Borromean Systems Research Articles

Rational Construction of Borromean Linked Crystalline Organic Polymers.

Attributed to the unique topological complexity and elegant beauty, Borromean systems are attracting intense attention. However, at present, the construction of Borromean linked organic polymers remains a challenge. To address this formidable challenge, we developed a supramolecular-synthon-driven approach to fabricate Borromean linked organic polymer. The solvothermal condensation reaction of a judiciously selected trigonal pyramidal building block, 1,3,5-Tris(4-aminophenyl)adamantane, with linear dialdehyde building blocks allowed the construction of two rare covalent organic frameworks (COFs) with high crystallinity and robustness. Structure refinement unveiled the successful formation of entangled 2D→2D Borromean arrayed structures. Both the two COFs were of microporosity and thus demonstrated the potentials for gas separation. The successful synthesis of the first two Borromean linked organic polymers paves the avenue to expand the supramolecular-synthon-driven approach to other building blocks and topologies, and broadens the family and scope of COFs.

Rational Construction of Borromean Linked Crystalline Organic Polymers

AbstractAttributed to the unique topological complexity and elegant beauty, Borromean systems are attracting intense attention. However, at present, the construction of Borromean linked organic polymers remains a challenge. To address this formidable challenge, we developed a supramolecular‐synthon‐driven approach to fabricate Borromean linked organic polymer. The solvothermal condensation reaction of a judiciously selected trigonal pyramidal building block, 1,3,5‐Tris(4‐aminophenyl)adamantane, with linear dialdehyde building blocks allowed the construction of two rare covalent organic frameworks (COFs) with high crystallinity and robustness. Structure refinement unveiled the successful formation of entangled 2D→2D Borromean arrayed structures. Both the two COFs were of microporosity and thus demonstrated the potentials for gas separation. The successful synthesis of the first two Borromean linked organic polymers paves the avenue to expand the supramolecular‐synthon‐driven approach to other building blocks and topologies, and broadens the family and scope of COFs.

Capture reactions into borromean two-proton systems at rp-waiting points

We investigate even-even two-proton borromean systems at prominent intermediate heavy waiting points for the rapid proton capture process. The most likely single-particle levels are used to calculate three-body energy and structure as a function of proton-core resonance energy. We establish a linear dependence between two- and three-body energies with the same slope, but the absolute value slightly dependent on partial wave structure. Using these relations we estimate low-lying excited states in the isotones following the critical waiting points. The capture rate for producing a borromean bound state is described based on a full three-body calculation for temperatures about 0.1 – 10 GK. In addition, a simple rate expression, depending only on a single resonance state, is found to comply with the three-body calculation for temperatures between 0.1 and 4 GK. The rate calculations are valid for both direct and sequential capture paths. As a result the relevant path of the radiative capture reactions can be determined.

Capture reactions into Borromean two-proton systems atrpwaiting points

We investigate even-even two-proton borromean systems at prominent intermediate heavy waiting points for the rapid proton capture process. The most likely single-particle levels are used to calculate three-body energy and structure as a function of proton-core resonance energy. We establish a linear dependence between two- and three-body energies with the same slope, but the absolute value slightly dependent on partial wave structure. Using these relations we predict low-lying excited states in the isotones following the critical waiting points. The capture rate for producing a borromean bound state is described both based on a full three-body calculation and on a very simple analytic rate expression for temperatures about $1-5$~GK. This rate is valid for both direct and sequential capture paths, and it only depends on the three-body resonance energy. As a result the relevant path of the radiative capture reactions can be determined. We present numerical results for $E1$ and $E2$ photon emission, and discuss occurrence preferences in general as well as relative sizes of these most likely processes. Finally, we present narrow estimated intervals for the proton capture rates relevant for the critical waiting points.

Wave function for two-neutron halo states

In this work we investigate the theoretical aspects associated with the few-body universal properties of the weakly-bound two neutron halo in light nuclei. We emphasize that our study of wave functions can be used as inputs in calculations of reaction processes with light exotic nuclei. Starting from the Faddeev decomposition of the wave function for 3-body systems interacting through zero range forces, we calculate two-neutron halo states for large two-body scattering lengths coming closer to what is know today as Efimov's Physics. We report our findings for the wave function for a three-body n — n — C system, where we consider two neutrons as a halo around a compact core C. We focus our study on halo structure of Borromean systems like 11Li, 14Be, and 22C.

