From nucleons to nucleus: concepts of microscopic nuclear theory
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| Language: | English |
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Berlin [u.a.]
Springer
2007
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| Series: | Theoretical and mathematical physics
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| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXI, 645 S. Ill., graph. Darst. |
| ISBN: | 9783540488590 3540488596 |
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| 100 | 1 | |a Suhonen, Jouni |e Verfasser |0 (DE-588)133087557 |4 aut | |
| 245 | 1 | 0 | |a From nucleons to nucleus |b concepts of microscopic nuclear theory |c Jouni Suhonen |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a XXI, 645 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Theoretical and mathematical physics | |
| 650 | 4 | |a Structure nucléaire | |
| 650 | 4 | |a Nuclear structure | |
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Contents
Part I Particles and Holes
1 Angular Momentum Coupling 3
1.1 Clebsch Gordan Coefficients and 3j Symbols 3
1.2 More on Clebsch Gordan Coefficients; 3j Symbols 7
1.2.1 Clebsch Gordan Coefficients 8
1.2.2 More Symmetry: 3j Symbols 9
1.2.3 Relations for 3j Symbols 10
1.3 The 6j Symbol 11
1.3.1 Symmetry Properties of the 6j Symbol 13
1.3.2 Relations for 6j Symbols 14
1.3.3 Explicit Expressions for 6j Symbols 14
1.4 The 9? Symbol 15
1.4.1 Symmetry Properties of the 9j Symbol 17
1.4.2 Relations for 9j Symbols 18
Exercises 19
2 Tensor Operators and the Wigner Eckart Theorem 23
2.1 Spherical Tensor Operators 23
2.1.1 Rotations of the Coordinate Axes 23
2.1.2 Wigner D Functions and Spherical Tensors 25
2.1.3 Contravariant and Covariant Components
of Spherical Tensors 27
2.2 The Wigner Eckart Theorem 29
2.2.1 Immediate Consequences of the Wigner Eckart Theorem 29
2.2.2 Pauli Spin Matrices 31
2.3 Matrix Elements of Coupled Tensor Operators 32
2.3.1 Theorem I 33
2.3.2 Theorem II 34
Exercises 35
XII Contents
3 The Nuclear Mean Field and Many Nucleon Configurations 39
3.1 The Nuclear Mean Field 39
3.1.1 The Mean Field Approximation 40
3.1.2 Phenomenological Potentials 44
3.1.3 The Spin Orbit Interaction 44
3.2 Woods Saxon Wave Functions 45
3.2.1 Harmonic Oscillator Wave Functions 48
3.2.2 Diagonalization of the Woods Saxon Hamiltonian 50
3.3 Many Nucleon Configurations 54
Exercises 60
4 Occupation Number Representation 63
4.1 Occupation Number Representation of Many Nucleon States . . 63
4.1.1 Fock Space: Particle Creation and Annihilation 64
4.1.2 Further Properties of Creation
and Annihilation Operators 66
4.2 Operators and Their Matrix Elements 67
4.2.1 Occupation Number Representation
of One Body Operators 67
4.2.2 Matrix Elements of One Body Operators 68
4.2.3 Occupation Number Representation
of Two Body Operators 69
4.3 Evaluation of Many Nucleon Matrix Elements 70
4.3.1 Normal Ordering 70
4.3.2 Contractions 71
4.3.3 Wick's Theorem 72
4.4 Particle Hole Representation 74
4.4.1 Properties of Particle and Hole Operators 75
4.4.2 Particle Hole Representation of Operators
and Excitations 77
4.5 Hartree Fock Equation from Wick's Theorem 78
4.5.1 Derivation of the Hartree Fock Equation 78
4.5.2 Residual Interaction; Ground State Energy 80
4.6 Hartree Fock Eigenvalue Problem 81
Exercises 83
5 The Mean Field Shell Model 87
5.1 Valence Space 87
5.2 One Particle and One Hole Nuclei 89
5.2.1 Examples of One Particle Nuclei 89
5.2.2 Examples of One Hole Nuclei 91
5.3 Two Particle and Two Hole Nuclei 93
5.3.1 Examples of Two Particle Nuclei 93
5.3.2 Examples of Two Hole Nuclei 97
5.4 Particle Hole Nuclei 99
Contents XIII
5.5 Isospin Representation of Few Nucleon Systems 105
5.5.1 General Isospin Formalism 105
5.5.2 Tensor Operators in Isospin Representation 107
5.5.3 Isospin Representation of Two Particle
and Two Hole Nuclei 109
5.5.4 Isospin Representation of Particle Hole Nuclei 112
Exercises 114
6 Electromagnetic Multipole Moments
and Transitions 117
6.1 General Properties of Electromagnetic Observables 117
6.1.1 Transition Probability and Half Life 118
6.1.2 Selection Rules for Electromagnetic Transitions 121
6.1.3 Single Particle Matrix Elements
of the Multipole Operators 122
6.1.4 Properties of the Radial Integrals 124
6.1.5 Tables of Numerical Values of Single Particle Matrix
Elements 127
6.1.6 Electromagnetic Multipole Moments 128
6.1.7 Weisskopf Units and Transition Rates 130
6.2 Electromagnetic Transitions in One Particle
and One Hole Nuclei 132
6.2.1 Reduced Transition Probabilities 132
6.2.2 Example: Transitions in One Hole Nuclei 15N and 15O . 134
6.2.3 Magnetic Dipole Moments: Schmidt Lines 136
6.3 Electromagnetic Transitions in Two Particle
and Two Hole Nuclei 137
6.3.1 Example: Transitions in Two Particle Nuclei 18O
and 18Ne 139
6.4 Electromagnetic Transitions in Particle Hole Nuclei 140
6.4.1 Transitions Involving Charge Conserving Particle
Hole Excitations 141
6.4.2 Example: Doubly Magic Nucleus 16O 143
6.4.3 Transitions Between Charge Changing Particle Hole
Excitations 146
6.4.4 Example: Odd Odd Nucleus 16N 147
6.5 Isoscalar and Isovector Transitions 148
6.5.1 Isospin Decomposition of the Electromagnetic
