Chapter 6
Three-Body Approach to Structural
Properties of Halo Nuclei and the Efimov
Effect
6.1 Introduction
In this chapter, we present a review of the work carried out during the last more
than two decades to investigate the structural properties of neutron-rich halo nuclei
within the framework of three-body model using separable interactions. The chapter
may be broadly divided into two parts. The first part being mainly concerned with
the study of structural properties of Borromean-type 2n-rich halo nuclei like
11 Li
where, in particular, sufficient experimental data, such as ground state energy, matter
radius, momentum distribution and n–n correlation, excited states in
11 Li above the
breakup threshold and β-decay of
11 Li into different channels, are available. The
second part is devoted to the search for the occurrence of Efimov states in halo
nuclei like
14 Be,
19 B,
22 C and
20 C. Specifically, in the case of
14 Be nucleus, where
we postulated the existence of low-lying virtual state of 2–4 keV in
13 Be to predict
the binding energy
14 Be, the experimental evidence of this low-lying
13 Be state was
later confirmed by the Michigan group. Among the nuclei studied here,
20 C, where
the n−
18 C two-body system has a weak binding to produce the 3-body n−n−
18 C
bound state, is found to be a promising candidate to search for the occurrence of the
Efimov states. This warranted us to extend the formulation to study n−
19 C scattering
at low energies to predict Efimov–Fano type resonant states near the three-body
threshold. Finally, the renormalization procedure employed in effective field theory
equations for the scattering amplitude in n−
19 C scattering, developed in Chap. 4, is
discussed by introducing the three-body scattering length as a subtraction parameter
for computing these equations to present a comparative study with those obtained in
separable potential model.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. S. Bhasin and I. Mazumdar, Few Body Dynamics, Efimov Effect and Halo Nuclei,
SpringerBriefs in Physics,
https://doi.org/10.1007/978-3-030-56171-0_6
69
Three-Body Approach to Structural
Properties of Halo Nuclei and the Efimov
Effect
6.1 Introduction
In this chapter, we present a review of the work carried out during the last more
than two decades to investigate the structural properties of neutron-rich halo nuclei
within the framework of three-body model using separable interactions. The chapter
may be broadly divided into two parts. The first part being mainly concerned with
the study of structural properties of Borromean-type 2n-rich halo nuclei like
11 Li
where, in particular, sufficient experimental data, such as ground state energy, matter
radius, momentum distribution and n–n correlation, excited states in
11 Li above the
breakup threshold and β-decay of
11 Li into different channels, are available. The
second part is devoted to the search for the occurrence of Efimov states in halo
nuclei like
14 Be,
19 B,
22 C and
20 C. Specifically, in the case of
14 Be nucleus, where
we postulated the existence of low-lying virtual state of 2–4 keV in
13 Be to predict
the binding energy
14 Be, the experimental evidence of this low-lying
13 Be state was
later confirmed by the Michigan group. Among the nuclei studied here,
20 C, where
the n−
18 C two-body system has a weak binding to produce the 3-body n−n−
18 C
bound state, is found to be a promising candidate to search for the occurrence of the
Efimov states. This warranted us to extend the formulation to study n−
19 C scattering
at low energies to predict Efimov–Fano type resonant states near the three-body
threshold. Finally, the renormalization procedure employed in effective field theory
equations for the scattering amplitude in n−
19 C scattering, developed in Chap. 4, is
discussed by introducing the three-body scattering length as a subtraction parameter
for computing these equations to present a comparative study with those obtained in
separable potential model.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. S. Bhasin and I. Mazumdar, Few Body Dynamics, Efimov Effect and Halo Nuclei,
SpringerBriefs in Physics,
https://doi.org/10.1007/978-3-030-56171-0_6
69