دانلود کتاب SU(3) symmetry in atomic nuclei

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Preface......Page 6
Contents......Page 8
About the Author......Page 13
1 Introduction......Page 14
References......Page 18
2.2 SU(3) supsetSO(3) supsetSO(2) Algebra: Quadrupole Operator......Page 22
2.3 SU(3) supset[SU(2) supsetSO(2)] otimesU(1) Algebra......Page 25
2.4.1 Young Tableaux......Page 26
2.4.2 Kronecker Products of SU(3) Irreps......Page 28
2.4.3 Dimension of (λµ) Irreps......Page 29
2.4.4 Leading SU(3) Irrep in U((η+1)(η+2)/2)......Page 30
2.5 SU(3) Quadratic and Cubic Casimir Operators......Page 33
2.6 SU(3) supsetSO(3) supsetSO(2) States: K Label......Page 34
2.7 SU(3) supsetSU(2) otimesU(1) States......Page 36
2.8.1 SU(3) in Shell Model......Page 37
2.8.2 SU(3) in Interacting Boson Model......Page 40
2.9 SU(3) in Particle Physics......Page 43
2.10 Summary......Page 45
References......Page 46
3.2.1 Plethysm Method......Page 48
3.2.2 Recursion Method......Page 51
3.2.3 Difference Method......Page 54
3.2.4 Method for Obtaining a Few Lower SU(3) Irreps......Page 57
3.3 SU(3) Wigner and Racah Coefficients......Page 61
3.3.1 SU(3) supsetSU(2) otimesU(1) Reduced Wigner Coefficients......Page 62
3.3.2 SU(3) supsetSO(3) Reduced Wigner Coefficients......Page 65
3.3.3 SU(3) Racah or U- and Z- Coefficients......Page 69
3.4 Building Up Principle and General Comments......Page 71
References......Page 75
4.2 SU(3) Tensorial Decomposition and Wigner–Eckart Theorem......Page 78
4.2.1 Examples from sd and sdgIBM......Page 79
4.2.2 Shell Model Two-Body Interactions......Page 80
4.2.3 Analytical Results for Electric Quadrupole Transition Strengths......Page 82
4.3 SU(3) Fractional Parentage Coefficients......Page 84
4.3.1 Construction of SU(3) Intrinsic States: IBM Examples......Page 85
4.3.2 SU(3) Intrinsic States: Fermion Examples......Page 88
4.3.3 Triple Barred SU(3) Reduced Matrix Elements......Page 89
4.4 9-SU(3) Coefficients......Page 90
4.5 SU(3) D-Functions......Page 93
References......Page 96
5.1 Introduction......Page 98
5.2 X3 and X4 Operators and Their Matrix Elements......Page 99
5.3 Shape Parameters and (λµ) Irreps Correspondence......Page 100
5.4 Integrity Basis Hamiltonian and Asymmetric Rotor......Page 101
5.5 K Quantum Number from X3 and X4 Operators......Page 102
5.6 Extension to KJ Quantum Number......Page 103
References......Page 104
6.2 Pseudo SU(3) Model with Pseudo-spin......Page 106
6.2.1 Mapping of Operators to Pseudo-(tildeell tildes) Basis......Page 107
6.2.2 Basic Results from Pseudo-spin and Pseudo-Nilsson Orbits......Page 109
6.2.3 Spectroscopy with Pseudo-SU(3) Symmetry......Page 111
6.3 Proxy-SU(3) Model......Page 115
6.3.1 Prolate Dominance over Oblate Shape......Page 117
6.3.2 Results for the Deformation Parameters (β, γ) and B(E2)\'s......Page 118
6.4 Sp(6,R) Model with SU(3) Subalgebra......Page 119
6.4.1 SU(3) Limit of Sp(6,R)......Page 121
6.5.1 i- Active and k- Active Schemes......Page 126
6.5.2 Fermion Dynamical Symmetry Model......Page 128
6.6 Summary......Page 130
References......Page 131
7.2 SU(3) in sdgIBM......Page 135
7.2.1 SUsd(3) times1g Limit......Page 137
7.2.2 SUsdg(3) Limit......Page 139
7.2.3 ΔL=4 Staggering in sdgIBM......Page 144
7.3.2 Dynamical Symmetries of sdpfIBM and the SU(3) Limit......Page 147
7.3.3 Analytical Results for E1 Transitions in SUsd(3) oplusSUpf(3) Limit......Page 149
7.4.1 SU(3) in pn-sdIBM......Page 153
7.4.2 SU(3) in pn-sdgIBM......Page 156