Decay Operator 148
6.5.2 Example: 3" States in 16O 149
6.5.3 Isospin Selection Rules in Two Particle
and Two Hole Nuclei 150
Exercises 153
XIV Contents
7 Beta Decay 157
7.1 General Properties of Nuclear Beta Decay 157
7.2 Allowed Beta Decay 162
7.2.1 Half Lives, Reduced Transition Probabilities
and ft Values 163
7.2.2 Fermi and Gamow Teller Matrix Elements 165
7.2.3 Phase Space Factors 166
7.2.4 Combined /3+ and Electron Capture Decays 168
7.2.5 Decay Q Values 169
7.2.6 Partial and Total Decay Half Lives; Decay Branchings . 169
7.2.7 Classification of Beta Decays 170
7.3 Beta Decay Transitions in One Particle and One Hole Nuclei. . 171
7.3.1 Matrix Elements and Reduced Transition Probabilities . 171
7.3.2 Application to Beta Decay of 15O; Other Examples 172
7.4 Beta Decay Transitions in Particle Hole Nuclei 174
7.4.1 Beta Decay to and from the Even Even Ground State . 174
7.4.2 Application to Beta Decay of 56Ni 175
7.4.3 Beta Decay Transitions Between Two Particle Hole
States 176
7.4.4 Application to Beta Decay of 16N 178
7.5 Beta Decay Transitions in Two Particle and Two Hole Nuclei . 180
7.5.1 Transition Amplitudes 181
7.5.2 Application to Beta Decay of 6He 183
7.5.3 Application to the Beta Decay Chain
18Ne _ 18F _, 18Q 184
7.5.4 Further Examples: Beta Decay in A = 42
and A = 54 Nuclei 187
7.6 Forbidden Unique Beta Decay 188
7.6.1 General Aspects of First Forbidden Beta Decay 188
7.6.2 First Forbidden Unique Beta Decay 190
7.6.3 Application to First Forbidden Unique Beta Decay
of 16N 192
7.6.4 Higher Forbidden Unique Beta Decay 193
7.6.5 Application to Third Forbidden Unique Beta Decay
of 40K 197
7.6.6 Forbidden Unique Beta Decay in Few Particle
and Few Hole Nuclei 199
7.6.7 Forbidden Non Unique Beta Decays 201
Exercises 202
8 Nuclear Two Body Interaction and Configuration Mixing. . 205
8.1 General Properties of the Nuclear Two Body Interaction 205
8.1.1 Coupled Two Body Interaction Matrix Elements 206
8.1.2 Relations for Coupled Two Body Matrix Elements 209
8.1.3 Different Types of Two Body Interaction 210
Contents XV
8.1.4 Central Forces with Spin and Isospin Dependendence . . 212
8.2 Separable Interactions; the Surface Delta Interaction 213
8.2.1 Multipole Decomposition of a General Separable
Interaction 214
8.2.2 Two Body Matrix Elements of the Surface Delta
Interaction 215
8.3 Configuration Mixing in Two Particle Nuclei 219
8.3.1 Matrix Representation of an Eigenvalue Problem 219
8.3.2 Solving the Eigenenergies of a Two by Two Problem . . . 221
8.3.3 Matrix Elements of the Hamiltonian
in the Two Nucleon Basis 223
8.3.4 Solving the Eigenvalue Problem
for a Two Particle Nucleus 224
8.3.5 Application to A = 6 Nuclei 225
8.3.6 Application to A = 18 Nuclei 228
8.4 Configuration Mixing in Two Hole Nuclei 231
8.4.1 Diagonalization of the Residual Interaction
in a Two Hole Basis 231
8.4.2 Application to A = 14 Nuclei 233
8.4.3 Application to A = 38 Nuclei 234
8.5 Electromagnetic and Beta Decay Transitions in Two Particle. . 236
8.5.1 Transition Amplitudes With Configuration Mixing 236
8.5.2 Application to Beta Decay of 6He 237
8.5.3 Application to E2 Decays in 18O and 18Ne 239
Exercises 240
9 Particle—Hole Excitations and the Tamm DancofF
Approximation 243
9.1 The Tamm Dancoff Approximation 243
9.1.1 Justification of the TDA: Brillouin's Theorem 243
9.1.2 Derivation of Explicit Expressions for the TDA Matrix . 246
9.1.3 Tabulated Values of Particle Hole Matrix Elements 248
9.1.4 TDA as an Eigenvalue Problem: Properties
of the Solutions 251
9.2 TDA for General Separable Forces 253
9.2.1 Schematic Model; Dispersion Equation 253
9.2.2 The Schematic Model for T = 0 and T = 1 256
9.2.3 The Schematic Model with the Surface
Delta Interaction 257
9.2.4 Application to 1~ Excitations in 4He 258
9.3 Excitation Spectra of Doubly Magic Nuclei 260
9.3.1 Block Decomposition of the TDA Matrix 260
9.3.2 Application to 1~ States in 4He 260
9.3.3 Application to Excited States in 16O 262
9.3.4 Further Examples: 40Ca and 48Ca 263
XVI Contents
9.4 Electromagnetic Transitions in Doubly Magic Nuclei 265
9.4.1 Transitions to the Particle Hole Ground State 266
9.4.2 Non Energy Weighted Sum Rule 267
9.4.3 Application to Octupole Transitions in 160 268
9.4.4 Collective Transitions in the TDA 271
9.4.5 Application to Octupole Transitions in 40Ca 272
9.4.6 El Transitions: Isospin Breaking
in the Nuclear Mean Field 274
9.4.7 Transitions Between Two TDA Excitations 277
9.4.8 Application to the 57/ 3^~ Transition in 40Ca 277
9.5 Electric Transitions on the Schematic Model 278
9.5.1 Transition Amplitudes 279
9.5.2 Application to Electric Dipole Transitions in 4He 280
Exercises 282
10 Charge Changing Particle—Hole Excitations
and the pnTDA 287
10.1 The Proton Neutron Tarnm Dancoff Approximation 287
10.1.1 Structure of the pnTDA Matrix 287
10.1.2 Application to |H3 and |Lix 289
10.1.3 Further Examples: States of :fN9 and ^K21 290
10.2 Electromagnetic Transitions in the pnTDA 294
10.2.1 Transition Amplitudes 294
10.2.2 Application to the E2 Transition 0," 2" in ^Ng 294
10.3 Beta Decay Transitions in the pnTDA 296
10.3.1 Transitions to the Particle Hole Vacuum 296
10.3.2 First Forbidden Unique Beta Decay of m7N9 297
