Simple Shell Model Research Articles

Dose distribution for a 32P-impregnated coronary stent: Comparison of theoretical calculations and measurements with radiochromic film

Purpose : Restenosis, caused by proliferation of smooth-muscle cells, limits the efficacy of catheter-based revascular of coronary arteries. Irradiation has been shown to growth of smooth-muscle cells in vitro and to prevent restenosis in animal models following stent placement. An intraarterial source of 32P, a pure β mitter with a half-life of 14.28 days and a 90% range in water of 3.6 mm, is almost ideal for irradiating just arterial wall without exposing any other part of the patients' heart or any organs, while posing minimal hazards to medical personnel. Two types of previously developed coronary stent impregnated with 32P were investigated. This study aimed to calculate and measure the dose outside of two types of 32P-impregnated β-emitting coronary stents under conditions closely simulating clinical use. Methods and Materials : The dose distributions in water surrounding these stents were calculated using a convolution method and measured by exposing radiochromic film in a solid-water phantom. Results : Experimental results were in excellent agreement with theoretical calculations. Conclusions : Radiochromic dosimetry can be used to measure the dose distribution around a β-emitting intraarterial stent at distances as smal as 0.1 mm from the stent surface. A simple cylindrical shell model is adequate for calculating the dose at points farther than 0.5 mm from the stent surface.

Stability of Bubble Nuclei through Shell Effects

We investigate the shell structure of bubble nuclei in simple phenomenological shell models and study their binding energy as a function of the radii and of the number of neutron and protons using Strutinsky's method. Shell effects come about, on the one hand, by the high degeneracy of levels with large angular momentum and, on the other, by the big energy gaps between states with a different number of radial nodes. Shell energies down to -40 MeV are shown to occur for certain magic nuclei. Estimates demonstrate that the calculated shell effects for certain magic numbers of constituents are probably large enough to produce stability against fission, alpha-, and beta-decay. No bubble solutions are found for mass number A < 450.

On the shell structure of nuclear bubbles

We investigate the shell structure of spherical nuclear bubbles in simple phenomenological shell model potentials. The bunching is produced by the energy gaps between single-particle states with a different number of radial nodes. The shell correction energies for doubly magic bubbles may be as large as −40 MeV and probably imply a very long lifetime against spontaneous fission. β-stability occurs for ratios of the neutron number N to the proton number Z which differ markably from the β-stability valley of ordinary compact nuclei. The α-decay probability is shown to be very small for proton rich bubbles with a moderately large outer radius. Metastable islands of nuclear bubbles are shown to exist for nucleon numbers in the range A = 450–3000.

Electrorotation of liposomes: verification of dielectric multi-shell model for cells

The reliability of multi-shell dielectric models, used to describe the ac electrokinetic behaviour of cells, has been tested by performing electrorotation and dielectrophoretic measurements on unilamellar, oligolamellar, and multilamellar liposomes of diameters ranging from 5 to 24 μm. Fluorescence microscopy, flow cytometry and electron spin resonance were used to characterise the morphology and membranes of the liposomes. The dielectric properties of the various types of liposomes, based on appropriate dielectric shell models, were then analysed using a general purpose, recursive, algorithm. Through simulations, the confidence levels that can be assigned to parameters derived through application of simple shell models are estimated. From this, we confirm that electrorotation data enable accurate determinations to be made of the dielectric properties of the outermost membrane of liposomes, and provide good indications of the level of complexity of the shells and internal compartments. We also demonstrate that, used with sufficient additional information, such as that provided by dielectrophoresis, electrorotation data yields unique solutions for the dielectric parameters of liposome-like particles.

Simple shell model for quantum dots in a tilted magnetic field

A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the wave functions are obtained by solving the classical problem. The ground state of the Fermi system is obtained by minimizing the total energy with regard to the confining frequencies. From this a dependence of the equilibrium shape of the quantum dot on the electron number, the magnetic field parameters, and the slab thickness is found.

Discussion: Nonlinear Dynamics of Simple Shell Model with Chaotic Snapping Behavior

Discussion: Nonlinear Dynamics of Simple Shell Model with Chaotic Snapping Behavior

Closure to “Nonlinear Dynamics of Simple Shell Model with Chaotic Snapping Behavior” by James M. Greer Jr. and Anthony N. Palazotto

Closure to “Nonlinear Dynamics of Simple Shell Model with Chaotic Snapping Behavior” by James M. Greer Jr. and Anthony N. Palazotto

Strength functions and spreading widths of simple shell model configurations.

