Cluster Shell Model Research Articles

Dual-Valence Characteristics of Be11: Tin/Lead-like Superatom.

To enhance the superatom family, the new superatom analogue Be11 of group IVA elements has been developed. Be11 can exhibit multiple valence states (+2 and +4), similar to carbon-group elements, and is capable of forming stable ionic compounds with other atoms such as carbon, chalcogen, (super)halogen, and hydroxyl. This resembles how tin and lead atoms combine with these elements to form stable molecules. Their special stability can be rationalized from the perspective of a cluster shell model. Sn or Pb could be the nearest atomic analogue to Be11 in group IVA, as the +2 oxidation state is more stable than the +4 oxidation state. This comparative investigation highlights the resemblance between Be11 and carbon-group elements, which encourages additional exploration within the superatom family.

The Algebraic Cluster Model (8Be, 12C) and the Cluster Shell Model (13C, 7Be, 19F, 8Be)

Bijker and Iachello’s algebraic cluster model (ACM) and its extension to the cluster shell model (CSM), provides a new theoretical platform for the study of alpha-clustering in light nuclei. It led to the discovery of the D3h symmetry in 12C and 20Ne, with the discovery in 12C of a new g.s. rotational band with the spin sequence of, 0+, 2+, 3-, 4+/4- and 5-, including the predicted 4+ and 4- parity doublet. Applications of the CSM shell model to particle molecular orbits in 9Be and 13C (C2’ and D3h’ particle symmetries, respectively), lead us to conjecture molecular hole states in 7Be and 19F. We observe in these nuclei the predicted phenomenological structure. And we further consider conjectured p-h states in 8Be with the predicted phenomenological p-h structure of rotational band at high excitations of approximately 20 MeV. A search for these rotational band in 8Be was performed at ISOLDE.

Structure of 13C in the Cluster Shell Model

We study the structure of 13C in the framework of the Cluster Shell Model. A comparison of the available experimental data with our model is made. Some predictions for level ordering and form factors are presented.

10Be in the Cluster Shell Model

The Cluster Shell Model describes light nuclei in terms of clusters of k α-particles and x extra nucleons, in which the extra nucleons move in the deformed field generated by geometric configuration of α-particles. We present the first study for the case of x = 2 nucleons in an application to 10Be as a cluster of two α-particles and two neutrons.

Signatures of α-clustering in 12C and 13C

We study the cluster structure of 12C and 13C in the framework of the cluster shell model. Simple relations are derived for ratios of longitudinal form factors as well as transition probabilities. It is shown that the available experimental data for 12C and 13C can be well described by a triangular structure with D3h and D3h′ symmetry, respectively.

Conjectured Hole States (7Be, 19F) and p-h states (8Be) of the CSM

The remarkable success of the Algebraic Cluster Model (ACM) to describe the N=Z even-even light nuclei, 8Be, 12C, 16O and 20Ne, and the neighbouring nuclei with one particle added, 9Be, 9B, 13C, 21Ne and 21Na, using the Cluster Shell Model (CSM), lead us to consider the phenomenology of data on conjectured hole states of the CSM in 7Be and 19F, and conjectured high lying particle-hole states (p-h) in 8Be.We propose the first application of the Cluster Shell Model (CSM) of Della Rocca and Iachello to conjectured p-h states in 8Be. We demonstrate a few essential phenomenological features of the CSM in 8Be: 1) All predicted conjectured p-h states of the CSM, and only the predicted p-h states, are observed near thresholds and up to 19.5 MeV in 8Be. 2) The states are observed in the predicted order, with positive parity states below negative parity states. 3) Some of the conjectured p-h states are already known to have the predicted rotational structure of the deformed p-h states. 4) The rotational structures observed at high excitations in the conjectured p-h bands in 8Be, resemble the ground state bands of 8Be, 9Be and 9B, with similar moment of inertia.Based on these observations we contemplate new measurements of the spectroscopy of 8Be at energies above 19.5 MeV, where our knowledge of states in 8Be is incomplete. We examine the observed B(M1)s and B(E2)s in these nuclei and contemplate a measurement of the B(E2) of the iso-baric Analog transition in 8Li.

Cluster structure of 21Ne and 21Na

We study the cluster structure of 21Ne and 21Na within the framework of the cluster shell model (CSM) and show that they have a complex cluster structure with the coexistence of a 20Ne+n, 20Ne+p structure and a 19Ne+2n, 19F+2p structure. Seven rotational bands are identified in 21Ne and four in 21Na and assigned to single-particle cluster states, single-hole cluster states and vibrational states. The single-particle states are associated with the 20Ne+n and 20Ne+p cluster structure, while the single-hole states are associated with the 19Ne+2n and 19F+2p structure.