10.3.3 Transitions between Particle Hole States 298
10.3.4 Allowed Beta Decay of M N9 to Excited States in ^Og . 299
Exercises 301
11 The Random Phase Approximation 305
11.1 The Equations of Motion Method 305
11.1.1 Derivation of the Equations of Motion 306
11.1.2 Derivation of the Hartree Fock Equations by the EOM. 310
11.2 Sophisticated Particle Hole Theories: The RPA 312
11.2.1 Derivation of the RPA Equations by the EOM 312
11.2.2 Explicit Form of the Correlation Matrix 315
11.2.3 Numerical Tables of Correlation Matrix Elements 317
11.3 Properties of the RPA Solutions 318
11.3.1 RPA Energies and Amplitudes 318
11.3.2 The RPA Ground State 322
11.3.3 RPA One Particle Densities 324
11.4 RPA Solutions of the Schematic Separable Model 327
11.4.1 The RPA Dispersion Equation 327
Contents XVII
11.4.2 Application to 1~ Excitations in 4He 329
11.4.3 The Degenerate Model 331
11.5 RPA Description of Doubly Magic Nuclei 332
11.5.1 Examples of the RPA Matrices 332
11.5.2 Diagonalization of the RPA Supermatrix
by Similarity Transformations 335
11.5.3 Application to 1~ Excitations in 4He Carried Through . 337
11.5.4 The 1~ Excitations of 4He Revisited 340
11.5.5 Further Examples 342
11.6 Electromagnetic Transitions in the RPA Framework 344
11.6.1 Transitions to the RPA Ground State 344
11.6.2 Extreme Collective Model 346
11.6.3 Octupole Decay in 16O 347
11.6.4 The Energy Weighted Sum Rule 349
11.6.5 Sum Rule for the Octupole Transitions in 16O 352
11.6.6 Electric Transitions to the RPA Ground State
on the Schematic Model 353
11.6.7 Electric Dipole Transitions in 4He on the Schematic
Model 354
11.6.8 The Degenerate Model 355
11.6.9 Electromagnetic Transitions Between Two RPA
Excitations 356
11.6.10The E2 Transition 5^ 3^ in 40Ca 359
Exercises 361
Part II Quasiparticles
12 Nucleon Pairing and Seniority 369
12.1 Evidence of Nucleon Pairing 370
12.2 The Pure Pairing Force 372
12.3 Two Particle Spectrum of the Pure Pairing Force 374
12.4 Seniority Model of the Pure Pairing Force 376
12.4.1 Derivation of the Seniority Zero Spectrum 376
12.4.2 Spectra of Seniority One and Seniority Two States . 377
12.4.3 States of Higher Seniority 379
12.4.4 Application of the Seniority Model to 0f7/2 Shell Nuclei 380
12.5 The Two Level Model 381
12.5.1 The Pair Basis 382
12.5.2 Matrix Elements of the Pairing Hamiltonian 383
12.5.3 Application to a Two Particle System 386
12.6 Two Particles in a Valence Space of Many j Shells 387
12.6.1 Dispersion Equation 387
12.6.2 The Three Level Case 388
Exercises 389
XVIII Contents
13 BCS Theory 391
13.1 BCS Quasiparticles and Their Vacuum 391
13.1.1 The BCS Ground State 392
13.1.2 BCS Quasiparticles 393
13.2 Occupation Number Representation
for BCS Quasiparticles 394
13.2.1 Contraction Properties 395
13.2.2 Quasiparticle Representation of the Nuclear
Hamiltonian 395
13.3 Derivation of the BCS Equations 398
13.3.1 BCS as a Constrained Variational Problem 398
13.3.2 The Gap Equation and the Quasiparticle Mean Field . . 400
13.4 Properties of the BCS Solutions 403
13.4.1 Physical Meaning of the Basic Parameters 403
13.4.2 Particle Number and Its Fluctuations 404
13.4.3 Odd Even Effect 406
13.5 Solution of the BCS Equations for Simple Models 406
13.5.1 Single j Shell 407
13.5.2 The Lipkin Model 408
13.5.3 Example: The Lipkin Model for Two j = \ Shells 411
13.5.4 The Two Level Model for Two j = \ Shells 412
Exercises 414
14 Quasiparticle Mean Field: BCS and Beyond 417
14.1 Numerical Solution of the BCS Equations 417
14.1.1 Iterative Numerical Procedure 418
14.1.2 Application to Nuclei in the d s and f p 0gg/2 Shells . . . 420
14.2 Lipkin Nogami BCS Theory 430
14.2.1 The Lipkin Nogami Model Hamiltonian 430
14.2.2 Derivation of the Lipkin Nogami BCS Equations 433
14.3 Lipkin Nogami BCS Theory in Simple Models 436
14.3.1 Single j Shell 436
14.3.2 The Lipkin Model 438
14.3.3 Example: The j = \ Case 441
14.4 The Two Level Model for j = j' = \ 443
14.5 Application of Lipkin Nogami Theory
to Realistic Calculations 445
Exercises 447
15 Transitions in the Quasiparticle Picture 449
15.1 Quasiparticle Representation of a One Body Transition
Operator 449
15.2 Transition Densities for Few Quasiparticle Systems 450
15.2.1 Transitions Between One Quasiparticle States 450
Contents XIX
15.2.2 Transitions Between a Two Quasiparticle State
and the BCS Vacuum 451
15.2.3 Transitions Between Two Quasiparticle States 451
15.3 Transitions in Odd ,4 Nuclei 452
15.3.1 Transition Amplitudes 453
15.3.2 Beta and Gamma Decays in the A = 25 Chain
of Isobars 455
15.3.3 Beta Decays in the A = 63 Chain of Isobars 457
15.4 Transitions Between a Two Quasiparticle State
and the BCS Vacuum 459
15.4.1 Formalism for Transition Amplitudes 459
15.4.2 Beta and Gamma Decays in the A = 30 Chain
of Isobars 463
15.5 Transitions Between Two Quasiparticle States 467
15.5.1 Electromagnetic Transitions 467
15.5.2 Beta Decay Transitions 469
15.5.3 Beta Decay of 30P 472
15.5.4 Magnetic Dipole Decay in 30P 473
Exercises 474
16 Mixing of Two Quasiparticle Configurations 479
16.1 Quasiparticle Representation of the Residual Interaction 479
16.2 Derivation of the Quasiparticle TDA Equation 484
16.3 General Properties of QTDA Solutions 490
