Nuclear Structure Physics

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Editors
Contributors
1 Magic Numbers of Cylindrical Symmetry
	1.1 Introduction
	1.2 The Origin of QQ Interaction
	1.3 The Nilsson Model
		1.3.1 The Nilsson Basis
	1.4 The Elliott SU(3)
		1.4.1 Derivation of the Highest Weight Irrep
		1.4.2 The Collective Operators
		1.4.3 The SU(3) →SU(2) × U(1) Decomposition
	1.5 Proxy-SU(3) Symmetry
		1.5.1 The Exact Symmetry Behind Proxy-SU(3)
	1.6 Magic Numbers Below 28
	1.7 Magic Numbers → Shape Coexistence → Inversion of States
	1.8 Conclusions
	Acknowledgements
	References
2 Skyrme and Relativistic Mean-Field Models in the Description of Symmetric, Asymmetric, and Stellar Nuclear Matter
	2.1 Introduction
	2.2 Relativistic Mean-Field Models
		2.2.1 Finite Range Model Description
		2.2.2 Energy Density and Pressure
		2.2.3 Incompressibility
		2.2.4 Chemical Potentials
		2.2.5 Symmetry Energy and Its Derivatives
		2.2.6 Neutron Star Environment
		2.2.7 Other Kind of Models
	2.3 The Skyrme Interaction
		2.3.1 Nuclear Matter
		2.3.2 Incompressibility and the Three-Body Force
		2.3.3 Full-Skyrme Equation of State for Symmetric Nuclear Matter
		2.3.4 Asymmetric Nuclear Matter
		2.3.5 Neutron Star Environments
		2.3.6 Beyond the Standard Skyrme Model
	2.4 Conclusion
	Acknowledgements
	References
3 Recent Parameterization in Relativistic Mean-Field Formalism
	3.1 Introduction
	3.2 The Relativistic Mean-Field Formalism
		3.2.1 Finite Nuclei
		3.2.2 Infinite Nuclear Matter
	3.3 New Parameterization
	3.4 Results and Discussions
		3.4.1 Finite Nuclei
			3.4.1.1 Binding Energy
			3.4.1.2 Isotopic Shift
			3.4.1.3 Neutron Skin Thickness (ΔR[sub(np)])
			3.4.1.4 Prediction of Magic Number in Superheavy Valley
		3.4.2 Infnite Nuclear Matter
			3.4.2.1 Equation of State (EOS) for Nuclear Matter
			3.4.2.2 Neutron Star
			3.4.2.3 Tidal Deformability
	3.5 Summary and Conclusions
	Acknowledgments
	References
4 Nuclear Symmetry Energy in Finite Nuclei
	4.1 Introduction
	4.2 Theoretical Formalism
		4.2.1 The Key EOS Parameters in Nuclear Matter
		4.2.2 Deformed HF+BCS Formalism and HFB Method with Skyrme Forces
		4.2.3 The Coherent Density Fluctuation Model (CDFM)
		4.2.4 Energy-Density Functionals for Infinite Nuclear Matter
		4.2.5 Temperature Dependence of the Symmetry Energy and Relationships Concerning Its Volume and Surface Contributions
	4.3 Results and Discussion
		4.3.1 Spherical Nuclei: Ni (A=74−84), Sn (A = 124−152), and Pb (A = 202−214)
		4.3.2 Deformed Nuclei: Kr (A=82−120) and Sm (A = 140−156)
		4.3.3 Neutron-Deficient and Neutron-Rich Mg Isotopes with A = 20–36
		4.3.4 Temperature-Dependent Symmetry Energy Coefficient, Densities, Nuclear Radii, and Neutron Skins
		4.3.5 Temperature Dependence of the Volume and Surface Components of the Nuclear Symmetry Energy
	4.4 Conclusions
	References
5 Theoretical Description of Low-Energy Nuclear Fusion
	5.1 Introduction
	5.2 Theoretical Formalisms
		5.2.1 Semi-classical Extended Thomas Fermi (ETF) Model
		5.2.2 Relativistic Mean-Field Approach
		5.2.3 São Paulo Potential
		5.2.4 Coupled Channel Approach
		5.2.5 The l-Summed Extended Wong Model and Wong Formula
	5.3 Results and Discussions
		5.3.1 Nuclear Potential from Skyrme Energy Density Formalism
		5.3.2 Nuclear Potential from Relativistic Mean-Field Theory
		5.3.3 Nuclear Potentials for São Paulo Potential
		5.3.4 Various Phenomenological Nuclear Potentials
	5.4 Factors Affecting Sub-barrier Fusion
		5.4.1 Deformation and Orientation
		5.4.2 Surface Energy Constant (Ý) and Angular Momentum (l)
		5.4.3 Barrier Modification through a Projectile Breakup
	5.5 Fusion Cross Section
		5.5.1 Cross Section from Skyrme Energy Density Formalism
