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E-raamat: Structure of Medium Mass Nuclei: Deformed Shell Model and Spin-Isospin Interacting Boson Model

(Physical Research Laboratory, Ahmedabad, India), (Professor Emeritus, Berhampur University, Orissa, India)
  • Formaat: 320 pages
  • Ilmumisaeg: 12-Dec-2016
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781351736947
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Structure of Medium Mass Nuclei: Deformed Shell Model and Spin-Isospin Interacting Boson ModelSuurem pilt
  • Formaat: 320 pages
  • Ilmumisaeg: 12-Dec-2016
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781351736947
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Medium heavy nuclei with mass number A=60-90 exhibit a variety of complex collective properties, provide a laboratory for double beta decay studies, and are a region of all heavy N=Z nuclei. This book discusses these three aspects of nuclear structure using Deformed Shell Model and the Spin-Isospin Invariant Interacting Boson Model naturally generated by fermionic SO(8) symmetry. Using these two models, the book describes properties of medium heavy nuclei with mass number A=60-90. It provides a good reference for future nuclear structure experiments using radioactive ion beam (RIB) facilities. Various results obtained by the authors and other research groups are also explained in this book.

Preface xiii
1 Introduction
1(6)
2 Deformed shell model
7(20)
2.1 Introduction
7(1)
2.2 Hartree--Fock method
8(3)
2.3 Angular momentum projection
11(1)
2.4 Matrix elements of a tensor operator
12(1)
2.5 Matrix elements of the Hamiltonian matrix
13(4)
2.5.1 One-body energy kernel
14(1)
2.5.2 Two-body energy kernel
15(2)
2.6 Orthonormalization and band mixing
17(1)
2.7 Matrix elements of E2 and Ml transition operators
18(5)
2.7.1 Matrix elements of E2 transition operator
18(4)
2.7.2 Matrix elements of Ml transition operator
22(1)
2.8 Summary
23(4)
3 DSM results for spectroscopy of Ge, Se, Br, Kr, and Sr isotopes
27(32)
3.1 Structure of collective bands and triple forking in 68Ge
27(6)
3.1.1 Preliminaries
27(1)
3.1.2 Results: Triple forking of 8+ levels
28(5)
3.1.3 Conclusions
33(1)
3.2 Shape coexistence and role of 1g9/2 orbit in Se isotopes
33(7)
3.2.1 Preliminaries
33(4)
3.2.2 Results: Shape coexistence
37(3)
3.2.3 Conclusions
40(1)
3.3 Band structures and 3qp bands in 77,79,81Br isotopes
40(7)
3.3.1 Preliminaries
40(2)
3.3.2 Results: Three-quasi-particle bands
42(4)
3.3.3 Conclusions
46(1)
3.4 Collective bands and yrast band alignments in 78Kr
47(5)
3.4.1 Preliminaries
47(2)
3.4.2 Results: Band structures
49(3)
3.4.3 Conclusions
52(1)
3.5 Identical bands and collectivity in 77,79Sr
52(6)
3.5.1 Preliminaries
52(2)
3.5.2 Results: Identical bands
54(2)
3.5.3 Conclusions
56(2)
3.6 Summary
58(1)
4 Applications of DSM to GT distributions, muon-electron conversion, and dark matter
59(16)
4.1 GT distributions in Ge, Se, Kr, and Sr isotopes
59(5)
4.1.1 Formulation
59(1)
4.1.2 Results for GT distributions and β+/EC half lives
60(4)
4.2 Transition matrix elements for μ -- e conversion in 72Ge
64(5)
4.2.1 Formulation
64(1)
4.2.2 Results for 72Ge and discussion
65(4)
4.3 DSM application to dark matter: Elastic scattering of LSP from 73Ge
69(3)
4.3.1 Formulation
70(1)
4.3.2 Results and discussion
71(1)
4.4 Summary
72(3)
5 DSM results for double beta decay in A=60--90 nuclei