16.3.1 Orthogonality 490
16.3.2 Completeness 491
16.4 Excitation Spectra of Open Shell Even Even Nuclei 491
16.4.1 Explicit Form of the QTDA Matrix 492
16.4.2 Excitation Energies of 2+ States in 24Mg 493
16.4.3 Pairing Strength Parameters from Empirical Pairing
Gaps 498
16.4.4 Excitation Spectrum of ^Mg12 501
16.4.5 Excitation Spectra of the Mirror Nuclei fjSi,,; and ^Sur,02
16.4.6 Excitation Spectrum of 66Zn 503
16.5 Electromagnetic Transitions to the Ground State 506
16.5.1 Decay Amplitude 506
16.5.2 E2 Decay of the Lowest 2+ State in 2JMg 507
16.5.3 Collective States and Electric Transitions 509
16.6 QTDA Sum Rule for Electromagnetic Transitions 513
16.6.1 Formalism 513
16.6.2 Examples of the NEWSR in the Od ls and 0f lp 0g9/2
Shells 514
16.7 Transitions Between QTDA Excited States 515
16.7.1 Transition Amplitudes 515
16.7.2 Example: The 0+ 2+ Transition in 24Mg 516
XX Contents
Exercises 519
17 Two Quasiparticle Mixing in Odd Odd Nuclei 523
17.1 The Proton Neutron QTDA 523
17.1.1 Equation of Motion 524
17.1.2 Properties of Solutions 525
17.2 Excitation Spectra of Open Shell Odd Odd Nuclei 525
17.2.1 1+ States in the Mirror Nuclei 24Na and 24A1 526
17.2.2 Energy Spectra in the d s and f p 0g9/2 Shells 527
17.2.3 Average Particle Number in the pnQTDA 530
17.3 Electromagnetic Transitions in the pnQTDA 533
17.3.1 Decay of the i\ State in 24Na 534
17.4 Beta Decay Transitions in the pnQTDA 537
17.4.1 Transitions to and from an Even Even Ground State . . 537
17.4.2 Gamow Teller Beta Decay of 30S 538
17.4.3 The Ikeda Sum Rule and the pnQTDA 541
17.4.4 Examples of the Ikeda Sum Rule 545
17.4.5 Gamow Teller Giant Resonance 548
17.4.6 Beta Decay Transitions Between a QTDA
and a pnQTDA State 550
17.4.7 Gamow Teller Beta Decay of 30P 550
Exercises 553
18 Two Quasiparticle Mixing by the QRPA 557
18.1 The QRPA Equations 557
18.1.1 Derivation of the QRPA Equations by the EOM 558
18.1.2 Explicit Form of the Correlation Matrix 559
18.2 General Properties of QRPA Solutions 562
18.2.1 QRPA Energies and Wave Functions 563
18.2.2 The QRPA Ground State and Transition Densities 567
18.3 QRPA Description of Open Shell Even Even Nuclei 569
18.3.1 Structure of the Correlation Matrix 569
18.3.2 Excitation Energies of 2+ States in 24Mg 570
18.3.3 Further Examples in the Od ls Shell 572
18.3.4 Spurious Contributions to 1~ States 573
18.4 Electromagnetic Transitions
in the QRPA Framework 575
18.4.1 Transitions to the QRPA Ground State 575
18.4.2 E2 Decays in the Od ls and 0f lp 0g9/2 Shells 577
18.4.3 Energy Weighted Sum Rule of the QRPA 579
18.4.4 Electric Quadrupole Sum Rule in 24Mg 580
18.4.5 Electromagnetic Transitions Between Two QRPA
Excitations 582
18.4.6 Electric Quadrupole Transition 4f » 2f in 24Mg 584
18.4.7 Collective Vibrations and Rotations 587
Contents XXI
18.5 Collective Vibrational Two Phonon States 587
Exercises 590
19 Proton Neutron QRPA 595
19.1 The pnQRPA Equation and its Basic Properties 595
19.1.1 The pnQRPA Equation 595
19.1.2 Basic Properties of the Solutions of the pnQRPA
Equation 596
19.2 Description of Open Shell Odd Odd Nuclei
by the pnQRPA 599
19.2.1 Low Lying 1+ States in 24Na and 24A1 599
19.2.2 Other Examples 602
19.3 Average Particle Number in the pnQRPA 604
19.4 Electromagnetic Transitions in the pnQRPA 605
19.4.1 Transition Amplitudes 605
19.4.2 Decay of the 2+ State in 24Na 606
19.5 Beta Decay Transitions in the pnQRPA Framework 608
19.5.1 Transitions Involving the Even Even Ground State . 608
19.5.2 Gamow Teller Decay of the 1^ Isomer in 24A1 610
19.6 The Ikeda Sum Rule for the pnQRPA 612
19.6.1 Derivation of the Sum Rule 612
19.6.2 Examples of the Sum Rule 613
19.7 Beta Decay Transitions Between a QRPA
and a pnQRPA State 616
19.7.1 Derivation of the Transition Amplitude 616
19.7.2 The Gamow Teller Decay 24A1(1 + ) 24Mg(2f) 618
19.7.3 First Forbidden Unique Beta Decay in the 0f lp 0g9/ 2
Shell 620
19.7.4 Empirical Particle Hole and Particle Particle Forces . . . 624
Exercises 625
References 629
Index 033 |
| adam_txt |
Contents
Part I Particles and Holes
1 Angular Momentum Coupling 3
1.1 Clebsch Gordan Coefficients and 3j Symbols 3
1.2 More on Clebsch Gordan Coefficients; 3j Symbols 7
1.2.1 Clebsch Gordan Coefficients 8
1.2.2 More Symmetry: 3j Symbols 9
1.2.3 Relations for 3j Symbols 10
1.3 The 6j Symbol 11
1.3.1 Symmetry Properties of the 6j Symbol 13
1.3.2 Relations for 6j Symbols 14
1.3.3 Explicit Expressions for 6j Symbols 14
1.4 The 9? Symbol 15
1.4.1 Symmetry Properties of the 9j Symbol 17
1.4.2 Relations for 9j Symbols 18
Exercises 19
2 Tensor Operators and the Wigner Eckart Theorem 23
2.1 Spherical Tensor Operators 23
2.1.1 Rotations of the Coordinate Axes 23
2.1.2 Wigner D Functions and Spherical Tensors 25
2.1.3 Contravariant and Covariant Components
of Spherical Tensors 27
2.2 The Wigner Eckart Theorem 29
2.2.1 Immediate Consequences of the Wigner Eckart Theorem 29
2.2.2 Pauli Spin Matrices 31
2.3 Matrix Elements of Coupled Tensor Operators 32
2.3.1 Theorem I 33
2.3.2 Theorem II 34
Exercises 35
XII Contents
3 The Nuclear Mean Field and Many Nucleon Configurations 39
3.1 The Nuclear Mean Field 39
3.1.1 The Mean Field Approximation 40
3.1.2 Phenomenological Potentials 44