		5.5.2 Cross Section from Relativistic Mean-Field Theory
		5.5.3 Effect of Orientation and Deformation on the Cross Section
	5.6 Summary and Conclusions
	Acknowledgments
	References
6 Cluster-Decay Model for Hot and Rotating Compound Nuclei
	6.1 Introduction
	6.2 Methodology
		6.2.1 Dynamical Cluster-Decay Model (DCM)
	6.3 Results and Discussion
		6.3.1 Clustering Effects and Fragmentation in Light-Mass Nuclear Systems
		6.3.2 Effect of N/Z Ratio of Nuclear Systems on the Decay Channels
		6.3.3 Fusion Cross Sections, Neck-Length Parameter and Predictability of DCM
			6.3.3.1 [sup(7)]Li-, [sup(7)]Be-, and [sup(9)]Be-Induced Reactions Leading to A =30–200
			6.3.3.2 [sup(20)]Ne-Induced Reactions in Medium-Mass Region
	6.4 Summary
	Acknowledgment
	References
7 Explorations within the Preformed Cluster Decay Model
	7.1 Introduction
		7.1.1 Alpha and Cluster Radioactivity
		7.1.2 Shell Corrections and Cluster Radioactivity
	7.2 The Preformed Cluster Decay Model
	7.3 Alpha, Cluster Radioactivity, and Preformed Cluster Decay Model
		7.3.1 α-Radioactivity and α-Cluster Preformation Probability P[sub(0)][sup(α)]
		7.3.2 Cluster Radioactivity in trans-Pb Region and Effects of Deformation
		7.3.3 Shell Correction and Cluster Radioactivity
	7.4 Conclusions
	Acknowledgments
	Bibliography
8 Studies on Synthesis and Decay of Superheavy Elements with Z = 122
	8.1 Introduction
	8.2 Phenomenological Model for Production Cross Section (PMPC)
	8.3 Results and Discussion
	8.4 Conclusions
	References
9 Decay Dynamics of Ground- and Excited-State Nuclear Systems Using Collective Clusterization Approach
	9.1 Introduction
	9.2 Collective Clusterization Method (CCM) for Ground- and Excited-State Decays
		9.2.1 Dynamical (or Quantum Mechanical) Fragmentation Theory
		9.2.2 Preformed Cluster Decay Model (PCM) for Ground-State Emission Channels
			9.2.2.1 Application of Preformed Cluster Decay Model (PCM) for Ground-State Decays
		9.2.3 Dynamical Cluster Decay Model (DCM) for Excited-State Emissions
			9.2.3.1 Dynamics of Compound Nuclei Formed in Heavy-Ion-Induced Reactions
	9.3 Summary and Outlook
	Acknowledgments
	References
10 Spectroscopic Properties of Nuclei in Generalized Seniority Scheme
	10.1 Introduction
	10.2 Pairing Operators
	10.3 Pairing in Quasi-spin Scheme: Seniority
	10.4 Generalized Seniority
	10.5 Seniority Isomerism
	10.6 Summary
	Acknowledgment
	Appendix: Quasi-Spin Algebra
	References
11 Nuclear High-Spin Spectroscopy in the A ∼ 60 Mass Region
	11.1 Introduction
		11.1.1 Shape Coexistence
		11.1.2 Band Termination
		11.1.3 Superdeformation
		11.1.4 Interesting Facts in the A ∼ 60 Mass Region
		11.1.5 Why Cranking Model Is Good at High Spin in the A ∼ 60 Mass Region
	11.2 Cranked Nilsson–Strutinsky (CNS) Model
		11.2.1 Nilsson Model
		11.2.2 Cranking Model
		11.2.3 Cranked Nilsson–Strutinsky (CNS)
	11.3 Results on Few Nuclei
		11.3.1 Ni[sup(60)]
		11.3.2 Cu[sup(59)]
		11.3.3 Zn[sup(61)]
		11.3.4 Zn[sup(62)]
	11.4 Configuration Assignment on Superdeformed Bands
	11.5 New Nilsson Parameters
		11.5.1 Results with the New Nilsson Parameters
	11.6 Conclusion
	References
12 Nuclear Structure Aspects of Bubble Nuclei
	12.1 Introduction
	12.2 Bubble Effect in Light- and Medium-Mass Nuclei
	12.3 Bubble Effect in Superheavy Nuclei
	12.4 Roles of Tensor Forces, Pairing, and Deformation in Bubble Nuclei
	12.5 Roles of Shell Gaps and Spin-Orbit Splitting in the Formation of Bubble Nuclei
	12.6 Anti-bubble Effect in Magic Nuclei
	12.7 Summary and Conclusion
	Acknowledgments
	References
13 Correlation of Nuclear Structure Observable with the Nuclear Reaction Measurable in the Aspect of Astrophysical P-Process