7.5 SU(3) in IBM-3 and IBM-4 Models......Page 157
7.5.1 SU(3) Limit of IBM-3......Page 158
7.5.2 SU(3) Limit of IBM-4......Page 159
References......Page 161
8.1 Introduction......Page 166
8.2 SU(3) timesj Limit of IBFM for Odd-A Nuclei......Page 167
8.3 SUBF(3) Limit of IBFM for Odd-A Nuclei......Page 170
8.3.1 Nilsson Correspondence I......Page 172
8.3.2 Nilsson Correspondence II......Page 174
8.3.3 Application to E2 Transition Strengths: 187Os Example......Page 176
8.3.4 Application to M1 Transition Strengths: 185Re Example......Page 178
8.3.5 Single Nucleon Transfer: 185W Example......Page 181
8.4 SU(3) in IBFFM for Odd–Odd Nuclei......Page 182
8.4.1 SUBF(3) otimesU(2j+1) Limit: 186Re Example......Page 183
8.4.2 SUBFF(3) Limit : 190Ir Example......Page 186
8.5 SU(3) in IBF2M for 2 Quasi-particle Excitations......Page 191
8.6 SU(3) in sdgIBFM-2 and M1 Distributions......Page 193
8.7 Summary......Page 197
References......Page 198
9.2 Phase Transitions with SU(3)......Page 201
9.2.1 U(5) to SU(3) Transition......Page 202
9.2.2 Example of an Analytically Solvable QPT......Page 203
9.2.3 Critical Point X(5) Symmetry for U(5) rightarrowSU(3) Transition......Page 205
9.3 Partial SU(3) Dynamical Symmetry......Page 206
9.4 SU(3) for Removal of Spurious c.m. States......Page 209
9.5 SU(3) for Clustering in Nuclei......Page 212
9.5.1 Nuclear Vibron Model......Page 213
9.5.2 Semi-microscopic Algebraic Cluster Model with SU(3)......Page 214
9.6.1 Symmetry Adopted SU(3) Based No-Core Shell Model (SA-NCSM)......Page 217
9.6.2 No-Core Symplectic Shell Model (NCSpM)......Page 219
9.7 Summary......Page 220
References......Page 221
10.1 Introduction......Page 225
10.2.1 Averages, Traces, State Densities, and Partial Densities......Page 226
10.2.2 General Principles of Trace Propagation......Page 228
10.3.1 (2s1d) Shell Model Example......Page 231
10.3.2 Sp(6,R) supsetSU(3) Example......Page 233
10.4 Application of SU(3) Energy Centroids: Regularities with Random Interactions......Page 234
10.4.1 Regular Structures from Random Interactions: sdpfIBM Example......Page 235
10.4.2 Regular Structures from Random Interactions: sdIBM-T Example......Page 236
10.5 Partition Functions and Level Density Enhancement in Deformed Nuclei with SU(3)......Page 238
10.6 Statistical Group Theory for SU(3) Multiplicities......Page 240
10.7.1 Definition of EGUE(2)-SU(3) Ensemble......Page 245
10.7.2 Basic Formulation for Analytical Treatment of EGUE(2)-SU(3)......Page 248
10.7.3 Results for Lower Order Moments of One- and Two-Point Functions......Page 251
References......Page 254
11.1 Introduction......Page 257
11.2 Four SU(3) Algebras in sdgIBM: Results for Quadrupole Properties......Page 258
11.2.1 Structure of Intrinsic States......Page 259
11.2.2 Large-N Limit Results for Quadrupole Moments and B(E2)\'s......Page 260
11.3 Eight SU(3) Algebras in sdgiIBM: Results for Quadrupole Properties......Page 261
11.4.1 (sdg)6p,2n Example......Page 265
11.4.2 (sdgi)6p Example......Page 269
References......Page 270
12 Summary and Future Outlook......Page 272
References......Page 273
Appendix A Angular Momentum Algebra......Page 274
Appendix B Elements of U(n) Lie Algebra and Its Subalgebras......Page 280
Appendix C Asymptotic Nilsson Wavefunctions......Page 288
Appendix D Correspondence Between SUBF2(3) Irreps and 2 q.p. Nilsson Configurations for η= 3 Shell......Page 292
Appendix E Bivariate Moments, Cumulants, and Edgeworth Expansion......Page 295
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