Related papers: The Algebraic Cluster Model: Structure of 16O
It is shown that there exists a particular associative ring with unity of order 16 such that the relations between nonunimodular free cyclic submodules of its two-dimensional free left module can be expressed in terms of the structure of…
Starting from constrained Skyrme-mean-field calculations, the low-energy excitation spectrum of 16O is calculated by configuration mixing of particle-number and angular-momentum projected mean-field states in the framework of the Generator…
Both the stretch and bend vibrational spectrum and the intensity of infrared transitions in a tetrahedral molecule are studied in a U(2) algebraic model, where the spurious states in the model Hamiltonian and the wavefunctions are exactly…
Since the discovery of molecular resonances in $^{12}$C+$^{12}$C in the early sixties a great deal of research work has been undertaken to study alpha-clustering. Our knowledge on physics of nuclear molecules has increased considerably and…
Compact polyhedra of cubic point symmetry Oh, exhibit surfaces of planar sections (facets) characterized by normal vector families {abc} with up to 48 members each, compatible with Oh symmetry. We focus first on polyhedra confined by facets…
The interior structure of arbitrary sets of quaternion units is analyzed using general methods of the theory of matrices. It is shown that the units are composed of quadratic combinations of fundamental objects having a dual mathematical…
Several commonly observed physical and biological systems are arranged in shapes that closely resemble an honeycomb cluster, that is, a tessellation of the plane by regular hexagons. Although these shapes are not always the direct product…
Context Mixed-metal clusters have long been studied because of their peculiar properties and how they change with cluster size, composition and charge state and their potential roles in catalysis. The characterization of these clusters is…
As part of the ongoing NUCLEI-PACK project, this study presents a semi-classical framework for exploring the microscopic geometry of light and exotic nuclei based on optimized sphere packing of nucleons and clusters. Starting from explicit…
We consider toroidal asymmetric orbifolds of the heterotic string preserving all 16 supercharges, developing a general formalism to study components of the moduli space characterized by rank reduction of the gauge group. In particular we…
We describe the upper seminormal crystal structure for the $\mu$-supported $\delta$-vectors for any quiver with potential with reachable frozen vertices, or equivalently for the tropical points of the corresponding cluster $\mc{X}$-variety.…
A new symplectic-based shell-model approach to clustering in atomic nuclei is proposed by considering the simple system $^{20}$Ne. Its relation to the collective excitations of this system is mentioned as well. The construction of the Pauli…
We derive and implement a new way of solving coupled cluster equations with lower computational scaling. Our method is based on decomposition of both amplitudes and two electron integrals, using a combination of tensor hypercontraction and…
In the present paper we examine the relationship between several type $A$ cluster theories and structures. We define a 2D geometric model of a cluster theory, which generalizes cluster algebras from surfaces, and encode several existing…
We introduce new objects, called $(G,c)$-bands, associated with a simple simply-connected algebraic group $G$, and a Coxeter element $c$ in its Weyl group. We show that bands of a given type are the $K$-points of an infinite dimensional…
Clusters of galaxies are studied from a theoretical point of view, comparing with observational results whenever possible. The problem is approached both analytically as well as by means of high-resoultion numerical simulations. The dark…
The $^{4}$He nucleus is a well bound and highly correlated four-nucleon system that is also found in form of $\alpha$-clusters as substructure in nuclear many-body systems. The standard single-particle shell model cannot represent these…
Strongly interacting binary mixtures of superparamagnetic colloidal particles confined to a two-dimensional water-air interface are examined by theory, computer simulation and experiment. The mixture exhibits a partial clustering in…
The inherent nodal structures of the wavefunctions of 6-nucleon systems have been investigated. The existence of a group of six low-lying states dominated by L=0 has been deduced. The spatial symmetries of these six states are found to be…
The relation between the monopole transition strength and existence of cluster structure in the excited states is discussed based on an algebraic cluster model. The structure of $^{12}$C is studied with a 3$\alpha$ model, and the wave…