Efimov in 1970 [13] discovered a remarkable phenomenon that can occur in
three-body sector for non-relativistic particles when at least two of the three pairs of
particles have a large scattering length. Using the hyperspherical approach for the
three-body system, he pointed out that when the two-body scattering length a
j j is
sufficiently large compared to the range r 0 of the potential, there is a sequence of
three-body bound states whose binding energies are spaced roughly geometrically
in the interval between h
2
=ðmr
2
0 Þ and h
2
=ðma
2
Þ. As a is increased, new bound states
appear and, in the limit, as a ! Æ1, there are infinitely many three-body bound
states accumulating near the three-body scattering threshold. An important feature
of the Efimov effect is that the sequence of three-body bound states has universal
properties which are insensitive to the details of the two-body potential at short
distances. Dating back to1970 up to the recent times, tremendous progress in
research of universal Efimov physics in the field of nuclear, atomic and molecular
physics has taken off, driven particularly by a combination of experimental and
theoretical studies [14].
With the advent of facilities for producing intense radioactive nuclear beams
through high-energy fragmentation along with the developments in the state of the
art involving detectors and isotope separators, experiments were carried out during
1990s at various laboratories which opened a new rich field of nuclear physics—the
neutron-rich unstable nuclei. Such light exotic nuclei lie almost on the limit of
nuclear stability corresponding roughly to zero binding energy of the last few
neutrons and are commonly referred as neutron drip line nuclei. The pioneering
experiments [15] which were carried out to investigate the properties of these
so-called halo nuclei such as
8
He,
11
Li,
11
Be,
14
Be,
17
B,
20
C and
22
C, etc., revealed
several striking features such as (i) abnormally large interaction cross sections,
(ii) very weak binding of the last few nucleons leading to systems with qualitatively
new structures and surface densities and (iii) large dissociation cross sections of a
halo nucleus by a high Z-target of a new exotic mode of collective vibrations in the
nucleus.
From the theoretical standpoint, these experimental findings posed serious
challenging problems in studying the structural properties of such halo nuclei using
conventional models, as nuclear shell model and Hartree–Fock formalism [16]. In
certain cases, there was sufficient experimental evidence for the existence of a
structure-less core with two loosely bound neutrons orbiting around it. A typical
example is the
11
Li nucleus where experimental measurements [17] on the magnetic
dipole and electric quadrupole moments give values which are close to those
obtained for
9
Li. Such halo nuclei are the natural candidates for studying their
ground state properties within the framework of three-body formalism.
A characteristic property observed in such nuclei is that for a two-body system such
as n À
9
Li; there exists no bound state but as soon as we bring a second neutron, it
forms a loosely bound three-body system. For this reason, such nuclei were named
as ‘Borromean nuclei’ (‘Borromean’ refers to the famous three-ring system interlinked in such a way that breaking-off any pair causes all the three rings to
separate).
vi
Preface
three-body sector for non-relativistic particles when at least two of the three pairs of
particles have a large scattering length. Using the hyperspherical approach for the
three-body system, he pointed out that when the two-body scattering length a
j j is
sufficiently large compared to the range r 0 of the potential, there is a sequence of
three-body bound states whose binding energies are spaced roughly geometrically
in the interval between h
2
=ðmr
2
0 Þ and h
2
=ðma
2
Þ. As a is increased, new bound states
appear and, in the limit, as a ! Æ1, there are infinitely many three-body bound
states accumulating near the three-body scattering threshold. An important feature
of the Efimov effect is that the sequence of three-body bound states has universal
properties which are insensitive to the details of the two-body potential at short
distances. Dating back to1970 up to the recent times, tremendous progress in
research of universal Efimov physics in the field of nuclear, atomic and molecular
physics has taken off, driven particularly by a combination of experimental and
theoretical studies [14].
With the advent of facilities for producing intense radioactive nuclear beams
through high-energy fragmentation along with the developments in the state of the
art involving detectors and isotope separators, experiments were carried out during
1990s at various laboratories which opened a new rich field of nuclear physics—the
neutron-rich unstable nuclei. Such light exotic nuclei lie almost on the limit of
nuclear stability corresponding roughly to zero binding energy of the last few
neutrons and are commonly referred as neutron drip line nuclei. The pioneering
experiments [15] which were carried out to investigate the properties of these
so-called halo nuclei such as
8
He,
11
Li,
11
Be,
14
Be,
17
B,
20
C and
22
C, etc., revealed
several striking features such as (i) abnormally large interaction cross sections,
(ii) very weak binding of the last few nucleons leading to systems with qualitatively
new structures and surface densities and (iii) large dissociation cross sections of a
halo nucleus by a high Z-target of a new exotic mode of collective vibrations in the
nucleus.
From the theoretical standpoint, these experimental findings posed serious
challenging problems in studying the structural properties of such halo nuclei using
conventional models, as nuclear shell model and Hartree–Fock formalism [16]. In
certain cases, there was sufficient experimental evidence for the existence of a
structure-less core with two loosely bound neutrons orbiting around it. A typical
example is the
11
Li nucleus where experimental measurements [17] on the magnetic
dipole and electric quadrupole moments give values which are close to those
obtained for
9
Li. Such halo nuclei are the natural candidates for studying their
ground state properties within the framework of three-body formalism.
A characteristic property observed in such nuclei is that for a two-body system such
as n À
9
Li; there exists no bound state but as soon as we bring a second neutron, it
forms a loosely bound three-body system. For this reason, such nuclei were named
as ‘Borromean nuclei’ (‘Borromean’ refers to the famous three-ring system interlinked in such a way that breaking-off any pair causes all the three rings to
separate).
vi
Preface