Kota, V. K. B.,
Structure of medium mass nuclei : deformed shell model and spin-isospin interacting boson model / by V K B Kota and R Sahu. - 1 online resource (320 pages) : 86 illustrations
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- 1: Introduction -- 2: Deformed shell model -- 2.1 Introduction -- 2.2 Hartree�Fock method -- 2.3 Angular momentum projection -- 2.4 Matrix elements of a tensor operator -- 2.5 Matrix elements of the Hamiltonian matrix -- 2.6 Orthonormalization and band mixing -- 2.7 Matrix elements of E2 and M1 transition operators -- 2.8 Summary -- 3: DSM results for spectroscopy of Ge, Se, Br, Kr, and Sr isotopes -- 3.1 Structure of collective bands and triple forking in 68Ge -- 3.2 Shape coexistence and role of 1g9/2 orbit in Se isotopes -- 3.3 Band structures and 3qp bands in 77,79,81Br isotopes -- 3.4 Collective bands and yrast band alignments in 78Kr -- 3.5 Identical bands and collectivity in 77,79Sr -- 3.6 Summary -- 4: Applications of DSM to GT distributions, muon-electron conversion, and dark matter -- 4.1 GT distributions in Ge, Se, Kr, and Sr isotopes -- 4.2 Transition matrix elements for - e conversion in 72Ge -- 4.3 DSM application to dark matter: Elastic scattering of LSP from 73Ge -- 4.4 Summary -- 5: DSM results for double beta decay in A60-90 nuclei -- 5.1 Introduction -- 5.2 Half-lives and nuclear structure matrix elements for double beta decay -- 5.3 DSM results for two neutrino positron double beta decay -- 5.4 DSM results for two neutrino double beta decay -- 5.5 DSM results for 0?DBD and 0? e+DBD -- 5.6 Shape effects on double beta decay matrix elements -- 5.7 Summary -- 6: Heavy NZ nuclei: SU(4) structure, Wigner energy, and pn pairing -- 6.1 Introduction -- 6.2 Spin�isospin SU(4) algebra in shell model -- 6.3 Double binding energy differences and SU(4) symmetry -- 6.4 Wigner energy, SU(4) symmetry and T 0 and T 1 states in NZ odd-odd nuclei -- 6.5 Isoscalar and isovector pairing in NZ nuclei and new structures due to pn pairing -- 6.6 SO(5) isovector pairing model in j - j coupling -- 6.7 Summary -- 7: Shell model SO(8) pairing algebra and Dyson mapping to IBM-ST -- 7.1 SO(8) pairing model and its three symmetry limits -- 7.2 Shell model complimentary subalgebra I -- 7.3 Shell model complimentary subalgebra II -- 7.4 Shell model complimentary subalgebra III -- 7.5 Applications of SO(8) model -- 7.6 Dyson boson mapping of SO(8) model to spin�isospin interacting boson model -- 7.7 Summary -- 8: Spin�isospin interacting boson model (sdIBM-ST) -- 8.1 Introduction to interacting boson model (IBM). 8.2 sdIBM-ST model and its symmetry limits -- 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 -- 8.4 Usd(6) UST (6) limit chains -- 8.5 SOsdST (36) SOsST (6) SOdST (30) limit -- 8.6 Simple applications of SOsdST (36) SOsST (6) SOdST (30) limit -- 8.7 Summary -- 9: sdIBM-ST applications with competition between T 0 and T 1 pairing -- 9.1 Number of T 0 pairs in heavy NZ nuclei -- 9.2 Deuteron transfer in heavy NZ nuclei -- 9.3 GT strengths in heavy NZ nuclei -- 9.4 a-transfer strengths -- 9.5 Summary -- 10: Interacting boson model with isospin (sdIBM-T) -- 10.1 Dynamical symmetries of sdIBM-T: General classification -- 10.2 Symmetry limits with good s and d boson isospins -- 10.3 Symmetry limits with U(18). U(6) SUT (3) algebra -- 10.4 IBM-T investigations by Elliott and others : A summary -- 10.5 Summary -- 11: Spectroscopy of heavy N ~ Z nuclei: Results from DSM, IBM, and other models -- 11.1 Introduction -- 11.2 Heavy NZ odd-odd nuclei in DSM and other models -- 11.3 Structure of heavy even-even NZ nuclei: 64Ge to 92Pd and results from various models -- 11.4 Summary -- 12: Future outlook -- Appendix A: DSM with three-body interactions -- A.1 HF approximation with a three-body interaction -- Appendix B: U(n) and SO(n) algebras and other group theoretical aspects -- B.1 U(n) algebra -- B.2 SO(n) algebra -- B.3 Other Lie algebras -- B.4 Kronecker products -- Appendix C: Subalgebras, irrep reductions, and SO(n) and SU(3) examples in nuclei -- C.1 General principles for generating group-subgroup chains -- C.2 Irrep reductions: Some general rules -- C.3 Further examples for irrep reductions -- C.4 U(n) SO(n) example for boson systems -- C.5 U((? + 1)(? + 2)/2) SU(3) SO(3) example -- Appendix D :Isospin projection for 3, 4, 5, and 6 particles -- D.1 Isospin projection for 3 particles -- D.2 Isospin projection for 4 particles -- D.3 Isospin projection for 5 particles -- D.4 Isospin projection for 6 particles -- References -- Index.
Medium heavy nuclei with mass number A=60-90 exhibit a variety of complex collective properties, provide a laboratory for double beta decay studies, andare 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.
9781315186382 9781498753708
10.1201/9781315186382 doi
Nuclear excitation.
Nuclear models.
Nuclear structure.
