98
6 Three-Body Approach to Structural Properties …
region of 60 keV < E n−c < 200 keV supports the existence of one Efimov state ε 1
(solid line). However, for E n−c > 100 keV the second excited state, ε 2 (broken line),
gets destroyed. The conclusions arrived here are in overall qualitative agreement
with the analysis of Amorim et al. [95] who also conclude the presence of not more
than one Efimov state with an estimated binding energy less than 14 keV below the
n − (nc) scattering threshold. The size of the first excited state obtained by us is also
in qualitative agreement with the value of Amorim et al. [95] who estimate the size
to be at least 35 fm. In conclusion, we find that the 2n-rich halo nuclei in which the
halo neutron is in the intruder low-lying bound state appear to be the most promising
candidates to search for the occurrence of Efimov states at energies which may well
be within experimental limits to observe.
6.7 Movement of Efimov States in 20 C Causing Resonance
in n− 19 C Scattering Near Threshold
In 1972, Amado and Noble [96], studying the analytic properties of the Fredholm
determinant in a three-boson model, showed that with the increase of potential
strength, the Efimov states move into the unphysical sheet associated with the twobody unitarity cut. A detailed analysis was followed by Adhikari et al. [97] to study
the movement of the Efimov states in the three-boson model and in the s-wave spindoublet
2 S 1/2
three-nucleon system. The key question addressed there was whether
the Efimov states, with the increase in potential strength, move over to the virtual
states in the unphysical sheet or two of the Efimov states collide to produce a resonance, one of which comes close to the scattering region and produce an observable
effect on the physical scattering process.
In the analysis carried in the preceding section, we found the occurrence of Efimov
state in
20 C near the three-body threshold. For instance, for the n−
18 C binding energy
around 140 keV, an Efimov state at about 152 keV was predicted along with the ground
state energy of
20 C to be 3.18 MeV. We also noticed that if the n−
18 C binding energy
is lowered to about 100 keV or even less than that, there could be even more than
one bound Efimov states.
In light of further experimental data available on Coulomb dissociation of
19 C into
n+
18 C studied at 67A [98], where the angular distribution of n+
18 C in the cm system
led to the determination of neutron separation energy in
19 C to be 530 ± 130 keV, we
extended our previous analysis [99] to investigate the behavior of the movement of the
Efimov states increasing the n−
18 C binding energy from 200 keV to about 500 keV.
Table 6.9 presents the revised estimates of the three-body energy for
20 C ground
state and excited Efimov states for different two-body (n −
18 C) binding energies.
As noticed earlier, when the n–c pair interaction just binds the two-body (n −
18 C)
system having binding energy around 60–100 keV, the three-body system shows
more than one Efimov state but for binding energy equal to or greater than 140 keV,
there appears only one Efimov state, the second one moving over to the unphysical
6 Three-Body Approach to Structural Properties …
region of 60 keV < E n−c < 200 keV supports the existence of one Efimov state ε 1
(solid line). However, for E n−c > 100 keV the second excited state, ε 2 (broken line),
gets destroyed. The conclusions arrived here are in overall qualitative agreement
with the analysis of Amorim et al. [95] who also conclude the presence of not more
than one Efimov state with an estimated binding energy less than 14 keV below the
n − (nc) scattering threshold. The size of the first excited state obtained by us is also
in qualitative agreement with the value of Amorim et al. [95] who estimate the size
to be at least 35 fm. In conclusion, we find that the 2n-rich halo nuclei in which the
halo neutron is in the intruder low-lying bound state appear to be the most promising
candidates to search for the occurrence of Efimov states at energies which may well
be within experimental limits to observe.
6.7 Movement of Efimov States in 20 C Causing Resonance
in n− 19 C Scattering Near Threshold
In 1972, Amado and Noble [96], studying the analytic properties of the Fredholm
determinant in a three-boson model, showed that with the increase of potential
strength, the Efimov states move into the unphysical sheet associated with the twobody unitarity cut. A detailed analysis was followed by Adhikari et al. [97] to study
the movement of the Efimov states in the three-boson model and in the s-wave spindoublet
2 S 1/2
three-nucleon system. The key question addressed there was whether
the Efimov states, with the increase in potential strength, move over to the virtual
states in the unphysical sheet or two of the Efimov states collide to produce a resonance, one of which comes close to the scattering region and produce an observable
effect on the physical scattering process.
In the analysis carried in the preceding section, we found the occurrence of Efimov
state in
20 C near the three-body threshold. For instance, for the n−
18 C binding energy
around 140 keV, an Efimov state at about 152 keV was predicted along with the ground
state energy of
20 C to be 3.18 MeV. We also noticed that if the n−
18 C binding energy
is lowered to about 100 keV or even less than that, there could be even more than
one bound Efimov states.
In light of further experimental data available on Coulomb dissociation of
19 C into
n+
18 C studied at 67A [98], where the angular distribution of n+
18 C in the cm system
led to the determination of neutron separation energy in
19 C to be 530 ± 130 keV, we
extended our previous analysis [99] to investigate the behavior of the movement of the
Efimov states increasing the n−
18 C binding energy from 200 keV to about 500 keV.
Table 6.9 presents the revised estimates of the three-body energy for
20 C ground
state and excited Efimov states for different two-body (n −
18 C) binding energies.
As noticed earlier, when the n–c pair interaction just binds the two-body (n −
18 C)
system having binding energy around 60–100 keV, the three-body system shows
more than one Efimov state but for binding energy equal to or greater than 140 keV,
there appears only one Efimov state, the second one moving over to the unphysical