Borromean ground state of fermions in two dimensions

The study of quantum mechanical bound states is as old as quantum theory itself. Yet, it took many years to realize that three-body Borromean systems that are bound when any two-body subsystem is unbound are abundant in nature. Here we demonstrate the existence of Borromean systems of spin-polarized (spinless) identical fermions in two spatial dimensions. The ground state with zero orbital (planar) angular momentum exists in a Borromean window between critical two- and three-body strengths. The doubly degenerate first excited states of angular momentum one appears only very close to the two-body threshold. They are the lowest in a possible sequence of so-called super-Efimov states. While the observation of the super-Efimov scaling could be very difficult, the Borromean ground state should be observable in cold atomic gases and could be the basis for producing a quantum gas of three-body states in two dimensions.

Higher-order Brunnian structures and possible physical realizations

We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied to the binding of systems in nature. It now appears that recent generalization to higher-order Brunnian structures may potentially be realized as laboratory-made or naturally occurring systems. With the binding energy as measure, we discuss possibilities of physical realization in nuclei, cold atoms, and condensedmatter systems. Appearance is not excluded. However, both the form and the strengths of the interactions must be rather special. The most promising subfields for present searches would be in cold atoms because of external control of effective interactions, or perhaps in condensed-matter systems with nonlocal interactions. In nuclei, it would only be by sheer luck due to a lack of tunability.

Higher-Order Brunnian Structures and Possible Physical Realizations

We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied to the binding of systems in nature. It now appears that recent generalization to higher order Brunnian structures may potentially be realized as laboratory made or naturally occurring systems. With the binding energy as measure, we discuss possibilities of physical realization in nuclei, cold atoms, and condensed matter systems. Appearance is not excluded. However, both the form and the strengths of the interactions must be rather special. The most promising subfields for present searches would be in cold atoms because of external control of effective interactions, or perhaps in condensed-matter systems with non-local interactions. In nuclei, it would only be by sheer luck due to a lack of tunability.

Occurrence conditions for two-dimensional Borromean systems

We search for Borromean three-body systems of identical bosons in two dimensional geometry, i.e. we search for bound three-boson system without bound two-body subsystems. Unlike three spatial dimensions, in two-dimensional geometry the two- and three-body thresholds often coincide ruling out Borromean systems. We show that Borromean states can only appear for potentials with substantial attractive and repulsive parts. Borromean states are most easily found when a barrier is present outside an attractive pocket. Extensive numerical search did not reveal Borromean states for potentials without an outside barrier. We outline possible experimental setups to observe Borromean systems in two spatial dimensions.

Borromean three-body heteroatomic resonances

We present an approach to analyze recent experimental evidences of Efimov resonant states in mixtures of ultracold gases, by considering two-species three-body atomic systems bound in a Borromean configuration, where all the two-body interactions are unbound. For such Borromean three-body systems, it is shown that a continuum three-body s-wave resonance emerges from an Efimov state as a scattering length or a three-body scale is moved. The energy and width of the resonant state are determined from a scaling function with arguments given by dimension-less energy ratios relating the two-body virtual state subsystem energies with the shallowest three-body bound state. The peculiar behavior of such resonances is that their peaks are expected to move to lower values of the scattering length, with increasing width, as one raises the temperature. For Borromean systems, two resonant peaks are expected in ultralow-temperature regimes, which will disappear at higher energies. It is shown how a Borromean-Efimov excited bound state turns out to a resonant state by tuning the virtual two-body subsystem energies or scattering lengths, with all energies written in units of the next deeper shallowest Efimov state energy. The resonance position and width for the decay into the continuum are obtained as universal scaling functions (limit cycle) of the dimensionless ratios of the two and three-body scales, which are calculated numerically within a zero-range renormalized three-body model.

A DOORWAY TO BORROMEAN HALO NUCLEI: THE SAMBA CONFIGURATION

We exploit the possibility of new configurations in three-body halo nuclei, Samba type (the neutron-core form a bound system) as a doorway to Borromean systems. The nuclei 12 Be , 15 B , 23 N and 27 F are of such nature, in particular 23 N with a half-life of 37.7 s and a halo radius of 6.07 fm is an excellent example of Samba-halo configuration. The fusion below the barrier of the Samba halo nuclei with heavy targets could reveal the so far elusive enhancement and a dominance of one-neutron over two-neutron transfers, in contrast to what was found recently for the Borromean halo nucleus 6 He +238 U .