75(26)
5.1 Introduction
75(2)
5.2 Half-lives and nuclear structure matrix elements for double beta decay
77(3)
5.2.1 2v DBD formulation
77(1)
5.2.2 2v e+DBD formulation
77(1)
5.2.3 0v DBD formulation
78(1)
5.2.4 0v e+DBD formulation
79(1)
5.2.5 DSM formulas for nuclear transition matrix elements
79(1)
5.3 DSM results for two neutrino positron double beta decay
80(5)
5.3.1 Results for 64Zn
80(1)
5.3.2 Results for 74Se
81(2)
5.3.3 Results for 78Kr
83(1)
5.3.4 Results for 84Sr
84(1)
5.4 DSM results for two neutrino double beta decay
85(6)
5.4.1 Results for 70Zn
85(2)
5.4.2 Results for 76Ge
87(1)
5.4.3 Results for 80Se
88(1)
5.4.4 Results for 82Se
88(3)
5.5 DSM results for 0vDBD and 0v e+DBD
91(3)
5.5.1 DSM results for 0vDBD NTME for 70Zn, 80Se, and 82Se
91(2)
5.5.2 DSM results for 0v e+DBD NTME for 64Zn, 74Se, 78Kr, and 84Sr
93(1)
5.6 Shape effects on double beta decay matrix elements
94(6)
5.6.1 Introduction
94(1)
5.6.2 Results for spherical and deformed shapes for 70Zn
95(3)
5.6.3 Results for spherical and deformed shapes for 150Nd
98(2)
5.7 Summary
100(1)
6 Heavy N=Z nuclei: SU(4) structure, Wigner energy, and pn pairing
101(24)
6.1 Introduction
101(2)
6.2 Spin--isospin SU(4) algebra in shell model
103(6)
6.2.1 Quadratic Casimir operators of U(Ω) and SU(4) and the Majorana operator
105(1)
6.2.2 Identification of the ground state U(Ω) and SU(4) irreducible representations
106(3)
6.3 Double binding energy differences and SU(4) symmetry
109(2)
6.4 Wigner energy, SU(4) symmetry and T = 0 and T = 1 states in N=Z odd-odd nuclei
111(3)
6.5 Isoscalar and isovector pairing in N=Z nuclei and new structures due to pn pairing
114(4)
6.6 SO(5) isovector pairing model in j -- j coupling
118(5)
6.6.1 Introduction
118(1)
6.6.2 Shell model Sp(2j +1) algebra for nucleons in a single-j shell
119(1)
6.6.3 SO(5) algebra and its equivalence to Sp(2j + 1) for nucleons with isospin
120(2)
6.6.4 pp, nn and pn pairs in the ground states of nuclei
122(1)
6.7 Summary
123(2)
7 Shell model SO(8) pairing algebra and Dyson mapping to IBM-ST
125(22)
7.1 SO(8) pairing model and its three symmetry limits
125(3)
7.2 Shell model complimentary subalgebra I
128(4)
7.2.1 Algebra with U(Ω) ⊗ SUST(4)
128(1)
7.2.2 Energy spectra
129(2)
7.2.3 Irreps for SO(8) seniority v = 0, 1, 2, 3 and 4 and γ-soft like structure in isospace
131(1)
7.3 Shell model complimentary subalgebra II
132(7)
7.3.1 Algebra with Sp(2Ω) ⊃ SO(Ω) ⊗ SUT(2)
132(3)
7.3.2 Energy spectra
135(1)
7.3.3 Irreps for SO(8) seniority v = 0, 1, 2, 3 and 4 and vibrational structure in isospace
136(3)
7.4 Shell model complimentary subalgebra III
139(1)
7.4.1 Algebra with Sp(2Ω) ⊃ SO(Ω) ⊗ SUS(2)
139(1)
7.4.2 Irreps for SO(8) seniority v = 0, 1, and 2 and rotational structure in isospace
139(1)
7.5 Applications of SO(8) model
140(2)
7.6 Dyson boson mapping of SO(8) model to spin--isospin interacting boson model
142(3)
7.7 Summary
145(2)
8 Spin--isospin interacting boson model (sdIBM-ST)
147(24)
8.1 Introduction to interacting boson model (IBM)
147(3)
8.2 sdIBM-ST model and its symmetry limits
150(6)
8.3 Transformation brackets between U(n) ⊃ U(na) U(nb) ⊃ SO(na) SO(nb) and U(n) ⊃ SO(n) ⊃ SO(na) SO(nb) chains
156(2)
8.4 Usd(6) ⊗ UST(6) limit chains
158(2)
8.5 SOsdST(36) ⊃ SOsST(6) SOdST(30) limit
160(2)
8.6 Simple applications of SOsdST(36) ⊃ SOsST(6) SOdST(30) limit
162(7)
8.6.1 Number of T = 0 pairs in ground states
165(1)
