We had undertaken this project from early nineties to investigate the structural
properties of such halo nuclei. Soon after we realized that these nuclei with halo
structure and very weak binding characterized by large n-n scattering length could
well be suited to study the Efimov effect. Subsequently, in 2n-halo nuclei like
14
Be;
19
B;
22
C and
20
C, we carried out the analysis of the occurrence of Efimov
states. The analysis showed that Borromean-type nuclei, where n-n and n-core are
both unbound, are much less vulnerable to respond to the existence of Efimov
states. On the contrary, nuclei like
20
C in which the halo neutron is supposed to be
in the intruder low-lying bound state with the core appear to be promising candidates for the occurrence of the Efimov states at energies below the n-(nc) breakup
threshold. This motivated us to extend our study of the scattering of neutron on a
bound (n À
18
CÞ system and showed that the Efimov states in
20
C move over to the
physical scattering region causing a resonance in n À
19
C scattering around neutron
incident energy of 1.6 keV. The scope of this work was enlarged beyond
20
Cto
include heavier nuclei like
32
Ne and
38
Mg in which the two neutrons are very
weakly bound to the core.
In addition to the study of Efimov effect in halo nuclei, the structural properties
of
11
Li as for instance (i) matter radius, momentum distributions of the halo neutrons and the core and n-n and n-c correlations, (ii) the resonant states of
11
Li in the
continuum and (iii) b-decay of
11
Li were also investigated. The details of these
results along with the discussions will be presented in the following chapters.
Another area in the field of universal Efimov physics which has witnessed
tremendous progress during the last decade is the subject of ultra-cold atomic systems. The first experimental evidence of Efimov resonance was reported in 2006 by
Kraemer et al. [18] in an optically trapped ultra-cold gas of cesium atoms.
Experimentally, its signature as a giant three-body recombination loss was noticed
by magnetically tuning the s-wave scattering length in a range between –2500 a 0
and +1600 a 0 (a 0 being the Bohr radius). In addition to the prominent three-body
Efimov resonance at a
3b
1 ¼ À850a 0 , a broad, weaker resonance feature was visible at
a scattering length near a = –370 Bohr radii. The agreement of its position with the
predicted universal four-body resonance location suggests that this feature is in fact
associated with four-body loss and represents the lower energy tetramer resonance
state. The four-body nature of those loss features was subsequently verified in 2009
by Ferlaino et al. [19]. Before these universal features were observed experimentally,
a number of independent theoretical studies, carried out during 1999 and 2006 [20],
provided significant quantitative understanding of the link between three-body
recombination and universal physics. As a result, it appears that many body gas
under suitable conditions has a promise to display a tremendously rich variety of
phases in the universality range of large negative scattering lengths. Indeed, at a
theoretical level, quantitative calculations of the four-body recombination loss rate in
the universal regime have recently been carried out as an application of more general
developments in the theory of N-body recombination [21].
Preface
vii
properties of such halo nuclei. Soon after we realized that these nuclei with halo
structure and very weak binding characterized by large n-n scattering length could
well be suited to study the Efimov effect. Subsequently, in 2n-halo nuclei like
14
Be;
19
B;
22
C and
20
C, we carried out the analysis of the occurrence of Efimov
states. The analysis showed that Borromean-type nuclei, where n-n and n-core are
both unbound, are much less vulnerable to respond to the existence of Efimov
states. On the contrary, nuclei like
20
C in which the halo neutron is supposed to be
in the intruder low-lying bound state with the core appear to be promising candidates for the occurrence of the Efimov states at energies below the n-(nc) breakup
threshold. This motivated us to extend our study of the scattering of neutron on a
bound (n À
18
CÞ system and showed that the Efimov states in
20
C move over to the
physical scattering region causing a resonance in n À
19
C scattering around neutron
incident energy of 1.6 keV. The scope of this work was enlarged beyond
20
Cto
include heavier nuclei like
32
Ne and
38
Mg in which the two neutrons are very
weakly bound to the core.
In addition to the study of Efimov effect in halo nuclei, the structural properties
of
11
Li as for instance (i) matter radius, momentum distributions of the halo neutrons and the core and n-n and n-c correlations, (ii) the resonant states of
11
Li in the
continuum and (iii) b-decay of
11
Li were also investigated. The details of these
results along with the discussions will be presented in the following chapters.
Another area in the field of universal Efimov physics which has witnessed
tremendous progress during the last decade is the subject of ultra-cold atomic systems. The first experimental evidence of Efimov resonance was reported in 2006 by
Kraemer et al. [18] in an optically trapped ultra-cold gas of cesium atoms.
Experimentally, its signature as a giant three-body recombination loss was noticed
by magnetically tuning the s-wave scattering length in a range between –2500 a 0
and +1600 a 0 (a 0 being the Bohr radius). In addition to the prominent three-body
Efimov resonance at a
3b
1 ¼ À850a 0 , a broad, weaker resonance feature was visible at
a scattering length near a = –370 Bohr radii. The agreement of its position with the
predicted universal four-body resonance location suggests that this feature is in fact
associated with four-body loss and represents the lower energy tetramer resonance
state. The four-body nature of those loss features was subsequently verified in 2009
by Ferlaino et al. [19]. Before these universal features were observed experimentally,
a number of independent theoretical studies, carried out during 1999 and 2006 [20],
provided significant quantitative understanding of the link between three-body
recombination and universal physics. As a result, it appears that many body gas
under suitable conditions has a promise to display a tremendously rich variety of
phases in the universality range of large negative scattering lengths. Indeed, at a
theoretical level, quantitative calculations of the four-body recombination loss rate in
the universal regime have recently been carried out as an application of more general
developments in the theory of N-body recombination [21].
Preface
vii