3.1.3 The Spin Orbit Interaction 44
3.2 Woods Saxon Wave Functions 45
3.2.1 Harmonic Oscillator Wave Functions 48
3.2.2 Diagonalization of the Woods Saxon Hamiltonian 50
3.3 Many Nucleon Configurations 54
Exercises 60
4 Occupation Number Representation 63
4.1 Occupation Number Representation of Many Nucleon States . . 63
4.1.1 Fock Space: Particle Creation and Annihilation 64
4.1.2 Further Properties of Creation
and Annihilation Operators 66
4.2 Operators and Their Matrix Elements 67
4.2.1 Occupation Number Representation
of One Body Operators 67
4.2.2 Matrix Elements of One Body Operators 68
4.2.3 Occupation Number Representation
of Two Body Operators 69
4.3 Evaluation of Many Nucleon Matrix Elements 70
4.3.1 Normal Ordering 70
4.3.2 Contractions 71
4.3.3 Wick's Theorem 72
4.4 Particle Hole Representation 74
4.4.1 Properties of Particle and Hole Operators 75
4.4.2 Particle Hole Representation of Operators
and Excitations 77
4.5 Hartree Fock Equation from Wick's Theorem 78
4.5.1 Derivation of the Hartree Fock Equation 78
4.5.2 Residual Interaction; Ground State Energy 80
4.6 Hartree Fock Eigenvalue Problem 81
Exercises 83
5 The Mean Field Shell Model 87
5.1 Valence Space 87
5.2 One Particle and One Hole Nuclei 89
5.2.1 Examples of One Particle Nuclei 89
5.2.2 Examples of One Hole Nuclei 91
5.3 Two Particle and Two Hole Nuclei 93
5.3.1 Examples of Two Particle Nuclei 93
5.3.2 Examples of Two Hole Nuclei 97
5.4 Particle Hole Nuclei 99
Contents XIII
5.5 Isospin Representation of Few Nucleon Systems 105
5.5.1 General Isospin Formalism 105
5.5.2 Tensor Operators in Isospin Representation 107
5.5.3 Isospin Representation of Two Particle
and Two Hole Nuclei 109
5.5.4 Isospin Representation of Particle Hole Nuclei 112
Exercises 114
6 Electromagnetic Multipole Moments
and Transitions 117
6.1 General Properties of Electromagnetic Observables 117
6.1.1 Transition Probability and Half Life 118
6.1.2 Selection Rules for Electromagnetic Transitions 121
6.1.3 Single Particle Matrix Elements
of the Multipole Operators 122
6.1.4 Properties of the Radial Integrals 124
6.1.5 Tables of Numerical Values of Single Particle Matrix
Elements 127
6.1.6 Electromagnetic Multipole Moments 128
6.1.7 Weisskopf Units and Transition Rates 130
6.2 Electromagnetic Transitions in One Particle
and One Hole Nuclei 132
6.2.1 Reduced Transition Probabilities 132
6.2.2 Example: Transitions in One Hole Nuclei 15N and 15O . 134
6.2.3 Magnetic Dipole Moments: Schmidt Lines 136
6.3 Electromagnetic Transitions in Two Particle
and Two Hole Nuclei 137
6.3.1 Example: Transitions in Two Particle Nuclei 18O
and 18Ne 139
6.4 Electromagnetic Transitions in Particle Hole Nuclei 140
6.4.1 Transitions Involving Charge Conserving Particle
Hole Excitations 141
6.4.2 Example: Doubly Magic Nucleus 16O 143
6.4.3 Transitions Between Charge Changing Particle Hole
Excitations 146
6.4.4 Example: Odd Odd Nucleus 16N 147
6.5 Isoscalar and Isovector Transitions 148
6.5.1 Isospin Decomposition of the Electromagnetic
Decay Operator 148
6.5.2 Example: 3" States in 16O 149
6.5.3 Isospin Selection Rules in Two Particle
and Two Hole Nuclei 150
Exercises 153
XIV Contents
7 Beta Decay 157
7.1 General Properties of Nuclear Beta Decay 157
7.2 Allowed Beta Decay 162
7.2.1 Half Lives, Reduced Transition Probabilities
and ft Values 163
7.2.2 Fermi and Gamow Teller Matrix Elements 165
7.2.3 Phase Space Factors 166
7.2.4 Combined /3+ and Electron Capture Decays 168
7.2.5 Decay Q Values 169
7.2.6 Partial and Total Decay Half Lives; Decay Branchings . 169
7.2.7 Classification of Beta Decays 170
7.3 Beta Decay Transitions in One Particle and One Hole Nuclei. . 171
7.3.1 Matrix Elements and Reduced Transition Probabilities . 171
7.3.2 Application to Beta Decay of 15O; Other Examples 172
7.4 Beta Decay Transitions in Particle Hole Nuclei 174
7.4.1 Beta Decay to and from the Even Even Ground State . 174
7.4.2 Application to Beta Decay of 56Ni 175
7.4.3 Beta Decay Transitions Between Two Particle Hole
States 176
7.4.4 Application to Beta Decay of 16N 178
7.5 Beta Decay Transitions in Two Particle and Two Hole Nuclei . 180
7.5.1 Transition Amplitudes 181
7.5.2 Application to Beta Decay of 6He 183
7.5.3 Application to the Beta Decay Chain
18Ne _ 18F _, 18Q 184
7.5.4 Further Examples: Beta Decay in A = 42
and A = 54 Nuclei 187
7.6 Forbidden Unique Beta Decay 188
7.6.1 General Aspects of First Forbidden Beta Decay 188
7.6.2 First Forbidden Unique Beta Decay 190
7.6.3 Application to First Forbidden Unique Beta Decay
of 16N 192
7.6.4 Higher Forbidden Unique Beta Decay 193
7.6.5 Application to Third Forbidden Unique Beta Decay
of 40K 197
7.6.6 Forbidden Unique Beta Decay in Few Particle
and Few Hole Nuclei 199
7.6.7 Forbidden Non Unique Beta Decays 201
Exercises 202
8 Nuclear Two Body Interaction and Configuration Mixing. . 205
8.1 General Properties of the Nuclear Two Body Interaction 205
8.1.1 Coupled Two Body Interaction Matrix Elements 206
8.1.2 Relations for Coupled Two Body Matrix Elements 209
8.1.3 Different Types of Two Body Interaction 210
Contents XV
8.1.4 Central Forces with Spin and Isospin Dependendence . . 212
8.2 Separable Interactions; the Surface Delta Interaction 213