QC793.3.S8 / K68 2017
539.7/43
Structure of medium mass nuclei : deformed shell model and spin-isospin interacting boson model / by V K B Kota and R Sahu. - 1 online resource (320 pages) : 86 illustrations
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- 1: Introduction -- 2: Deformed shell model -- 2.1 Introduction -- 2.2 Hartree�Fock method -- 2.3 Angular momentum projection -- 2.4 Matrix elements of a tensor operator -- 2.5 Matrix elements of the Hamiltonian matrix -- 2.6 Orthonormalization and band mixing -- 2.7 Matrix elements of E2 and M1 transition operators -- 2.8 Summary -- 3: DSM results for spectroscopy of Ge, Se, Br, Kr, and Sr isotopes -- 3.1 Structure of collective bands and triple forking in 68Ge -- 3.2 Shape coexistence and role of 1g9/2 orbit in Se isotopes -- 3.3 Band structures and 3qp bands in 77,79,81Br isotopes -- 3.4 Collective bands and yrast band alignments in 78Kr -- 3.5 Identical bands and collectivity in 77,79Sr -- 3.6 Summary -- 4: Applications of DSM to GT distributions, muon-electron conversion, and dark matter -- 4.1 GT distributions in Ge, Se, Kr, and Sr isotopes -- 4.2 Transition matrix elements for - e conversion in 72Ge -- 4.3 DSM application to dark matter: Elastic scattering of LSP from 73Ge -- 4.4 Summary -- 5: DSM results for double beta decay in A60-90 nuclei -- 5.1 Introduction -- 5.2 Half-lives and nuclear structure matrix elements for double beta decay -- 5.3 DSM results for two neutrino positron double beta decay -- 5.4 DSM results for two neutrino double beta decay -- 5.5 DSM results for 0?DBD and 0? e+DBD -- 5.6 Shape effects on double beta decay matrix elements -- 5.7 Summary -- 6: Heavy NZ nuclei: SU(4) structure, Wigner energy, and pn pairing -- 6.1 Introduction -- 6.2 Spin�isospin SU(4) algebra in shell model -- 6.3 Double binding energy differences and SU(4) symmetry -- 6.4 Wigner energy, SU(4) symmetry and T 0 and T 1 states in NZ odd-odd nuclei -- 6.5 Isoscalar and isovector pairing in NZ nuclei and new structures due to pn pairing -- 6.6 SO(5) isovector pairing model in j - j coupling -- 6.7 Summary -- 7: Shell model SO(8) pairing algebra and Dyson mapping to IBM-ST -- 7.1 SO(8) pairing model and its three symmetry limits -- 7.2 Shell model complimentary subalgebra I -- 7.3 Shell model complimentary subalgebra II -- 7.4 Shell model complimentary subalgebra III -- 7.5 Applications of SO(8) model -- 7.6 Dyson boson mapping of SO(8) model to spin�isospin interacting boson model -- 7.7 Summary -- 8: Spin�isospin interacting boson model (sdIBM-ST) -- 8.1 Introduction to interacting boson model (IBM). 8.2 sdIBM-ST model and its symmetry limits -- 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 -- 8.4 Usd(6) UST (6) limit chains -- 8.5 SOsdST (36) SOsST (6) SOdST (30) limit -- 8.6 Simple applications of SOsdST (36) SOsST (6) SOdST (30) limit -- 8.7 Summary -- 9: sdIBM-ST applications with competition between T 0 and T 1 pairing -- 9.1 Number of T 0 pairs in heavy NZ nuclei -- 9.2 Deuteron transfer in heavy NZ nuclei -- 9.3 GT strengths in heavy NZ nuclei -- 9.4 a-transfer strengths -- 9.5 Summary -- 10: Interacting boson model with isospin (sdIBM-T) -- 10.1 Dynamical symmetries of sdIBM-T: General classification -- 10.2 Symmetry limits with good s and d boson isospins -- 10.3 Symmetry limits with U(18). U(6) SUT (3) algebra -- 10.4 IBM-T investigations by Elliott and others : A summary -- 10.5 Summary -- 11: Spectroscopy of heavy N ~ Z nuclei: Results from DSM, IBM, and other models -- 11.1 Introduction -- 11.2 Heavy NZ odd-odd nuclei in DSM and other models -- 11.3 Structure of heavy even-even NZ nuclei: 64Ge to 92Pd and results from various models -- 11.4 Summary -- 12: Future outlook -- Appendix A: DSM with three-body interactions -- A.1 HF approximation with a three-body interaction -- Appendix B: U(n) and SO(n) algebras and other group theoretical aspects -- B.1 U(n) algebra -- B.2 SO(n) algebra -- B.3 Other Lie algebras -- B.4 Kronecker products -- Appendix C: Subalgebras, irrep reductions, and SO(n) and SU(3) examples in nuclei -- C.1 General principles for generating group-subgroup chains -- C.2 Irrep reductions: Some general rules -- C.3 Further examples for irrep reductions -- C.4 U(n) SO(n) example for boson systems -- C.5 U((? + 1)(? + 2)/2) SU(3) SO(3) example -- Appendix D :Isospin projection for 3, 4, 5, and 6 particles -- D.1 Isospin projection for 3 particles -- D.2 Isospin projection for 4 particles -- D.3 Isospin projection for 5 particles -- D.4 Isospin projection for 6 particles -- References -- Index.
Medium heavy nuclei with mass number A=60-90 exhibit a variety of complex collective properties, provide a laboratory for double beta decay studies, andare 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.
9781315186382 9781498753708
10.1201/9781315186382 doi
Nuclear excitation.
Nuclear models.
Nuclear structure.
QC793.3.S8 / K68 2017
539.7/43