10.6.4 DOUBLE PROJECTION 418 10.7 DERIVATION OF A COLLECTIVE HAMILTONIAN 419 10.7.1 GENERAL CONSIDERATIONS 419 10.7.2 THE SYMMETRIC MOMENT EXPANSION (SME) 420 10.7.3 THE LOCAL APPROXIMATION (LA) 423 10.7.4 THE GAUSSIAN OVERLAP APPROXIMATION (GOAL) 424 10.7.5 THE LIPKIN MODEL 428 10.7.6 THE MULTIDIMENSIONAL CASE 430 10.8 THE CHOICE OF THE COLLECTIVE COORDINATE 430 10.9 APPLICATION.OF THE GENERATOR COORDINATE METHOD FOR BOUND STATES 433 10.9.1 GIANT RESONANCES 433 10.9.2 PAIRING VIBRATIONS 435 CONTENTS XV 11 RESTORATION OF BROKEN SYMMETRIES 438 11.1 INTRODUCTION 438 11.2 SYMMETRY VIOLATION IN THE MEAN FIELD THEORY 441 11.3 TRANSFORMATION TO AN INTRINSIC SYSTEM 451 11.3.1 GENERAL CONCEPTS 451 11.3.2 TRANSLATIONAL MOTION 454 11.3.3 ROTATIONAL MOTION 457 11.4 PROJECTION METHODS 458 11.4.1 PROJECTION OPERATORS 458 11.4.2 PROJECTION BEFORE AND AFTER THE VARIATION 460 11.4.3 PARTICLE NUMBER PROJECTION 463 11.4.4 APPROXIMATE PROJECTION FOR LARGE DEFORMATIONS 466 11.4.5 THE INERTIAL PARAMETERS 470 11.4.6 ANGULAR MOMENTUM PROJECTION 473 11.4.7 THE STRUCTURE OF THE INTRINSIC WAVE FUNCTIONS 482 12 THE TIME DEPENDENT HARTREE-FOCK METHOD (TDHF) 485 12.1 INTRODUCTION 485 12.2 THE FULL TIME-DEPENDENT HARTREE-FOCK THEORY 486 12.2.1 DERIVATION OF THE TDHF EQUATION 486 12.2.2 PROPERTIES OF THE TDHF EQUATION 489 12.2.3 QUASI-STATIC SOLUTIONS 492 12.2.4 GENERAL DISCUSSION OF THE TDHF METHOD 493 12.2.5 AN EXACTLY SOLUBLE MODEL 499 12.2.6 APPLICATIONS OF THE TDHF THEORY 500 12.3 ADIABATIC TIME-DEPENDENT HARTREE-FOCK THEORY (ATDHF) 505 12.3.1 THE ATDHF EQUATIONS 505 12.3.2 THE COLLECTIVE HAMILTONIAN 510 12.3.3 REDUCTION TO A FEW COLLECTIVE COORDINATES 513 12.3.4 THE CHOICE OF THE COLLECTIVE COORDINATES 516 12.3.5 GENERAL DISCUSSION OF THE ATDHF METHODS 519 12.3.6 APPLICATIONS OF THE ATDHF METHOD 521 12.3.7 ADIABATIC PERTURBATION THEORY AND THE CRANKING FORMULA 523 13 SEMICLASSICAL METHODS IN NUCLEAR PHYSICS 527 13.1 INTRODUCTION 527 13.2 THE STATIC CASE 528 13.2.1 THE THOMAS-FERMI THEORY 528 13.2.2 WIGNER-KIRKWOOD A-EXPANSION 534 XVI CONTENTS 13.2.3 PARTIAL RESUMMATION OF THE ^-EXPANSION 545 13.2.4 THE SADDLE POINT METHOD 547 13.2.5 APPLICATION TO A SPERICAL WOODS-SAXON POTENTIAL 549 13.2.6 SEMICLASSICAL TREATMENT OF PAIRING PROPERTIES 550 13.3 THE DYNAMIC CASE 552 13.3.1 THE BOLTZMANN EQUATION 553 13.3.2 FLUID DYNAMIC EQUATIONS FROM THE BOLTZMANN EQUATION 555 13.3.3 APPLICATION OF ORDINARY FLUID DYNAMICS TO NUCLEI 558 13.3.4 VARIATIONAL DERIVATION OF FLUID DYNAMICS 562 13.3.5 MOMENTUM DISTRIBUTION OF THE DENSITY P 0 564 13.3.6 IMPOSED FLUID DYNAMIC MOTION 568 13.3.7 AN ILLUSTRATIVE EXAMPLE 573 APPENDICES A ANGULAR MOMENTUM ALGEBRA IN THE LABORATORY AND THE BODY-FIXED SYSTEM 575 B ELECTROMAGNETIC MOMENTS AND TRANSITIONS 580 B.I THE GENERAL FORM OF THE HAMILTONIAN 580 B.2 STATIC MULTIPOLE MOMENTS 581 B.3 THE MULTIPOLE EXPANSION OF THE RADIATION FIELD 584 B.4 MULTIPOLE TRANSITIONS 587 B.5 SINGLE-PARTICLE MATRIX ELEMENTS IN A SPHERICAL BASIS 591 B.6 TRANSLATIONAL INVARIANCE AND ELECTROMAGNETIC TRANSITIONS 592 B.7 THE CROSS SECTION FOR THE ABSORPTION OF DIPOLE RADIATION 593 SECOND QUANTIZATION 595 C. 1 CREATION AND ANNIHILATION OPERATORS 595 C.2 FIELD OPERATORS IN THE COORDINATE SPACE 598 C.3 REPRESENTATION OF OPERATORS 599 C.4 WICK S THEOREM 601 CONTENTS