Origin of Borromean systems

The complex energies of the three-body resonances for one infinitely heavy particle and two non-interacting light particles are the sum of the two contributing two-body complex resonance energies. The bound state of a Borromean system originates from a resonance when the third interaction is introduced, a finite mass is allowed and proper angular momentum coupling is included. The relative importance of these contributions are investigated and the resulting structure of Borromean systems are traced back to the two-body continuum properties. The 0 + and 2 + states in 6He result from neutron-core p-states and the ground and first excited state of 11Li originate from neutron-core s 2 and sp-states.

Structure and reactions of quantum halos

This article provides an overview of the basic principles of the physics of quantum halo systems, defined as bound states of clusters of particles with a radius extending well into classically forbidden regions. Exploiting the consequences of this definition, the authors derive the conditions for occurrence in terms of the number of clusters, binding energy, angular momentum, cluster charges, and excitation energy. All these quantities must be small. The article discusses the transitions between different cluster divisions and the importance of thresholds for cluster or particle decay, with particular attention to the Efimov effect and the related exotic states. The pertinent properties can be described by the use of dimensionless variables. Then universal and specific properties can be distinguished, as shown in a series of examples selected from nuclear, atomic, and molecular systems. The neutron dripline is especially interesting for nuclei and negative ions for atoms. For molecules, in which the cluster division comes naturally, a wider range of possibilities exists. Halos in two dimensions have very different properties, and their states are easily spatially extended, whereas Borromean systems are unlikely and spatially confined. The Efimov effect and the Thomas collapse occur only for dimensions between 2.3 and 3.8 and thus not for 2. High-energy reactions directly probe the halo structure. The authors discuss the reaction mechanisms for high-energy nuclear few-body halo breakup on light, intermediate, and heavy nuclear targets. For light targets, the strong interaction dominates, while for heavy targets, the Coulomb interaction dominates. For intermediate targets these processes are of comparable magnitude. As in atomic and molecular physics, a geometric impact-parameter picture is very appropriate. Finally, the authors briefly consider the complementary processes involving electroweak probes available through beta decay, electromagnetic transitions, and capture reactions.

Necessary conditions for binding in few-body systems

With the help of the variational principle we derive general necessary conditions for the existence of a bound state in few-body systems. The conditions we obtain are used to explain some characteristic qualitative features of nuclear Borromean systems like ${}^{6}\mathrm{He}.$

Structure and Occurrence of Three-Body Halos in Two Dimensions

The quantum-mechanical three-body problem is reformulated in two dimensions by use of hyperspherical coordinates and an adiabatic expansion of the Faddeev equations. The effective radial potentials are calculated and their large-distance asymptotic behavior is derived analytically for short-range two-body interactions. Energies and wave functions are computed numerically for various potentials. An infinite series of Efimov states does not exist in two dimensions. Borromean systems, i.e. bound three-body systems without bound binary subsystems, can only appear when a short-range repulsive barrier at finite distance is present in the two-body interaction. The corresponding Borromean state is never spatially extended. For a system of three weakly interacting identical bosons we find two bound states with both binding energies proportional to the two-body binding energy. In the limit of small binding these states are spatially located at the very large distances characterized by the scattering length. Their properties are universal and independent of the details of the potential. We compare throughout with the corresponding properties in three dimensions.

Three-body halos in two dimensions

A method to study weakly bound three-body quantum systems in two dimensions is formulated in coordinate space for short-range potentials. Occurrences of spatially extended structures (halos) are investigated. Borromean systems are shown to exist in two dimensions for a certain class of potentials. An extensive numerical investigation shows that a weakly bound two-body state gives rise to two weakly bound three-body states, a reminiscence of the Efimov effect in three dimensions. The properties of these two states in the weak binding limit turn out to be universal.

Clustering aspects of light exotic nuclei

The discovery of light nuclei with neutron halos has opened new perspectives for nuclear structure and a possibility to study genuine few-body aspects of matter. A number of borromean systems where the system is bound but where no binary subsystems are bound, are realized by nature in the context of nuclei, 11Li being the nucleus which has had most recent attention. Although a large number of calculations have addressed the detailed structure of the 11Li neutron halo, no single model has yet explained all the data presently available. This is in part due to uncertainties in the n+9Li interaction. For 6He, also a borromean system, where the n + core interaction is known, the best three-body and reaction models succeed in reproducing the data. In the 11Li case, a major uncertainty concerns the effect of possible 1s intruder states.