Borromean Structure Research Articles

Collapse of the N=28 shell closure in the newly discovered Na39 nucleus and the development of deformed halos towards the neutron dripline

Halos and changes of nuclear magicities have been extensively investigated in exotic nuclei during past decades. The newly discovered $^{39}\mathrm{Na}$ with the neutron number $N=28$ provides a new platform to explore such novel phenomena near the neutron dripline of the sodium isotopic chain. We study the shell property and the possible halo structure in $^{39}\mathrm{Na}$ within the deformed relativistic Hartree-Bogoliubov theory in continuum. It is found that the lowering of $2p$ orbitals in the spherical limit results in the collapse of the $N=28$ shell closure in $^{39}\mathrm{Na}$, and a well-deformed ground state is established. The pairing correlations and the mixing of $pf$ components driven by deformation lead to the occupation of weakly bound or continuum $p$-wave neutron orbitals. An oblate halo is therefore formed around the prolate core in $^{39,41}\mathrm{Na}$, making $^{39}\mathrm{Na}$ a single nucleus with the coexistence of several exotic structures, including the quenched $N=28$ shell closure, Borromean structure, deformed halo, and shape decoupling. The microscopic mechanisms behind the shape decoupling phenomenon and the development of halos towards dripline are revealed.

Borromean rings redux. A missing link found - a Borromean triplet of Borromean triplets.

This paper describes a nine-component Borromean structure - a Borromean triplet of Borromean triplets - that was missing from an earlier enumeration.

Percolation and dissolution of Borromean networks.

Inspired by experiments on topologically linked DNA networks, we consider the connectivity of Borromean networks, in which no two rings share a pairwise-link, but groups of three rings form inseparable triplets. Specifically, we focus on square lattices at which each node is embedded a loop which forms a Borromean link with pairs of its nearest neighbors. By mapping the Borromean link network onto a lattice representation, we investigate the percolation threshold of these networks (the fraction of occupied nodes required for a giant component), as well as the dissolution properties: the spectrum of topological links that would be released if the network were dissolved to varying degrees. We find that the percolation threshold of the Borromean square lattice occurs when approximately 60.75% of nodes are occupied, slightly higher than the 59.27% typical of a square lattice. Compared to the dissolution of Hopf-linked networks, a dissolved Borromean network will yield more isolated loops, and fewer isolated triplets per single loop. Our simulation results may be used to predict experiments from Borromean structures produced by synthetic chemistry.

Guest inclusion by Borromean weave coordination networks

Reaction of N,Nʺ-ethylene-1,2-diylbis(3-pyridin-3-ylurea) (L) with AgNO3 in a variety of solvents gives a total of five 2-D Borromean weave coordination polymer networks that adopt three structural types depending on the interactions to the solvent pocket. The Borromean network is of formula [Ag2(L)3](NO3)2 ·solvent where the solvent is either a cluster of water molecules, mixtures of water and acetonitrile, water and methanol or chloroform and methanol. The Borromean structure is a thermodynamic sink and under fast crystallization conditions an alternative 2 + 2 metallomacrocycle forms that can result in metallogel formation. The metallogel structure transforms into the crystalline Borromean network over time.

Open versus Interpenetrated: Switchable Supramolecular Trajectories in Mechanosynthesis of a Halogen-Bonded Borromean Network

Summary Precise control over topologically intricate molecular architectures remains an open challenge for chemists due to their inherent structural complexity. We report a simple solvent-free strategy to selectively prepare two multi-component supramolecular crystalline systems based on the halogen bond, endowed with either an unknot topology or a Borromean-type entanglement. Real-time in situ monitoring of the solvent-free mechanochemical synthesis of these three-component halogen-bonded ionic co-crystals reveals that the choice of milling conditions leads to a switch in the supramolecular reaction trajectory, resulting in the selective formation of an open halogen-bonded network or a halogen-bonded Borromean-type assembly.

