7 Summary and Future Outlook
123
We also made an attempt to enlarge the scope of present analysis for studying the
Efimov effect beyond
20 C and found that heavy nuclei such as
32 Ne and
38 Mg, exhibit
a structure dynamically similar to
20 C [108]. In fact, we generalized the analysis by
including a system of a very heavy core (A = 100) with two halo neutrons, to find
the conditions for the occurrence of the Efimov states in these systems [109] and see
how these states evolve into the Feshbach-type resonances.
7.1 Future Outlook
The key question to be addressed in the context of Efimov–Fano resonances predicted
in
20 C, in the present analysis, is: How far the Efimov criterion, viz. |a|/r eff 1, is
satisfied? Experimentally, our knowledge regarding the two-body n−
18 C interaction,
employed in
20 C, is rather limited; the only parameter experimentally known is the
binding energy. Obviously, this is not sufficient to determine precisely the parameters
of the realistic two-body potential. The question raised above is also important from
the point of view of the scaling criterion, i.e., E
(n+1)
T
/E
(n)
T
→ exp(−2π/s 0 ) →
1/515.03, as n → ∞ at a = ±∞. Efimov has also shown that this scaling
limit also holds for large scattering length. In the present case, this ratio in the case
of first excited state to the ground state is predicted to be around 1/20, which is
quite far off from the scaling law. Interestingly, experimental studies with ultra-cold
atoms also reported only a couple of Efimov states without exhibiting the universal
scaling. In atomic systems, as, for instance, in the case of Cs atoms, their interaction
measurements in the lowest internal state are experimentally determined by applying
varying magnetic fields, thereby changing the s-wave scattering length all the way
from −2500 a 0 to +1600 a 0 , where a 0 is Bohr’s radius. When an Efimov state
interacts with the continuum threshold at negative scattering lengths a, three free
atoms in the ultra-cold limit resonantly couple to a trimer—evolving into a tri-atomic
Efimov resonance. Another type of Efimov resonance appears at positive values of
scattering length, a, for collisions between a free atom and a dimer. In the domain of
nuclear physics with halo nuclei, we do not enjoy such a privilege to get the scattering
lengths changed by applying varying magnetic fields. However, by changing the twobody binding energy in case of
19 B and
22 C halo nuclei, we found [94] that excited
Efimov states could appear by getting the scattering lengths at −179.6 fm for n −
17 B
system at 0.67 keV and at −121.5 fm for n −
20 C system at 1.46 keV. In the case
of positive scattering length, we have the example of
20 C where the occurrence of
Efimov states has been studied in detail. These objects may, therefore, be considered,
from the experimental standpoint, as possible candidates to search for the occurrence
of Efimov resonances. In particular, we should expect that experimentally, in addition
to the scattering of low-energy n −
19 C scattering, the photo-excitation processes,
through the absorption of gamma rays from the ground states of these halo targets
near threshold energies, should possibly show Efimov–Fano resonances. Let us hope
123
We also made an attempt to enlarge the scope of present analysis for studying the
Efimov effect beyond
20 C and found that heavy nuclei such as
32 Ne and
38 Mg, exhibit
a structure dynamically similar to
20 C [108]. In fact, we generalized the analysis by
including a system of a very heavy core (A = 100) with two halo neutrons, to find
the conditions for the occurrence of the Efimov states in these systems [109] and see
how these states evolve into the Feshbach-type resonances.
7.1 Future Outlook
The key question to be addressed in the context of Efimov–Fano resonances predicted
in
20 C, in the present analysis, is: How far the Efimov criterion, viz. |a|/r eff 1, is
satisfied? Experimentally, our knowledge regarding the two-body n−
18 C interaction,
employed in
20 C, is rather limited; the only parameter experimentally known is the
binding energy. Obviously, this is not sufficient to determine precisely the parameters
of the realistic two-body potential. The question raised above is also important from
the point of view of the scaling criterion, i.e., E
(n+1)
T
/E
(n)
T
→ exp(−2π/s 0 ) →
1/515.03, as n → ∞ at a = ±∞. Efimov has also shown that this scaling
limit also holds for large scattering length. In the present case, this ratio in the case
of first excited state to the ground state is predicted to be around 1/20, which is
quite far off from the scaling law. Interestingly, experimental studies with ultra-cold
atoms also reported only a couple of Efimov states without exhibiting the universal
scaling. In atomic systems, as, for instance, in the case of Cs atoms, their interaction
measurements in the lowest internal state are experimentally determined by applying
varying magnetic fields, thereby changing the s-wave scattering length all the way
from −2500 a 0 to +1600 a 0 , where a 0 is Bohr’s radius. When an Efimov state
interacts with the continuum threshold at negative scattering lengths a, three free
atoms in the ultra-cold limit resonantly couple to a trimer—evolving into a tri-atomic
Efimov resonance. Another type of Efimov resonance appears at positive values of
scattering length, a, for collisions between a free atom and a dimer. In the domain of
nuclear physics with halo nuclei, we do not enjoy such a privilege to get the scattering
lengths changed by applying varying magnetic fields. However, by changing the twobody binding energy in case of
19 B and
22 C halo nuclei, we found [94] that excited
Efimov states could appear by getting the scattering lengths at −179.6 fm for n −
17 B
system at 0.67 keV and at −121.5 fm for n −
20 C system at 1.46 keV. In the case
of positive scattering length, we have the example of
20 C where the occurrence of
Efimov states has been studied in detail. These objects may, therefore, be considered,
from the experimental standpoint, as possible candidates to search for the occurrence
of Efimov resonances. In particular, we should expect that experimentally, in addition
to the scattering of low-energy n −
19 C scattering, the photo-excitation processes,
through the absorption of gamma rays from the ground states of these halo targets
near threshold energies, should possibly show Efimov–Fano resonances. Let us hope