8.2.1 Multipole Decomposition of a General Separable
Interaction 214
8.2.2 Two Body Matrix Elements of the Surface Delta
Interaction 215
8.3 Configuration Mixing in Two Particle Nuclei 219
8.3.1 Matrix Representation of an Eigenvalue Problem 219
8.3.2 Solving the Eigenenergies of a Two by Two Problem . . . 221
8.3.3 Matrix Elements of the Hamiltonian
in the Two Nucleon Basis 223
8.3.4 Solving the Eigenvalue Problem
for a Two Particle Nucleus 224
8.3.5 Application to A = 6 Nuclei 225
8.3.6 Application to A = 18 Nuclei 228
8.4 Configuration Mixing in Two Hole Nuclei 231
8.4.1 Diagonalization of the Residual Interaction
in a Two Hole Basis 231
8.4.2 Application to A = 14 Nuclei 233
8.4.3 Application to A = 38 Nuclei 234
8.5 Electromagnetic and Beta Decay Transitions in Two Particle. . 236
8.5.1 Transition Amplitudes With Configuration Mixing 236
8.5.2 Application to Beta Decay of 6He 237
8.5.3 Application to E2 Decays in 18O and 18Ne 239
Exercises 240
9 Particle—Hole Excitations and the Tamm DancofF
Approximation 243
9.1 The Tamm Dancoff Approximation 243
9.1.1 Justification of the TDA: Brillouin's Theorem 243
9.1.2 Derivation of Explicit Expressions for the TDA Matrix . 246
9.1.3 Tabulated Values of Particle Hole Matrix Elements 248
9.1.4 TDA as an Eigenvalue Problem: Properties
of the Solutions 251
9.2 TDA for General Separable Forces 253
9.2.1 Schematic Model; Dispersion Equation 253
9.2.2 The Schematic Model for T = 0 and T = 1 256
9.2.3 The Schematic Model with the Surface
Delta Interaction 257
9.2.4 Application to 1~ Excitations in 4He 258
9.3 Excitation Spectra of Doubly Magic Nuclei 260
9.3.1 Block Decomposition of the TDA Matrix 260
9.3.2 Application to 1~ States in 4He 260
9.3.3 Application to Excited States in 16O 262
9.3.4 Further Examples: 40Ca and 48Ca 263
XVI Contents
9.4 Electromagnetic Transitions in Doubly Magic Nuclei 265
9.4.1 Transitions to the Particle Hole Ground State 266
9.4.2 Non Energy Weighted Sum Rule 267
9.4.3 Application to Octupole Transitions in 160 268
9.4.4 Collective Transitions in the TDA 271
9.4.5 Application to Octupole Transitions in 40Ca 272
9.4.6 El Transitions: Isospin Breaking
in the Nuclear Mean Field 274
9.4.7 Transitions Between Two TDA Excitations 277
9.4.8 Application to the 57/ 3^~ Transition in 40Ca 277
9.5 Electric Transitions on the Schematic Model 278
9.5.1 Transition Amplitudes 279
9.5.2 Application to Electric Dipole Transitions in 4He 280
Exercises 282
10 Charge Changing Particle—Hole Excitations
and the pnTDA 287
10.1 The Proton Neutron Tarnm Dancoff Approximation 287
10.1.1 Structure of the pnTDA Matrix 287
10.1.2 Application to |H3 and |Lix 289
10.1.3 Further Examples: States of :fN9 and ^K21 290
10.2 Electromagnetic Transitions in the pnTDA 294
10.2.1 Transition Amplitudes 294
10.2.2 Application to the E2 Transition 0," 2" in ^Ng 294
10.3 Beta Decay Transitions in the pnTDA 296
10.3.1 Transitions to the Particle Hole Vacuum 296
10.3.2 First Forbidden Unique Beta Decay of m7N9 297
10.3.3 Transitions between Particle Hole States 298
10.3.4 Allowed Beta Decay of M N9 to Excited States in ^Og . 299
Exercises 301
11 The Random Phase Approximation 305
11.1 The Equations of Motion Method 305
11.1.1 Derivation of the Equations of Motion 306
11.1.2 Derivation of the Hartree Fock Equations by the EOM. 310
11.2 Sophisticated Particle Hole Theories: The RPA 312
11.2.1 Derivation of the RPA Equations by the EOM 312
11.2.2 Explicit Form of the Correlation Matrix 315
11.2.3 Numerical Tables of Correlation Matrix Elements 317
11.3 Properties of the RPA Solutions 318
11.3.1 RPA Energies and Amplitudes 318
11.3.2 The RPA Ground State 322
11.3.3 RPA One Particle Densities 324
11.4 RPA Solutions of the Schematic Separable Model 327
11.4.1 The RPA Dispersion Equation 327
Contents XVII
11.4.2 Application to 1~ Excitations in 4He 329
11.4.3 The Degenerate Model 331
11.5 RPA Description of Doubly Magic Nuclei 332
11.5.1 Examples of the RPA Matrices 332
11.5.2 Diagonalization of the RPA Supermatrix
by Similarity Transformations 335
11.5.3 Application to 1~ Excitations in 4He Carried Through . 337
11.5.4 The 1~ Excitations of 4He Revisited 340
11.5.5 Further Examples 342
11.6 Electromagnetic Transitions in the RPA Framework 344
11.6.1 Transitions to the RPA Ground State 344
11.6.2 Extreme Collective Model 346
11.6.3 Octupole Decay in 16O 347
11.6.4 The Energy Weighted Sum Rule 349
11.6.5 Sum Rule for the Octupole Transitions in 16O 352
11.6.6 Electric Transitions to the RPA Ground State
on the Schematic Model 353
11.6.7 Electric Dipole Transitions in 4He on the Schematic
Model 354
11.6.8 The Degenerate Model 355
11.6.9 Electromagnetic Transitions Between Two RPA
Excitations 356
11.6.10The E2 Transition 5^ 3^ in 40Ca 359
Exercises 361
Part II Quasiparticles
12 Nucleon Pairing and Seniority 369
12.1 Evidence of Nucleon Pairing 370
12.2 The Pure Pairing Force 372
12.3 Two Particle Spectrum of the Pure Pairing Force 374
12.4 Seniority Model of the Pure Pairing Force 376
12.4.1 Derivation of the Seniority Zero Spectrum 376
12.4.2 Spectra of Seniority One and Seniority Two States . 377
12.4.3 States of Higher Seniority 379