Continuum and three-nucleon force in Borromean system: The 17Ne case

Starting from chiral two-nucleon (2NF) and chiral three-nucleon (3NF) potentials, we present a detailed study of 17Ne, a Borromean system, with the Gamow shell model which can capture continuum effects. More precisely, we take advantage of the normal-ordering approach to include the 3NF and the Berggren representation to treat bound, resonant and continuum states on equal footing in a complex-momentum plane. In our framework, 3NF is essential to reproduce the Borromean structure of 17Ne, while the continuum is more crucial for the halo property of the nucleus. The two-proton halo structure is demonstrated by calculating the valence proton density and correlation density. The astrophysically interesting 3/2− excited state has its energy above the threshold of the proton emission, and therefore the two-proton decay should be expected from the state.

Covalent Post-assembly Modification Triggers Structural Transformations of Borromean Rings.

A series of supramolecular transformation cascades are presented here, employing ligand exchange reactions, concentration-dependent Borromean ring (BR) linking and unlinking, and inverse electron-demand Diels-Alder (IEDDA) reactions. The new family of template-free, tetrazine-edged BRs are constructed by using ligand exchange reactions, and their concentration-dependent linking and unlinking reactions have been observed. Moreover, Borromean precursors have been demonstrated to further undergo supramolecular structural transformations induced by rapid and efficient IEDDA reactions to afford corresponding post-assembly modified architectures. Remarkably, subtle steric increases of the pyridazine fragments obtained by IEDDA reactions is regarded to induce controlled topological transformations in the cascade, unlinking the Borromean structures by using electron-rich dienophiles as triggering signals.

Weakly bound Borromean structures of the exotic 6,8He nuclei through direct reactions on proton

The data set of the direct reactions induced by the radioactive nuclei 6, 8He can be used as benchmarks to test the validity of the microscopic structure theories. The reactions were analyzed and compared to microscopic calculations including various structure inputs. The interpretation for the structure of He isotopes is compared to the ones proposed via other probes. The consistency of the various data sets and of the reaction analysis using structure models is discussed. The root mean square radii of the matter and neutron densities, and the multipole moments M p, n and B(E2) values are extracted in our approach and compared to the previous experiments and to the theories. From this comparison, we can discuss and point out the microscopic inputs of the models (like correlations, continuum-coupling effects), which are required to reach a consistent understanding for both the radii and the spectroscopy of the nuclei close to the drip-line.

Borromean structures in medium-heavy nuclei

Borromean nuclear cluster structures are expected at the corresponding driplines. We locate the regions in the nuclear chart with the most promising constituents, it being protons and alpha-particles and investigate in details the properties of the possible borromean two-alpha systems in medium heavy nuclei. We find in all cases that the alpha-particles are located at the surface of the core-nucleus as dictated by Coulomb and centrifugal barriers. The two lowest three-body bound states resemble a slightly contracted $^{8}\text{Be}$ nucleus outside the core. The next two excited states have more complex structures but with strong components of linear configurations with the core in the middle. Alpha-removal cross sections would be enhanced with specific signatures for these two different types of structures. The even-even borromean two-alpha nucleus, $^{142}$Ba, is specifically investigated and predicted to have $^{134}\text{Te}-\alpha-\alpha$ structure in its ground state and low-lying spectrum.

Coordination assembly of Borromean structures

The state-of-art advances in the assembly of coordination supramolecular structures featuring Borromean topological character have been introduced.

Variations of Structures and Gas Sorption Properties of Three Coordination Polymers Induced by Fluorine Atom Positions in Azamacrocyclic Ligands