	13.1 Introduction
		13.1.1 Nucleosynthesis: What Is the Origin of Chemical Elements? How Are They Formed?
			13.1.1.1 Nucleosynthesis of Elements Z > 26
		13.1.2 Abundance of Elements
		13.1.3 Theoretical Research Advancements in the Study of P-Process
	13.2 Formalism
		13.2.1 Nuclear Structure Formalism
		13.2.2 Pairing Approach in RMF
		13.2.3 RMF Parametrization
		13.2.4 Nuclear Reaction Formalism
			13.2.4.1 Reaction Cross Section
	13.3 Results and Discussion
		13.3.1 Ground-State Properties: Nuclear Densities, Binding Energy, rms Matter Radii, and rms Charge Radii
		13.3.2 The Cross Section of [sup(92,94,98)]Mo (p, γ) [sup(93,95,99)]Tc
		13.3.3 Cross Section of [sup(92,94,98)]Mo (α, γ) [sup(96,98,102)]Ru
	13.4 Conclusion
	References
14 Constraining the Nuclear Matter EoS from the Properties of Celestial Objects
	14.1 Introduction
	14.2 Theoretical Framework
		14.2.1 The Relativistic Mean-Field Theory
		14.2.2 Skyrme Energy Density Functional
		14.2.3 Properties of Nuclear Matter and Tidal Deformability
	14.3 Results and Discussions
		14.3.1 Nuclear Matter Equation of State
		14.3.2 Tidal Deformability
	14.4 Conclusions
	References
15 Weak Interactions and Nuclear Structure
	15.1 Introduction: Weak Interactions, Standard Model, and Nuclear Physics
	15.2 Beta Decay in Nuclei
		15.2.1 Weak Processes in Nuclei
		15.2.2 Fermi and Gamow-Teller Transitions
		15.2.3 Lifetime in Beta Decay
		15.2.4 Briefly about Actual Data
		15.2.5 Gamow-Teller Transitions and the Quenching Problem
	15.3 Relation to Fundamental Theory
		15.3.1 Quark Mixing (CKM) Matrix
		15.3.2 Isospin Violation
		15.3.3 To the Evaluation of Unitarity
	15.4 Weak Interactions and Astrophysics
	15.5 Parity Violation
		15.5.1 Parity Violation and Neutrino
		15.5.2 Mixing of Neutron Resonances
		15.5.3 Parity Violation in Fission
		15.5.4 The Doorway State Model
		15.5.5 Anapole Moment
		15.5.6 Parity Violation in Neutral Currents
	15.6 Electric Dipole Moment
		15.6.1 Possible Nuclear Enhancement of EDM
		15.6.2 Schiff Moment
		15.6.3 The EDM of [sup(199)] Hg
		15.6.4 Rotational Doublets and T-, P-Odd Moments
		15.6.5 Enhancement Factors in Pear-Shaped Nuclei
		15.6.6 Experiments with Pear-Shaped Nuclei
	15.7 Neutrino-Nucleus Reactions
		15.7.1 Introduction
		15.7.2 Experimental Studies
		15.7.3 Theoretical Framework
		15.7.4 Random Phase Approximation and the Shell Model
	Acknowledgments
	References
Index