122
7 Summary and Future Outlook
include the higher-order loop diagram, the ultraviolet divergence arising from high
momentum modes of loop diagram in the Lagrangian can be regulated by a floating
ultraviolet cutoff . As all the observables are to be independent of the cutoff, the
theory is normalized by absorbing the -dependence into the effective field theory
couplings, thereby making the theory to be model independent.
To extend this theory to three-body sector, three-body integral equations for bound
and scattering states using the two-body zero-range or contact interactions were
obtained long ago [36]. Recently, Bedaque and collaborators [22] derived this equation within the framework of effective field theory. In order to renormalize this
equation, they introduced a three-body force in the leading order three-body EFT
equation and adjusted this force to reproduce the experimental 1 + 2 scattering length.
Following an alternative approach used in ref. [40] where the three-body scattering
length parameter was introduced to renormalize the amplitude of the EFT equation,
we employed a similar procedure to set up integral equations starting from separable
potential approach to obtain the EFT equations for studying the resonant structure in
n −
19 C scattering, where
19 C is assumed to consist of dimer (n −
18 C) system. The
detailed renormalization procedure along with numerical calculations is deferred to
Chap. 6.
Chapter 5 highlights the experimental status reviewing the attempts made in the
early 1990s on the discovery of halo structure in light neutron and proton drip-line
nuclei. In particular, in the case of 2n-halo nuclei experimental attempts made and
the evidence produced for the existence of three-body structure with two neutrons
orbiting around the core, specifically in nuclei like,
11 Li has been highlighted.
Finally, in Chap. 6, theoretical investigations carried out during the last more than
two decades on studying the structural properties of halo nuclei within the framework
of three-body formalism have been reviewed. Primarily, the ground state properties
(binding energy, matter radius, n-n and n-core correlations) and resonant states of
11 Li, probability distributions in
11 Li and β–decay of
11 Li into halo analog states
and to
9 Li +deuteron channel have been reported in the first part of the chapter. The
second part is devoted to the search for Efimov states in halo nuclei like
14 Be,
19 B,
22 C and
20 C. The promising candidate,
20 C, which is characterized by a (2n–
18 C)
three-body system and where one of the neutrons halo is weakly bound to the core
18 C has been investigated in detail, where the possibility of the occurrence of more
than one Efimov state is predicted. A detailed analysis of the movement of the Efimov
states leads to the demonstration of resonances in n −
19 C scattering near threshold.
The appearance of resonances in elastic scattering cross section, as the Efimov states
just become unbound, led us to tie this result to yet another interesting result that
a general resonance profile is asymmetric, which was pointed out by Fano [103]
over four decades ago. While such asymmetric profiles have been widely observed
in atoms and molecules, resonances in nuclear and particle physics generally show
symmetric Lorentzian or Breit–Wigner shapes. It is the combination of the features
of the Efimov and Fano phenomena which, in fact, holds promise for the possible
observation of such resonances with the asymmetry being used as a diagnostic for
the Efimov effect.
7 Summary and Future Outlook
include the higher-order loop diagram, the ultraviolet divergence arising from high
momentum modes of loop diagram in the Lagrangian can be regulated by a floating
ultraviolet cutoff . As all the observables are to be independent of the cutoff, the
theory is normalized by absorbing the -dependence into the effective field theory
couplings, thereby making the theory to be model independent.
To extend this theory to three-body sector, three-body integral equations for bound
and scattering states using the two-body zero-range or contact interactions were
obtained long ago [36]. Recently, Bedaque and collaborators [22] derived this equation within the framework of effective field theory. In order to renormalize this
equation, they introduced a three-body force in the leading order three-body EFT
equation and adjusted this force to reproduce the experimental 1 + 2 scattering length.
Following an alternative approach used in ref. [40] where the three-body scattering
length parameter was introduced to renormalize the amplitude of the EFT equation,
we employed a similar procedure to set up integral equations starting from separable
potential approach to obtain the EFT equations for studying the resonant structure in
n −
19 C scattering, where
19 C is assumed to consist of dimer (n −
18 C) system. The
detailed renormalization procedure along with numerical calculations is deferred to
Chap. 6.
Chapter 5 highlights the experimental status reviewing the attempts made in the
early 1990s on the discovery of halo structure in light neutron and proton drip-line
nuclei. In particular, in the case of 2n-halo nuclei experimental attempts made and
the evidence produced for the existence of three-body structure with two neutrons
orbiting around the core, specifically in nuclei like,
11 Li has been highlighted.
Finally, in Chap. 6, theoretical investigations carried out during the last more than
two decades on studying the structural properties of halo nuclei within the framework
of three-body formalism have been reviewed. Primarily, the ground state properties
(binding energy, matter radius, n-n and n-core correlations) and resonant states of
11 Li, probability distributions in
11 Li and β–decay of
11 Li into halo analog states
and to
9 Li +deuteron channel have been reported in the first part of the chapter. The
second part is devoted to the search for Efimov states in halo nuclei like
14 Be,
19 B,
22 C and
20 C. The promising candidate,
20 C, which is characterized by a (2n–
18 C)
three-body system and where one of the neutrons halo is weakly bound to the core
18 C has been investigated in detail, where the possibility of the occurrence of more
than one Efimov state is predicted. A detailed analysis of the movement of the Efimov
states leads to the demonstration of resonances in n −
19 C scattering near threshold.
The appearance of resonances in elastic scattering cross section, as the Efimov states
just become unbound, led us to tie this result to yet another interesting result that
a general resonance profile is asymmetric, which was pointed out by Fano [103]
over four decades ago. While such asymmetric profiles have been widely observed
in atoms and molecules, resonances in nuclear and particle physics generally show
symmetric Lorentzian or Breit–Wigner shapes. It is the combination of the features
of the Efimov and Fano phenomena which, in fact, holds promise for the possible
observation of such resonances with the asymmetry being used as a diagnostic for
the Efimov effect.