Discrete symmetries in the cluster shell model

The role of discrete (or point-group) symmetries is discussed in the framework of the Cluster Shell Model which describes the splitting of single-particle levels in the deformed field of cluster potentials. We discuss the classification of the eigenstates for the cases of a triangular and tetrahedral configuration of alpha-particles in terms of the irreducible representations of the double point groups D'(3h) and T'(d), respectively, and show how the discrete symmetry of a given eigenstate can be determined. Finally, we derive the Coriolis coupling for each one of these geometrical configurations.

Odd-mass nuclei in the cluster shell model

In this contribution, we present the cluster shell model which is analogous to the Nilsson model, but for cluster potentials. Special attention is paid to the consequences of the discrete symmetries of three α-particles in an equilateral triangle configuration. This configuration is characterized by a special structure of the rotational bands which can be used as a fingerprint of the underlying geometric configuration. The cluster shell model is applied to the nucleus 13C.

Particle-Hole Cluster Shell Model States in 8Be, a Challenge for Ab-Intio Nuclear Theories

We propose the first application of the Cluster Shell Model (CSM) of Della Rocca and Iachello to particle-hole (p-h) states in 8Be. We demonstrate a few essential features of the CSM in 8Be: 1) All predicted p-h states of the CSM, and only the predicted p-h states, are observed near thresholds and up to 19.5 MeV in 8Be. 2) The states are observed in the predicted order, with positive parity states below negative parity states. 3) Some of the p-h states are already known to have the rotational structure predicted for the deformed p-h states. 4) The rotational structures observed at high excitations in the p-h bands in 8Be, resemble the ground state bands of 8Be, 9Be and 9B, with similar moment of inertia. Based on these observations we contemplate new measurements of the spectroscopy of 8Be at energies above 19.5 MeV, where our knowledge of states in 8Be is scarce. We examine the observed B(M1)s and B(E2)s in these nuclei and contemplate a measurement of the B(E2) of the isobaric Analog transition in 8B. We discuss the observed rotational structure in 8Be as a challenge to ab-initio calculations that searched for “emerging rotational structures at high excitations" in beryllium nuclei, and reveal rotational structure at high excitations in 10Be and 12Be but not in 8Be.

Cluster shell model: I. Structure of 9Be, 9B

We calculate energy spectra, electromagnetic transition rates, longitudinal and transverse electron scattering form factors and log ft values for beta decay in 9Be, 9B, within the framework of a cluster shell model. By comparing with experimental data, we find strong evidence for the structure of these nuclei to be two α-particles in a dumbbell configuration with Z2 symmetry, plus an additional nucleon.

Single-particle levels in cluster potentials

We calculate single-particle levels in potentials with Z2 (dumbbell), D3h (triangle) and Td (tetrahedral) symmetry, appropriate to the α-cluster structure of 8Be, 12C and 16O respectively. We suggest that these can be used to study, within the framework of a cluster shell model (CSM), kα+x nucleon structures, with k=2,3,4 and x=1,2,…, in particular the single particle (x=1) structures 9Be, 9B; 13C, 13N; 17O, 17F.

Laser-induced semiconductor nanocluster structures on the solid surface: new physical principles to construct the hybrid elements for photonics

The laser synthesis technique for producing nanoparticles/nanoclusters of different topology for semiconductor samples (PbTe) is presented by two laser ablation methods: direct laser modification of thin films and laser evaporation of substance from the target in liquid (ethanol) to produce a colloidal system, and the subsequent laser deposition of the particles from colloid on solid substrate [under continuous wave (cw)-laser, λ = 1.06 μm, laser intensity—up to 106 W/cm2]. Electro-physical properties of the induced structures have been controlled by various induced topology. It is obtained that electroresistance can dramatically decrease due to spontaneous selected multichannel/parallel electron transportation trajectories in the inhomogeneous cluster system. Two conditions are principal for that: the characteristic cluster size a < l, where l is the inelastic length, and distance d between two neighboring clusters must be less than de Broglie wavelength λdB. So, the tunneling quantum effect takes place between correlated particles in two domains. Jump conductivity has also been detected under some experimental conditions for laser-induced cluster structures. The cluster shell model can be taken into account to explain the experimental results. For such laser-induced nanostructures we demonstrated the tendency of superconductivity to increase the electrical conductivity by several times (at room temperature) in our case as compared to the homogenous monolithic sample. The fact can be explained by analogy with the correlated particles/coupling pairs. Such approach is of great significance for constructing the elements and devices of optoelectronics and photonics in hybrid circuits on new physical principles.