8.6.2 B(E2) values for the yrast band in N=Z odd-odd nuclei with (ST) = (01)
166(1)
8.6.3 Some spectroscopic properties of 74Rb
167(2)
8.7 Summary
169(2)
9 sdIBM-ST applications with competition between T = 0 and T = 1 pairing
171(22)
9.1 Number of T = 0 pairs in heavy N=Z nuclei
171(5)
9.2 Deuteron transfer in heavy N=Z nuclei
176(6)
9.2.1 Transfer intensities
177(1)
9.2.2 Results and comparison with sIBM-ST and SO(8) models
178(4)
9.3 GT strengths in heavy N=Z nuclei
182(4)
9.3.1 Introduction
182(1)
9.3.2 GT operator in sdIBM-ST
183(2)
9.3.3 GT strengths in sdIBM-ST within SOsdST(36) ⊃ SOSST(6) SODST(30) scheme
185(1)
9.4 α-transfer strengths
186(6)
9.5 Summary
192(1)
10 Interacting boson model with isospin (sdIBM-T)
193(18)
10.1 Dynamical symmetries of sdIBM-T: General classification
193(2)
10.2 Symmetry limits with good s and d boson isospins
195(7)
10.2.1 [ Ud(5) ⊗ SUTd(3)] SUTs(3) limit
195(1)
10.2.2 [ Ud(15) ⊃ SOd(15)] SUts(3) limit
196(1)
10.2.3 SOsd(18) ⊃ SOd(15) SOTs(3) limit
197(4)
10.2.4 64Ge example
201(1)
10.3 Symmetry limits with U(18) ⊃ U(6) ⊗ SUT(3) algebra
202(4)
10.4 IBM-T investigations by Elliott et al.: A summary
206(3)
10.5 Summary
209(2)
11 Spectroscopy of heavy N ~ Z nuclei: Results from DSM, IBM, and other models
211(20)
11.1 Introduction
211(1)
11.2 Heavy N=Z odd-odd nuclei in DSM and other models
212(13)
11.2.1 Isospin projection for quasi-deuteron configurations in DSM: Applications to 46V and 50Mn
212(4)
11.2.2 Application to 62Ga
216(2)
11.2.3 Application to 66As
218(4)
11.2.4 Pairing energy in 62Ga and 66As
222(2)
11.2.5 70Br, 74Rb and other N=Z odd-odd nuclei
224(1)
11.3 Structure of heavy even-even N=Z nuclei: 64Ge to 92Pd and results from various models
225(4)
11.3.1 Structure of 64Ge to 88Ru
225(2)
11.3.2 Spin-aligned isoscalar pairs in 92Pd
227(1)
11.3.3 Optimal set of shell model orbits for A=60-100 nuclei
228(1)
11.4 Summary
229(2)
12 Future outlook
231(2)
Appendix A DSM with three-body interactions
233(4)
A.1 HF approximation with a three-body interaction
233(4)
A.1.1 Three-body energy kernels
234(3)
Appendix B U(n) and SO(n) algebras and other group theoretical aspects
237(14)
B.1 U(n) algebra
237(5)
B.1.1 Generators
237(1)
B.1.2 Irreducible representations
238(1)
B.1.3 Casimir operators and their eigenvalues
239(3)
B.2 SO(n) algebra
242(2)
B.2.1 Generators
242(1)
B.2.2 Irreducible representations and Casimir operators
243(1)
B.3 Other Lie algebras
244(4)
B.3.1 Sp(2n) algebra
244(1)
B.3.2 SU(1,1) algebra
245(3)
B.4 Kronecker products
248(3)
Appendix C Subalgebras, irrep reductions, and SO(n) and SU(3) examples in nuclei
251(14)
C.1 General principles for generating group-subgroup chains
252(2)
C.2 Irrep reductions: Some general rules
254(2)
C.3 Further examples for irrep reductions
256(1)
C.4 U(n) ⊃ SO(n) example for boson systems
256(4)
C.5 U((η + 1)(η + 2)/2) ⊃ SU(3) ⊃ SO(3) example
260(5)
C.5.1 {f}U((η + 1)(η + 2)/2) → (λμ)SU(3) irrep reductions and results for (sd) boson systems
262(2)
C.5.2 (λμ)SU(3) → (L)SO(3) reduction and geometric K quantum number
264(1)
Appendix D Isospin projection for 3, 4, 5, and 6 particles
265(8)
D.1 Isospin projection for 3 particles
265(1)
D.2 Isospin projection for 4 particles
266(1)
D.3 Isospin projection for 5 particles
267(2)
D.4 Isospin projection for 6 particles
269(4)
References 273(30)
Index 303
V K B Kota, R Sahu
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