XVII D DENSITY MATRICES 603 D.I NORMAL DENSITIES 603 D.2 DENSITIES OF SLATER DETERMINANTS 605 D.3 DENSITIES OF BCS AND HFB STATES 608 D.4 THE WIGNER TRANSFORMATION OF THE DENSITY MATRIX 609 THEOREMS CONCERNING PRODUCT WAVE FUNCTIONS 611 E.I THE BLOCH-MESSIAH THEOREM [BM 62] 611 E.2 OPERATORS IN THE QUASI-PARTICLE SPACE 613 E.3 THOULESS THEOREM 615 E.4 THE ONISHI FORMULA 618 E.5 BOGOLIUBOV TRANSFORMATIONS FOR BOSONS 620 MANY-BODY GREEN S FUNCTIONS 623 F.I SINGLE-PARTICLE GREEN S FUNCTION AND DYSON S EQUATION 623 F.2 PERTURBATION THEORY 628 F.3 SKELETON EXPANSION 631 F.4 FACTORIZATION AND BRIICKNER-HARTREE-FOCK 632 F.5 HARTREE-FOCK-BOGOLIUBOV EQUATIONS 634 F.6 THE BETHE-SALPETER EQUATION AND EFFECTIVE FORCES 640 BIBLIOGRAPHY 643 AUTHOR INDEX 681 SUBJECT INDEX 699
any_adam_object 1
author Ring, Peter 1941-
Schuck, Peter
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author_facet Ring, Peter 1941-
Schuck, Peter
author_role aut
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edition 1. ed., 3. printing, study ed.
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physical XVII, 716 S. graph. Darst.
publishDate 2004
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publishDateSort 2004
publisher Springer
record_format marc
series2 Texts and monographs in physics
spelling Ring, Peter 1941- Verfasser (DE-588)13140850X aut
The nuclear many-body problem Peter Ring ; Peter Schuck
1. ed., 3. printing, study ed.
Berlin Springer 2004
XVII, 716 S. graph. Darst.
txt rdacontent
n rdamedia
nc rdacarrier
Texts and monographs in physics
Literaturverz. S. 643 - 679
Atomkern - Vielkörperproblem
Vielkörperproblem (DE-588)4078900-7 gnd rswk-swf
Kerntheorie (DE-588)4163643-0 gnd rswk-swf
Atomkern (DE-588)4068924-4 gnd rswk-swf
Kernphysik (DE-588)4030340-8 gnd rswk-swf
Atomkern (DE-588)4068924-4 s
Vielkörperproblem (DE-588)4078900-7 s
DE-604
Kerntheorie (DE-588)4163643-0 s
Kernphysik (DE-588)4030340-8 s
1\p DE-604
Schuck, Peter Verfasser aut
HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012918369&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle Ring, Peter 1941-
Schuck, Peter
The nuclear many-body problem
Atomkern - Vielkörperproblem
Vielkörperproblem (DE-588)4078900-7 gnd
Kerntheorie (DE-588)4163643-0 gnd
Atomkern (DE-588)4068924-4 gnd
Kernphysik (DE-588)4030340-8 gnd
subject_GND (DE-588)4078900-7
(DE-588)4163643-0
(DE-588)4068924-4
(DE-588)4030340-8
title The nuclear many-body problem
title_auth The nuclear many-body problem
title_exact_search The nuclear many-body problem
title_full The nuclear many-body problem Peter Ring ; Peter Schuck
title_fullStr The nuclear many-body problem Peter Ring ; Peter Schuck
title_full_unstemmed The nuclear many-body problem Peter Ring ; Peter Schuck
title_short The nuclear many-body problem
title_sort the nuclear many body problem
topic Atomkern - Vielkörperproblem
Vielkörperproblem (DE-588)4078900-7 gnd
Kerntheorie (DE-588)4163643-0 gnd
Atomkern (DE-588)4068924-4 gnd
Kernphysik (DE-588)4030340-8 gnd
topic_facet Atomkern - Vielkörperproblem
Vielkörperproblem
Kerntheorie
Atomkern
Kernphysik
url http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012918369&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv AT ringpeter thenuclearmanybodyproblem
AT schuckpeter thenuclearmanybodyproblem