12.4.4 Application of the Seniority Model to 0f7/2 Shell Nuclei 380
12.5 The Two Level Model 381
12.5.1 The Pair Basis 382
12.5.2 Matrix Elements of the Pairing Hamiltonian 383
12.5.3 Application to a Two Particle System 386
12.6 Two Particles in a Valence Space of Many j Shells 387
12.6.1 Dispersion Equation 387
12.6.2 The Three Level Case 388
Exercises 389
XVIII Contents
13 BCS Theory 391
13.1 BCS Quasiparticles and Their Vacuum 391
13.1.1 The BCS Ground State 392
13.1.2 BCS Quasiparticles 393
13.2 Occupation Number Representation
for BCS Quasiparticles 394
13.2.1 Contraction Properties 395
13.2.2 Quasiparticle Representation of the Nuclear
Hamiltonian 395
13.3 Derivation of the BCS Equations 398
13.3.1 BCS as a Constrained Variational Problem 398
13.3.2 The Gap Equation and the Quasiparticle Mean Field . . 400
13.4 Properties of the BCS Solutions 403
13.4.1 Physical Meaning of the Basic Parameters 403
13.4.2 Particle Number and Its Fluctuations 404
13.4.3 Odd Even Effect 406
13.5 Solution of the BCS Equations for Simple Models 406
13.5.1 Single j Shell 407
13.5.2 The Lipkin Model 408
13.5.3 Example: The Lipkin Model for Two j = \ Shells 411
13.5.4 The Two Level Model for Two j = \ Shells 412
Exercises 414
14 Quasiparticle Mean Field: BCS and Beyond 417
14.1 Numerical Solution of the BCS Equations 417
14.1.1 Iterative Numerical Procedure 418
14.1.2 Application to Nuclei in the d s and f p 0gg/2 Shells . . . 420
14.2 Lipkin Nogami BCS Theory 430
14.2.1 The Lipkin Nogami Model Hamiltonian 430
14.2.2 Derivation of the Lipkin Nogami BCS Equations 433
14.3 Lipkin Nogami BCS Theory in Simple Models 436
14.3.1 Single j Shell 436
14.3.2 The Lipkin Model 438
14.3.3 Example: The j = \ Case 441
14.4 The Two Level Model for j = j' = \ 443
14.5 Application of Lipkin Nogami Theory
to Realistic Calculations 445
Exercises 447
15 Transitions in the Quasiparticle Picture 449
15.1 Quasiparticle Representation of a One Body Transition
Operator 449
15.2 Transition Densities for Few Quasiparticle Systems 450
15.2.1 Transitions Between One Quasiparticle States 450
Contents XIX
15.2.2 Transitions Between a Two Quasiparticle State
and the BCS Vacuum 451
15.2.3 Transitions Between Two Quasiparticle States 451
15.3 Transitions in Odd ,4 Nuclei 452
15.3.1 Transition Amplitudes 453
15.3.2 Beta and Gamma Decays in the A = 25 Chain
of Isobars 455
15.3.3 Beta Decays in the A = 63 Chain of Isobars 457
15.4 Transitions Between a Two Quasiparticle State
and the BCS Vacuum 459
15.4.1 Formalism for Transition Amplitudes 459
15.4.2 Beta and Gamma Decays in the A = 30 Chain
of Isobars 463
15.5 Transitions Between Two Quasiparticle States 467
15.5.1 Electromagnetic Transitions 467
15.5.2 Beta Decay Transitions 469
15.5.3 Beta Decay of 30P 472
15.5.4 Magnetic Dipole Decay in 30P 473
Exercises 474
16 Mixing of Two Quasiparticle Configurations 479
16.1 Quasiparticle Representation of the Residual Interaction 479
16.2 Derivation of the Quasiparticle TDA Equation 484
16.3 General Properties of QTDA Solutions 490
16.3.1 Orthogonality 490
16.3.2 Completeness 491
16.4 Excitation Spectra of Open Shell Even Even Nuclei 491
16.4.1 Explicit Form of the QTDA Matrix 492
16.4.2 Excitation Energies of 2+ States in 24Mg 493
16.4.3 Pairing Strength Parameters from Empirical Pairing
Gaps 498
16.4.4 Excitation Spectrum of ^Mg12 501
16.4.5 Excitation Spectra of the Mirror Nuclei fjSi,,; and ^Sur,02
16.4.6 Excitation Spectrum of 66Zn 503
16.5 Electromagnetic Transitions to the Ground State 506
16.5.1 Decay Amplitude 506
16.5.2 E2 Decay of the Lowest 2+ State in 2JMg 507
16.5.3 Collective States and Electric Transitions 509
16.6 QTDA Sum Rule for Electromagnetic Transitions 513
16.6.1 Formalism 513
16.6.2 Examples of the NEWSR in the Od ls and 0f lp 0g9/2
Shells 514
16.7 Transitions Between QTDA Excited States 515
16.7.1 Transition Amplitudes 515
16.7.2 Example: The 0+ 2+ Transition in 24Mg 516
XX Contents
Exercises 519
17 Two Quasiparticle Mixing in Odd Odd Nuclei 523
17.1 The Proton Neutron QTDA 523
17.1.1 Equation of Motion 524
17.1.2 Properties of Solutions 525
17.2 Excitation Spectra of Open Shell Odd Odd Nuclei 525
17.2.1 1+ States in the Mirror Nuclei 24Na and 24A1 526
17.2.2 Energy Spectra in the d s and f p 0g9/2 Shells 527
17.2.3 Average Particle Number in the pnQTDA 530
17.3 Electromagnetic Transitions in the pnQTDA 533
17.3.1 Decay of the i\ State in 24Na 534
17.4 Beta Decay Transitions in the pnQTDA 537
17.4.1 Transitions to and from an Even Even Ground State . . 537
17.4.2 Gamow Teller Beta Decay of 30S 538
17.4.3 The Ikeda Sum Rule and the pnQTDA 541
17.4.4 Examples of the Ikeda Sum Rule 545
17.4.5 Gamow Teller Giant Resonance 548
17.4.6 Beta Decay Transitions Between a QTDA
and a pnQTDA State 550
17.4.7 Gamow Teller Beta Decay of 30P 550
Exercises 553
18 Two Quasiparticle Mixing by the QRPA 557
18.1 The QRPA Equations 557
18.1.1 Derivation of the QRPA Equations by the EOM 558
18.1.2 Explicit Form of the Correlation Matrix 559
18.2 General Properties of QRPA Solutions 562
18.2.1 QRPA Energies and Wave Functions 563
18.2.2 The QRPA Ground State and Transition Densities 567
18.3 QRPA Description of Open Shell Even Even Nuclei 569
18.3.1 Structure of the Correlation Matrix 569