Stability effects of Au nX m+ (X=Cu, Al, Y, In) clusters

Bimetallic Au n X m clusters (X=Cu, Al, Y, In) have been produced by a dual-target dual-laser vaporization source. Following multiphoton absorption the stability patterns resulting from fragmentation are investigated by time-of-flight mass abundance spectrometry. Au n Cu m + clusters exhibit the same electronic shell effects as Au n +. Different abundance patterns are observed for Au n Al 1 + compared to Au n Y 1 + or Au n In 1 +. The patterns are related to the magic numbers of the electronic shell model for clusters. The differences between the bimetallic clusters are interpreted in terms of different cluster geometries dependent on the nature of the dopant atoms.

A simplified three-body model for 11Li and associated 9Li and neutron momentum distributions

A simple three-body oscillator cluster shell model is proposed to describe the wave functions of neutron-rich nuclei with a (core + 2n) structure. The model is applied to investigate the 11Li nucleus. With a few free parameters the model is able to reproduce the experimental r.m.s. matter radius of 11Li, as well as the experimental transverse momentum distribution of the 9Li nucleus from 11Li fragmentation on a carbon target, at an energy of 790 MeV/nucleon. The transverse momentum distributions of the neutrons from this reaction have also been calculated without any additional parameters. All geometric parameters of the 11Li nucleus are also calculated in the framework of the three-body model.

9Li and neutron momentum distributions in 11Li in a simplified three-body model.

A simple three-body oscillator cluster shell model is proposed as an approximation for wave functions of neutron-rich nuclei, having a (core+2n) structure. The model is applied to the $^{11}\mathrm{Li}$ nucleus. With a few free parameters the model reproduces the experimental rms matter radius of $^{11}\mathrm{Li}$, as well as the experimental transverse momentum distribution of the $^{9}\mathrm{Li}$ nucleus resulting from $^{11}\mathrm{Li}$ fragmentation on a carbon target at an energy of 790 MeV/nucleon. The transverse momentum distributions of the neutrons from this reaction have also been calculated without any additional parameters. All geometric parameters of the $^{11}\mathrm{Li}$ nucleus are also calculated within the framework of this three-body model.

Photoionization Mass Spectrometry and Valence Photoelectron‐Photoion Coincidence Spectroscopy of Isolated Clusters in a Molecular Beam

AbstractA new and versatile photoelectron‐photoion coincidence spectrometer has been developed and advanced to facilitate for the first time the investigation of the valence electronic structure of isolated metal atom clusters up to a mass range of approximately 40000 amu. The neutral cluster distribution, which is synthesized in a doubly skimmed seeded supersonic molecular beam, is probed 130 mm down‐stream by the pulsed and monochromatized output of a newly developed sub‐nanosecond vacuum‐UV/UV‐flashlamp in the photon energy range between 3 and 11.8 eV. Single photoelectrons are energy analyzed and time‐correlated detected either in a field‐free or in a magnetic type time‐of‐flight spectrometer. The corresponding cluster cations are mass analyzed and counted in coincidence in a modified Wiley‐McLaren time‐of‐flight mass spectrometer. The data acquisition electronics is capable of recording and storing simultaneously photoion‐photoelectron coincidence spectra of all those neutral clusters that have sufficient intensity in the molecular beam. First photoelectron spectroscopic results for mass selected mercury clusters up to Hg78 are used to discuss the performance of this new technique. — A photoionization mass spectrometry study of sodium cluster beams has revealed shell closings at the sizes being predicted by the cluster shell model. For the case of large mercury clusters a gradual transition from van der Waals type bonding to metallic cohesion occurs in the size range between 20 and 70 atoms. The occurrence of this transition, which has been observed by energy resolved mass spectrometry, is strongly confirmed by photoelectron‐photoion coincidence spectroscopy. Moreover, the photoelectron spectra clearly indicate that the evolution of the valence band structure toward the metallic state is almost fully accomplished for clusters larger than Hg70. The gradually size dependent transition is found to be induced by the rapid increase of the averaged number of nearest neighbours. Hence, the transition can be explained semi‐quantitatively in the framework of the tight‐binding approximation.

Shell Model for Clusters of Dense‐Packed s‐Scatterers and Calculation of the Density of States

AbstractThe local density of states is calculated a) for the central atom in real clusters of dense‐packed s‐scatterers, b) for the same atom surrounded by an appropriate spherically symmetric model potential. It is shown that in many cases the results for the model potential sufficiently approximate the original density of states.