The subject of effective field theory has, in recent years, attracted a great deal of
attention to provide a powerful method for describing non-relativistic quantum
mechanical systems composed of particles with wave numbers k much smaller than
the inverse of the characteristic range R of the effective potential. The underlying
premises of this approach are that particles with short-range interactions and a large
scattering length have universal low-energy properties that do not depend on the
details of their interactions at short distances. Effective field theory has recently
been used to investigate the properties of ultracold atomic systems including the
calculations of three-body recombination into deep bound states in Bose–Einstein
condensates, the Efimov effect in halo nuclei and in general studying the
low-energy properties of three-body scattering systems. Braaten and Hammer [22]
have carried out detailed and systematic studies to investigate the universal properties of few body systems in atomic and nuclear physics within the framework of
effective field theories introducing the concepts of renormalization group.
This brief introduction to the historical development of theoretical techniques of
few body physics, the discovery of the Efimov effect and their application to
understand the amazing structural features of the neutron-rich halo nuclei summarize the intent and scope of this book. Our efforts have been to provide an
overview of the few body scattering theory and techniques developed in nuclear
physics and their applications to explore the structural properties of neutron-rich
unstable nuclei, primarily, the so-called halo nuclei. Readers will gain in-depth
knowledge about the methods involved to solve the two- and three-body scattering
problems and a special focus is put on the Faddeev approach and the power of
separable potentials.
This book makes no attempts or is expected to replace classical and more
formidable texts on scattering theory, namely by Roger Newton, or Watson &
Goldeberger, or Charles Joachain. We basically provide the essentials of formal
scattering theory of two- and three-body systems so as to prepare the reader for their
practical application in the study of Halo nuclei and the Efimov effect in the
following chapters. Formal theory of two- and three-body scattering has been
discussed in Chaps. 1 and 2 in a compact and abridged form to initiate the beginners
who want to attack the problems of halo nuclei within the framework of three-body
models. In this sense, we address both the graduate students and senior researchers.
Chapter 3 is devoted to a detailed analysis of the Efimov effect in three-body
systems. We introduce the basic underlying physics of the Efimov effect in this
chapter and subsequently investigate several two-neutron halo nuclei, both
Borromean and non-Borromean to find whether they are the right candidates to
support Efimov state(s) in Chap. 6. We also discuss in detail, drawing primarily
from our work, how to analyze, within the framework of a three-body approach and
using realistic short-range forces, the structural properties of halo nuclei, namely
binding energies, momentum distributions, neutron-neutron and neutron-core correlations in two-neutron halo nuclei and the very challenging problem of beta decay
of two-neutron halo nuclei in Chap. 6. In Chap. 4, we discuss the recent progress
related to the use of effective field theories for investigating the properties of halo
nuclei. We derive the three-body scattering amplitude in Effective Field Theory
viii
Preface
attention to provide a powerful method for describing non-relativistic quantum
mechanical systems composed of particles with wave numbers k much smaller than
the inverse of the characteristic range R of the effective potential. The underlying
premises of this approach are that particles with short-range interactions and a large
scattering length have universal low-energy properties that do not depend on the
details of their interactions at short distances. Effective field theory has recently
been used to investigate the properties of ultracold atomic systems including the
calculations of three-body recombination into deep bound states in Bose–Einstein
condensates, the Efimov effect in halo nuclei and in general studying the
low-energy properties of three-body scattering systems. Braaten and Hammer [22]
have carried out detailed and systematic studies to investigate the universal properties of few body systems in atomic and nuclear physics within the framework of
effective field theories introducing the concepts of renormalization group.
This brief introduction to the historical development of theoretical techniques of
few body physics, the discovery of the Efimov effect and their application to
understand the amazing structural features of the neutron-rich halo nuclei summarize the intent and scope of this book. Our efforts have been to provide an
overview of the few body scattering theory and techniques developed in nuclear
physics and their applications to explore the structural properties of neutron-rich
unstable nuclei, primarily, the so-called halo nuclei. Readers will gain in-depth
knowledge about the methods involved to solve the two- and three-body scattering
problems and a special focus is put on the Faddeev approach and the power of
separable potentials.
This book makes no attempts or is expected to replace classical and more
formidable texts on scattering theory, namely by Roger Newton, or Watson &
Goldeberger, or Charles Joachain. We basically provide the essentials of formal
scattering theory of two- and three-body systems so as to prepare the reader for their
practical application in the study of Halo nuclei and the Efimov effect in the
following chapters. Formal theory of two- and three-body scattering has been
discussed in Chaps. 1 and 2 in a compact and abridged form to initiate the beginners
who want to attack the problems of halo nuclei within the framework of three-body
models. In this sense, we address both the graduate students and senior researchers.
Chapter 3 is devoted to a detailed analysis of the Efimov effect in three-body
systems. We introduce the basic underlying physics of the Efimov effect in this
chapter and subsequently investigate several two-neutron halo nuclei, both
Borromean and non-Borromean to find whether they are the right candidates to
support Efimov state(s) in Chap. 6. We also discuss in detail, drawing primarily
from our work, how to analyze, within the framework of a three-body approach and
using realistic short-range forces, the structural properties of halo nuclei, namely
binding energies, momentum distributions, neutron-neutron and neutron-core correlations in two-neutron halo nuclei and the very challenging problem of beta decay
of two-neutron halo nuclei in Chap. 6. In Chap. 4, we discuss the recent progress
related to the use of effective field theories for investigating the properties of halo
nuclei. We derive the three-body scattering amplitude in Effective Field Theory
viii
Preface