108
6 Three-Body Approach to Structural Properties …
It is, therefore, the Efimov effect which provides such a candidate for the subsequent Fano resonance we describe. There is a pleasing interplay between the two
phenomena, the loose binding of the Efimov effect being responsible for the substantial overlap between the two pathways that give rise to an asymmetric Fano profile
and that asymmetry being the diagnostic for the Efimov phenomenon.
Finally, the analogy provided in the above figure suggests a possible alternative
pathway for observing the Fano resonance instead of elastic scattering of neutrons,
namely photo-excitation. Just as in the atomic counterpart, where photo-absorption
from the ground state with photons of energy 60 eV (approximately) also accesses
doubly excited states (although not of
1 S
e but of
1 P
0 symmetry because of dipole
selection rules), we can expect that absorption of gamma rays from lower states such
as the ground state of
20 C will show Fano resonances from the Efimov states. A
further analogy with the observation of doubly excited states through collisions of
He with heavy charged particles such as positive ions provides yet another route for
observing the Efimov–Fano resonances in nuclei, namely fragmentation of
20 C on a
heavy target. With the advent of new machines for generating and studying neutronrich nuclei, we can look forward to the observation in nuclei of the effect which was
predicted by Efimov many years ago.
6.9 Generalizing the Study of Efimov Effect
in Neutron-Rich (2n-Heavy Core) Nuclei Employing
the Above Three-Body Approach
In an attempt to enlarge the scope of present analysis for studying the Efimov effect
beyond
20 C, we found, on scanning of nuclear data tables, that heavy nuclei such as
32 Ne and
38 Mg exhibit a structure dynamically similar to
20 C [108]. In addition to
these halo nuclei, we consider a system of a very heavy core (A = 100) with two halo
neutrons. Considering a loosely bound binary system of the neutron and the heavy
core, we vary the strength of the bound two-body n-core interaction and seek the
solutions for the ground and possible excited states.
Extending the above three-body formulation, it should be interesting 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. Without elaborating the
mathematical steps and the computational details which are similar to what has
been discussed in the relevant sections, we present in Table 6.11 the results of the
calculations for the three cases, namely mass 102,
38 Mg and
32 Ne considered as
2n-halo nuclei.
It can be seen from the table that when the n-core pair interaction just binds the
two-body system having binding energy between 40 and 60 keV, the three-body
system shows more than one Efimov state, the second one being moved over to the
unphysical region. When the two-body energy increases further, say beyond 120 keV,
even the first Efimov state disappears and moves over to the second unphysical sheet.
6 Three-Body Approach to Structural Properties …
It is, therefore, the Efimov effect which provides such a candidate for the subsequent Fano resonance we describe. There is a pleasing interplay between the two
phenomena, the loose binding of the Efimov effect being responsible for the substantial overlap between the two pathways that give rise to an asymmetric Fano profile
and that asymmetry being the diagnostic for the Efimov phenomenon.
Finally, the analogy provided in the above figure suggests a possible alternative
pathway for observing the Fano resonance instead of elastic scattering of neutrons,
namely photo-excitation. Just as in the atomic counterpart, where photo-absorption
from the ground state with photons of energy 60 eV (approximately) also accesses
doubly excited states (although not of
1 S
e but of
1 P
0 symmetry because of dipole
selection rules), we can expect that absorption of gamma rays from lower states such
as the ground state of
20 C will show Fano resonances from the Efimov states. A
further analogy with the observation of doubly excited states through collisions of
He with heavy charged particles such as positive ions provides yet another route for
observing the Efimov–Fano resonances in nuclei, namely fragmentation of
20 C on a
heavy target. With the advent of new machines for generating and studying neutronrich nuclei, we can look forward to the observation in nuclei of the effect which was
predicted by Efimov many years ago.
6.9 Generalizing the Study of Efimov Effect
in Neutron-Rich (2n-Heavy Core) Nuclei Employing
the Above Three-Body Approach
In an attempt to enlarge the scope of present analysis for studying the Efimov effect
beyond
20 C, we found, on scanning of nuclear data tables, that heavy nuclei such as
32 Ne and
38 Mg exhibit a structure dynamically similar to
20 C [108]. In addition to
these halo nuclei, we consider a system of a very heavy core (A = 100) with two halo
neutrons. Considering a loosely bound binary system of the neutron and the heavy
core, we vary the strength of the bound two-body n-core interaction and seek the
solutions for the ground and possible excited states.
Extending the above three-body formulation, it should be interesting 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. Without elaborating the
mathematical steps and the computational details which are similar to what has
been discussed in the relevant sections, we present in Table 6.11 the results of the
calculations for the three cases, namely mass 102,
38 Mg and
32 Ne considered as
2n-halo nuclei.
It can be seen from the table that when the n-core pair interaction just binds the
two-body system having binding energy between 40 and 60 keV, the three-body
system shows more than one Efimov state, the second one being moved over to the
unphysical region. When the two-body energy increases further, say beyond 120 keV,
even the first Efimov state disappears and moves over to the second unphysical sheet.