18.3.2 Excitation Energies of 2+ States in 24Mg 570
18.3.3 Further Examples in the Od ls Shell 572
18.3.4 Spurious Contributions to 1~ States 573
18.4 Electromagnetic Transitions
in the QRPA Framework 575
18.4.1 Transitions to the QRPA Ground State 575
18.4.2 E2 Decays in the Od ls and 0f lp 0g9/2 Shells 577
18.4.3 Energy Weighted Sum Rule of the QRPA 579
18.4.4 Electric Quadrupole Sum Rule in 24Mg 580
18.4.5 Electromagnetic Transitions Between Two QRPA
Excitations 582
18.4.6 Electric Quadrupole Transition 4f » 2f in 24Mg 584
18.4.7 Collective Vibrations and Rotations 587
Contents XXI
18.5 Collective Vibrational Two Phonon States 587
Exercises 590
19 Proton Neutron QRPA 595
19.1 The pnQRPA Equation and its Basic Properties 595
19.1.1 The pnQRPA Equation 595
19.1.2 Basic Properties of the Solutions of the pnQRPA
Equation 596
19.2 Description of Open Shell Odd Odd Nuclei
by the pnQRPA 599
19.2.1 Low Lying 1+ States in 24Na and 24A1 599
19.2.2 Other Examples 602
19.3 Average Particle Number in the pnQRPA 604
19.4 Electromagnetic Transitions in the pnQRPA 605
19.4.1 Transition Amplitudes 605
19.4.2 Decay of the 2+ State in 24Na 606
19.5 Beta Decay Transitions in the pnQRPA Framework 608
19.5.1 Transitions Involving the Even Even Ground State . 608
19.5.2 Gamow Teller Decay of the 1^ Isomer in 24A1 610
19.6 The Ikeda Sum Rule for the pnQRPA 612
19.6.1 Derivation of the Sum Rule 612
19.6.2 Examples of the Sum Rule 613
19.7 Beta Decay Transitions Between a QRPA
and a pnQRPA State 616
19.7.1 Derivation of the Transition Amplitude 616
19.7.2 The Gamow Teller Decay 24A1(1 + ) 24Mg(2f) 618
19.7.3 First Forbidden Unique Beta Decay in the 0f lp 0g9/ 2
Shell 620
19.7.4 Empirical Particle Hole and Particle Particle Forces . . . 624
Exercises 625
References 629
Index 033 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Suhonen, Jouni |
| author_GND | (DE-588)133087557 |
| author_facet | Suhonen, Jouni |
| author_role | aut |
| author_sort | Suhonen, Jouni |
| author_variant | j s js |
| building | Verbundindex |
| bvnumber | BV022354088 |
| callnumber-first | Q - Science |
| callnumber-label | QC793 |
| callnumber-raw | QC793.3.S8 |
| callnumber-search | QC793.3.S8 |
| callnumber-sort | QC 3793.3 S8 |
| callnumber-subject | QC - Physics |
| classification_rvk | UN 1000 |
| classification_tum | PHY 451f |
| ctrlnum | (OCoLC)77541316 (DE-599)BVBBV022354088 |
| dewey-full | 539.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 539 - Modern physics |
| dewey-raw | 539.74 |
| dewey-search | 539.74 |
| dewey-sort | 3539.74 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
| format | Book |
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| id | DE-604.BV022354088 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:00:50Z |
| indexdate | 2024-07-20T09:13:49Z |
| institution | BVB |
| isbn | 9783540488590 3540488596 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015563529 |
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| physical | XXI, 645 S. Ill., graph. Darst. |
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| publisher | Springer |
| record_format | marc |
| series2 | Theoretical and mathematical physics |
| spelling | Suhonen, Jouni Verfasser (DE-588)133087557 aut From nucleons to nucleus concepts of microscopic nuclear theory Jouni Suhonen Berlin [u.a.] Springer 2007 XXI, 645 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Theoretical and mathematical physics Structure nucléaire Nuclear structure Kerntheorie (DE-588)4163643-0 gnd rswk-swf Kerntheorie (DE-588)4163643-0 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2862001&prov=M&dok_var=1&dok_ext=htm Verlag Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015563529&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Suhonen, Jouni From nucleons to nucleus concepts of microscopic nuclear theory Structure nucléaire Nuclear structure Kerntheorie (DE-588)4163643-0 gnd |
| subject_GND | (DE-588)4163643-0 |
| title | From nucleons to nucleus concepts of microscopic nuclear theory |
| title_auth | From nucleons to nucleus concepts of microscopic nuclear theory |
| title_exact_search | From nucleons to nucleus concepts of microscopic nuclear theory |
| title_exact_search_txtP | From nucleons to nucleus concepts of microscopic nuclear theory |
| title_full | From nucleons to nucleus concepts of microscopic nuclear theory Jouni Suhonen |
| title_fullStr | From nucleons to nucleus concepts of microscopic nuclear theory Jouni Suhonen |
| title_full_unstemmed | From nucleons to nucleus concepts of microscopic nuclear theory Jouni Suhonen |
| title_short | From nucleons to nucleus |
| title_sort | from nucleons to nucleus concepts of microscopic nuclear theory |
| title_sub | concepts of microscopic nuclear theory |
| topic | Structure nucléaire Nuclear structure Kerntheorie (DE-588)4163643-0 gnd |
| topic_facet | Structure nucléaire Nuclear structure Kerntheorie |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2862001&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015563529&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT suhonenjouni fromnucleonstonucleusconceptsofmicroscopicnucleartheory |