Three coordination polymers of [(NiL(1))(3)(TCBA)(2)] (1), [(NiL(2))(3)(TCBA)(2)] (2), and [(NiL(3))(3)(TCBA)(2)] (3) have been constructed using azamacrocyclic Ni(II) complexes [NiL(1)](ClO(4))(2)/[NiL(2)](ClO(4))(2)/[NiL(3)](ClO(4))(2) and TCBA(3-) as building blocks (L(1) = 3,10-bis(2-fluorobenzyl)-1,3,5,8,10,12-hexaazacyclotetradecane; L(2) = 3,10-bis(3-fluorobenzyl)-1,3,5,8,10,12-hexaazacyclotetradecane; L(3) = 3,10-bis(4-fluorobenzyl)-1,3,5,8,10,12- hexaazacyclotetradecane; TCBA(3-) = tri(4-carboxy-benzyl)amine). The results of X-ray diffraction analyses reveal that 1 shows a 2D Borromean structure, while 2 and 3 form 2D layer structures, and the 2D layers are further connected by the interlayer F···F interactions in 2 and C-H···F interactions in 3 to generate two 3D porous structures with 1D fluorine atoms interspersed channels. Gas sorption measurements illustrate that the desolvated 2 and 3can adsorb N(2), H(2), and CO(2) molecules. The different structures and gas sorption properties of 1 and 2/3 are mainly induced by the different positions of F atoms in azamacrocycle ligands.

EXOTIC CARBON SYSTEMS IN TWO-NEUTRON HALO THREE-BODY MODELS

The general properties of exotic carbon systems, considered as a core with a two-neutron (n - n) halo, are described within a renormalized zero-range three-body model. In particular, it is addressed the cases with a core of 18C and 20C. In such a three-body framework, 20C has a bound subsystem (19C), whereas 22C has a Borromean structure with all subsystems unbound. 22C is also known as the heaviest carbon halo nucleus discovered. The spatial distributions of such weakly-bound three-body systems are studied in terms of a universal scaling function, which depends on the mass ratio of the particles, as well as on the nature of the subsystems.

O sinthome como a heresia teórica de Lacan

Pretende-se demonstrar, a partir da leitura do Seminário 23 de Jacques Lacan, a transformação do conceito psicanalítico de sintoma na categoria de sinthome, defendendo a ideia de que o mesmo possa ser compreendido como uma espécie de nova e "herética" maneira de articular os registros do Real, do Simbólico e do Imaginário (RSI). Trata-se, nesta nova abordagem, de uma rearticulação com o que estava na origem do sofrimento, transformando um legado de falta e interdição em algo de própria e singular invenção. Da ligação ao elemento paterno-divino, trinitário (tanto em relação à organização borromeana como em relação à trindade católica), passa-se ao aparentemente caótico e mundano do "diabo a quatro" (do nó borromeu acrescido da quarta consistência e dos quatro elementos da matéria no mundo secular).

New structures in complex systems

Networks represent a major modelling tool in complex systems and the natural sciences. When considering systems of interacting units, networks can only model pair interactions as represented by edges between nodes. This is a severe limitation when one tries to model higher order interactions, like triple interactions etc. Some higher order interactions may be reduced to systems of pair interactions, but as we will illustrate there are, for example, triple interactions which are not reducible to pair interactions for quite deep mathematical reasons (Borromean structures). Therefore there is a need for a new kind of structure extending and encompassing networks in such a way that we can describe and model truly higher order structures. We suggest that this can be done by the concept of a Hyperstructure as introduced in [1]. Hyperstructures encompass networks and hierarchies and incorporate the phenomenon of levelwise emergence. They represent a design principle for higher order structures. It is natural to ask how hyperstructures occur in the natural sciences and complex systems and how they may be synthesized. We will discuss this, and relate it to recent work in synthetic chemistry, nuclear physics, quantum mechanical many body systems and ultracold gases. Furthermore, we will introduce the notion of hyperstructured (higher order) molecular architectures and hyperstructured (higher order) materials. We will present suggestions and conjectures on these matters.

Continuum-discretized coupled-channels method for four-body nuclear breakup inHe6+C12scattering

We propose a fully quantum-mechanical method of treating four-body nuclear breakup processes in scattering of a projectile consisting of three constituents, by extending the continuum-discretized coupled-channels method. The three-body continuum states of the projectile are discretized by diagonalizing the internal Hamiltonian of the projectile with the Gaussian basis functions. For $^{6}\mathrm{He}+^{12}\mathrm{C}$ scattering at 18 and $229.8\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$, the validity of the method is tested by convergence of the elastic and breakup cross sections with respect to increasing the number of the basis functions. Effects of the four-body breakup and the Borromean structure of $^{6}\mathrm{He}$ on the elastic and total reaction cross sections are discussed.