Existence Of Cluster Structure Research Articles

Effect of source size and emission time on the p–p momentum correlation function in the two-proton emission process

The effect of source size and emission time on the proton–proton (p–p) momentum correlation function ($$C_\mathrm{pp}(q)$$) has been studied systematically. Assuming a spherical Gaussian source with space and time profile according to the function $$S(r,t)\sim \exp (-r^2/2r_{0}^{2}-t/\tau )$$ in the correlation function calculation code (CRAB), the results indicate that one $$C_\mathrm{pp}(q)$$ distribution corresponds to a unique combination of source size $$r_0$$ and emission time $$\tau $$. Considering the possible nuclear deformation from a spherical nucleus, an ellipsoidal Gaussian source characterized by the deformation parameter $$\epsilon =\Delta {R}/R$$ has been simulated. There is almost no difference of $$C_\mathrm{pp}(q)$$ between the results of spherically and ellipsoidally shaped sources with small deformation. These results indicate that a unique source size $$r_0$$ and emission time could be extracted from the p–p momentum correlation function, which is especially important for identifying the mechanism of two-proton emission from proton-rich nuclei. Furthermore, considering the possible existence of cluster structures within a nucleus, the double Gaussian source is assumed. The results show that the p–p momentum correlation function for a source with or without cluster structures has large systematical differences with the variance of $$r_{0}$$ and $$\tau $$. This may provide a possible method for experimentally observing the cluster structures in proton-rich nuclei.

Cluster varieties from Legendrian knots

Many interesting spaces --- including all positroid strata and wild character varieties --- are moduli of constructible sheaves on a surface with microsupport in a Legendrian link. We show that the existence of cluster structures on these spaces may be deduced in a uniform, systematic fashion by constructing and taking the sheaf quantizations of a set of exact Lagrangian fillings in correspondence with isotopy representatives whose front projections have crossings with alternating orientations. It follows in turn that results in cluster algebra may be used to construct and distinguish exact Lagrangian fillings of Legendrian links in the standard contact three space.

Direct HRTEM Observation of Ultrathin Freestanding Ionic Liquid Film on Carbon Nanotube Grid

Direct imaging of liquids by electron microscopy has been extremely difficult due to their high volatility. Ionic liquids are a unique liquid material with almost zero vapor pressure, which allows us to characterize them under high-vacuum conditions. Here we report the first direct observation of the microstructure and phase behavior of an imidazolium-based room-temperature ionic liquid by high-resolution transmission electron microscopy with the aid of a special carbon nanotube network, which is able to support a freestanding ultrathin ionic liquid film on its nanosized holes. It was found that the existence of cluster structures is one of the intrinsic properties of the ionic liquid in its whole liquid phase range. Furthermore, the size and mobility of the clusters play an important role during phase transition of the ionic liquid. We show that the direct HRTEM imaging on freestanding liquid film is a powerful technique to obtain insight into the structure of ionic liquids and their phase behavior. The present study can provide an important starting point for more sophisticated structural studies on the microstructure of liquidus materials.

Symplectic structure and monopole strength inC12

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 function for the relative motions between $\alpha$ clusters are described by the symplectic algebra $Sp(2,R)_z$, which corresponds to the linear combinations of $SU(3)$ states with different multiplicities. Introducing $Sp(2,R)_z$ algebra works well for reducing the number of the basis states, and it is also shown that states connected by the strong monopole transition are classified by a quantum number $\Lambda$ of the $Sp(2,R)_z$ algebra.

Physical interpretation and theory of existence of cluster structures in lattices of dynamical systems

The alternative theory of existence of cluster structures in lattices of dynamical systems (oscillators) is proposed. This theory is based on representation of structures as a result of classical (full) synchronization of structural objects called cluster oscillators (C-oscillators). Different types of C-oscillators, whose number is defined by the geometrical properties of lattices (dimensions and forms) are introduced. The completeness of all types of C-oscillators for lattices of different dimensions is proven. This fact provides a full set of types of cluster structures that can be realized in a given lattice. The solution is derived without the necessity to verify the existence of invariant (cluster) manifolds. The principles of coupling of C-oscillators into the cluster structures and principles of transformations of such structures are described. Having interpreted the processes of structuring in terms of the classical synchronization of C-oscillators, one can solve the problem of fusion of lattices with pre-described properties at the engineering level.

Cluster Model Calculation on the Energy Levels of the Lithium Isotopes

A variational procedure is adopted to determine the energies of the levels of the highest space symmetry type in ${\mathrm{Li}}^{6}$ and ${\mathrm{Li}}^{7}$. The trial wave functions employed take into consideration the existence of cluster structures in those nuclei. With a simple two-body force, it is shown that the computed energies of the various states are in reasonable agreement with experiment. The $^{2}F_{\frac{5}{2}}$ level in ${\mathrm{Li}}^{7}$, as yet undetermined experimentally, is found to have an excitation energy of about 5.6 Mev and a rather large level width. The calculation also indicates that to explain the splitting of levels in those nuclei, a constant two-body spin-orbit force of the pure neutral form is inadequate.