3.5 Predictions on the Properties of Three-Nucleon System . . . . . . . . 37
3.5.1 Studying the Anomalous Behavior Due to Efimov Effect
in Spin-Doublet N-D Scattering Near Threshold . . . . . . . 38
3.5.2 Appearance of Efimov Effect in Three-Body Separable
Potential Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4 Effective Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Two-Body Problem: N-N Scattering at Low Energies
in Effective Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Three-Body Scattering Problem in Effective Field Theory . . . . . . 46
4.4 Derivation of Three-Body Scattering Amplitude in Effective
Field Theory Approaching from Separable Potentials . . . . . . . . . 48
5 Halo Nuclei: Properties and Experimental Techniques . . . . . . . . . . . 57
5.1 Halo Nuclei: A Brief Introduction . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 Salient Structural Features of Halo Nuclei . . . . . . . . . . . . . . . . . 60
5.3 Known Halo Nuclei and Unbound Nuclei Beyond the Drip
Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.4 Production of RIB and Major Facilities . . . . . . . . . . . . . . . . . . . 66
5.5 Reaction Studies with Halo Nuclei . . . . . . . . . . . . . . . . . . . . . . 67
6 Three-Body Approach to Structural Properties of Halo Nuclei and
the Efimov Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2
11 Li Halo Nucleus as a Three-Body System: Ground State
Properties (Binding Energy, Matter Radius, n–n and n-core
Correlations) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.3 Resonant States of
11 Li, Probability Distributions and b-decay
of Halo Analog States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.3.1 Ground State of
11 Li . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.3.2 Probability Distribution in
11 Li . . . . . . . . . . . . . . . . . . . . 78
6.3.3 n–n Correlations in
11 Li from Momentum Distributions . . . 80
6.3.4 Resonant States of
11 Li Above the Three-Body
Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3.5 Wave Function of Analog
11 Be* (18.3 MeV) State
in a Three-Body (
9 Li + n + p) Model . . . . . . . . . . . . . . . 83
6.3.6 b-Decay of
11 Li to Halo Analog
11 Be* (18.3 MeV)
State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.3.7 b-Decay of
11 Li to
9 Li + deuteron Channel . . . . . . . . . . . 88
6.4 Search for Efimov States in Halo Nuclei like
14 Be,
19 B,
22 C
and
20 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.5 Theoretical Analysis/Interpretation for the Efimov States
from the Model Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.6 Occurrence of Efimov States in
20 C . . . . . . . . . . . . . . . . . . . . . . 96
xiv
Contents
3.5.1 Studying the Anomalous Behavior Due to Efimov Effect
in Spin-Doublet N-D Scattering Near Threshold . . . . . . . 38
3.5.2 Appearance of Efimov Effect in Three-Body Separable
Potential Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4 Effective Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Two-Body Problem: N-N Scattering at Low Energies
in Effective Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Three-Body Scattering Problem in Effective Field Theory . . . . . . 46
4.4 Derivation of Three-Body Scattering Amplitude in Effective
Field Theory Approaching from Separable Potentials . . . . . . . . . 48
5 Halo Nuclei: Properties and Experimental Techniques . . . . . . . . . . . 57
5.1 Halo Nuclei: A Brief Introduction . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 Salient Structural Features of Halo Nuclei . . . . . . . . . . . . . . . . . 60
5.3 Known Halo Nuclei and Unbound Nuclei Beyond the Drip
Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.4 Production of RIB and Major Facilities . . . . . . . . . . . . . . . . . . . 66
5.5 Reaction Studies with Halo Nuclei . . . . . . . . . . . . . . . . . . . . . . 67
6 Three-Body Approach to Structural Properties of Halo Nuclei and
the Efimov Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2
11 Li Halo Nucleus as a Three-Body System: Ground State
Properties (Binding Energy, Matter Radius, n–n and n-core
Correlations) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.3 Resonant States of
11 Li, Probability Distributions and b-decay
of Halo Analog States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.3.1 Ground State of
11 Li . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.3.2 Probability Distribution in
11 Li . . . . . . . . . . . . . . . . . . . . 78
6.3.3 n–n Correlations in
11 Li from Momentum Distributions . . . 80
6.3.4 Resonant States of
11 Li Above the Three-Body
Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3.5 Wave Function of Analog
11 Be* (18.3 MeV) State
in a Three-Body (
9 Li + n + p) Model . . . . . . . . . . . . . . . 83
6.3.6 b-Decay of
11 Li to Halo Analog
11 Be* (18.3 MeV)
State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.3.7 b-Decay of
11 Li to
9 Li + deuteron Channel . . . . . . . . . . . 88
6.4 Search for Efimov States in Halo Nuclei like
14 Be,
19 B,
22 C
and
20 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.5 Theoretical Analysis/Interpretation for the Efimov States
from the Model Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.6 Occurrence of Efimov States in
20 C . . . . . . . . . . . . . . . . . . . . . . 96
xiv
Contents