This book presents an overview of the different few-body techniques developed in nuclear physics and their applications to explore the structural properties of neutron-rich unstable nuclei, the so-called halo nuclei. Formal theory of two- and three-body scattering are discussed in a compact and abridged form to initiate the beginners who want to investigate the problems of halo nuclei within the framework of three-body models. Readers gain in-depth knowledge about the methods involved to solve the two- and three-body scattering problem and a special focus is put on the Faddeev approach. In this sense, the authors address both the graduate students and senior researchers. Subsequently, a detailed analysis of the Efimov effect in three-body systems is presented and the search for the effect in atomic nuclei, both Borromean and non-Borromean is addressed. The book also presents a detailed account of how to analyze, within the framework of a 3-body approach and using realistic short range forces, the structural properties of halo nuclei. Finally, the authors discuss the recent progress in effective field theory by setting up the integral equations for 3-body scattering and applying it to study low energy scattering of neutrons off halo nuclear targets.
Author(s): Vidya Sagar Bhasin; Indranil Mazumdar
Series: SpringerBriefs in Physics
Publisher: Springer
Year: 2021
Language: English
Pages: 127
City: Cham
Preface
Acknowledgements
Contents
About the Authors
1 Essentials of Non-relativistic Two-Body Scattering Theory
1.1 Introduction
1.2 Boundary Condition of the Scattering State: Basic Concepts
1.3 Moller Operator
1.4 Resolvent Equation and Lippmann–Schwinger Equation
1.5 The S-Matrix, T-Matrix and Differential Cross Section
1.6 The Unitarity of S-Matrix and Optical Theorem
2 Scattering Theory of Three-Particle System
2.1 Introduction
2.2 Three-Particle Hamiltonian, Channel Hamiltonian, Matrix-Elements for the Green’s Functions and T-Matrix
2.3 Boundary Conditions and Moller Operators
2.4 Difficulties with the 3-Particle Lippmann–Schwinger Equation
2.4.1 Non-uniqueness of the Boundary Conditions
2.4.2 Disconnectedness of the Kernel
2.5 The Faddeev Equations
2.6 Faddeev Equations for Scattering States
2.7 Three-Body Problem with Separable Potentials
2.7.1 How the Problems of Disconnectedness and the Uniqueness of Boundary Conditions Are Tackled Here?
3 Efimov’s Universal Three-Body Effect
3.1 Introduction
3.2 Relation Between Total Cross Section and Scattering Length for Two Particles at Low Energies
3.3 Efimov Effect in Three-Boson System
3.4 Salient Feature of Efimov Effect
3.5 Predictions on the Properties of Three-Nucleon System
3.5.1 Studying the Anomalous Behavior Due to Efimov Effect in Spin-Doublet N-D Scattering Near Threshold
3.5.2 Appearance of Efimov Effect in Three-Body Separable Potential Approach
4 Effective Field Theory
4.1 Introduction
4.2 Two-Body Problem: N-N Scattering at Low Energies in Effective Field Theory
4.3 Three-Body Scattering Problem in Effective Field Theory
4.4 Derivation of Three-Body Scattering Amplitude in Effective Field Theory Approaching from Separable Potentials
5 Halo Nuclei: Properties and Experimental Techniques
5.1 Halo Nuclei: A Brief Introduction
5.2 Salient Structural Features of Halo Nuclei
5.3 Known Halo Nuclei and Unbound Nuclei Beyond the Drip Line
5.4 Production of RIB and Major Facilities
5.5 Reaction Studies with Halo Nuclei
6 Three-Body Approach to Structural Properties of Halo Nuclei and the Efimov Effect
6.1 Introduction
6.2 11Li Halo Nucleus as a Three-Body System: Ground State Properties (Binding Energy, Matter Radius, n–n and n-core Correlations)
6.3 Resonant States of 11Li, Probability Distributions and β-decay of Halo Analog States
6.3.1 Ground State of 11Li
6.3.2 Probability Distribution in 11Li
6.3.3 n–n Correlations in 11Li from Momentum Distributions
6.3.4 Resonant States of 11Li Above the Three-Body Threshold
6.3.5 Wave Function of Analog 11Be* (18.3 MeV) State in a Three-Body (9Li + n + p) Model
6.3.6 β-Decay of 11Li to Halo Analog 11Be* (18.3 MeV) State
6.3.7 β-Decay of 11Li to 9Li + deuteron Channel
6.4 Search for Efimov States in Halo Nuclei like 14Be, 19B, 22C and 20C
6.5 Theoretical Analysis/Interpretation for the Efimov States from the Model Equation
6.6 Occurrence of Efimov States in 20C
6.7 Movement of Efimov States in 20 C Causing Resonance in n -19 C Scattering Near Threshold
6.8 Efimov States and Their Fano Resonances in a Neutron-Rich Nucleus
6.9 Generalizing the Study of Efimov Effect in Neutron-Rich (2n-Heavy Core) Nuclei Employing the Above Three-Body Approach
6.10 Efimov Effect in Halo Nuclei Using Effective Field Theory
7 Summary and Future Outlook
7.1 Future Outlook
Bibliography