The exact solution of the many-body problem in the framework of the nuclear shell model with a realistic residual Hamiltonian makes it possible to study the fragmentation of simple configurations as a function of excitation energy and interaction strength. The analysis is performed for 839 states with quantum numbers ${\mathit{J}}^{\mathrm{\ensuremath{\pi}}}$T=${0}^{+}$0 in a system of 12 valence particles within the sd shell. Our statistics allow us to establish the generic shape of the strength function in the region of strong mixing. For the realistic interaction, the strength function is close to Gaussian in the central part and has exponential wings. The spreading width is larger than predicted by the standard golden rule. At the artificially suppressed interaction strength, we recover the Breit-Wigner shape and the golden rule for the spreading width. The transition between these regimes agrees with theoretical considerations based on the idea of chaotic dynamics. \textcopyright{} 1996 The American Physical Society.

Local dynamics of YBa2Cu3O6+x and O(1)-defect dynamical stability.

Using Green{close_quote}s functions of the simple shell model of YBa{sub 2}Cu{sub 3}O{sub 6+{ital x}}, the local dynamics of the chain-defect O(1) ion is investigated. An {approximately}30{percent} softening of the effective noncentral force constants leads to dynamical instability of this ion with the perpendicular shift out of the chain in the {ital a} direction of the crystal. {copyright} {ital 1996 The American Physical Society.}

Magnetic moment in Ni clusters estimated by an electronic-shell model.

We estimate the size dependence of the magnetic moment of Ni clusters by using a simple electronic shell model, in which the 4{ital s} electron levels are described by the spherical harmonic oscillator model. This model reproduces the whole structure in the size dependence of the magnetic moment which has been experimentally observed. {copyright} {ital 1996 The American Physical Society.}

Scaling properties in MHD turbulence

The article first gives a brief review of the main properties of MHD turbulence, which are governed by the selective decay of the ideal invariants and the Alfvén effect. The inertial range behaviour is reflected in the geometric properties of level surfaces. These are predicted to have fractal dimension D = 11 4 (= 7 4 in 2- D) , which is verified in numerical simulations. The second part deals with the statistical properties. Probability density functions of the velocity and magnetic field increments and the energy dissipation rate are discussed. The simulations are complemented by the analysis of a simple shell model for MHD turbulence, taking into account the Alfvén effect. It is found that the latter is more subtle than anticipated.

Charge densities of the nuclei 86Sr, 89Y, 92Mo, 118Sn, and 152Sm and the proton occupancies of the shells 2s, 2p, 1g, and 1h.

The charge densities of several nuclei are calculated on the basis of a modified shell model with fractional number of states 2s,2p (eroding shells) and 1g,1h (gaining shells). The occupation probabilities of these states differ appreciably from the predictions of the simple shell model. Good agreement with model-independent (experimental) charge densities was obtained. The A dependence of oscillator parameters and root-mean-square radii are investigated.

Momentum and energy distributions of nucleons in finite nuclei due to short-range correlations.

The influence of short-range correlations on the momentum and energy distribution of nucleons in nuclei is evaluated assuming a realistic meson-exchange potential for the nucleon-nucleon interaction. Using the Green-function approach the calculations are performed directly for the finite nucleus $^{16}$O avoiding the local density approximation and its reference to studies of infinite nuclear matter. The nucleon-nucleon correlations induced by the short-range and tensor components of the interaction yield an enhancement of the momentum distribution at high momenta as compared to the Hartree-Fock description. These high-momentum components should be observed mainly in nucleon knockout reactions like $(e,e'p)$ leaving the final nucleus in a state of high excitation energy. Our analysis also demonstrates that non-negligible contributions to the momentum distribution should be found in partial waves which are unoccupied in the simple shell-model. The treatment of correlations beyond the Brueckner-Hartree-Fock approximation also yields an improvement for the calculated ground-state properties.

Nonlinear Dynamics of Simple Shell Model with Chaotic Snapping Behavior

A simple spring-mass numerical model (MSHELL), is developed as a tool to find appropriate integration time steps for nonlinear finite-element analysis. MSHELL possesses many features of nonlinearly deforming deep shells and, by matching some physical parameters of the MSHELL system and a nonlinear finite-element model (DSHELL), their dynamic behavior is both qualitatively and quantitatively similar. MSHELL is used to develop time-step criteria for both pre- and postsnapping behavior of a transversely point-loaded cylindrical shell. The criteria are then applied in a multiple-time-step method to DSHELL. The results indicate the simple model's correlation with the finite-element model and potential for saving computer time by changing the integration time step during a finite-element analysis based on MSHELL's behavior. Chaotic motion, characterized by one or more positive Lyapunov exponents, is seen in the simple model and likely explains unpredictable postcollapse results in the DSHELL finite-element code.

Subdaily northern hemisphere ionospheric maps using an extensive network of GPS receivers

Ionospheric total electron content (TEC) data derived from dual‐frequency Global Positioning System (GPS) signals from 30 globally distributed network sites are fit to a simple ionospheric shell model, yielding a map of the ionosphere in the northern hemisphere every 12 hours during the January 1–15, 1993 period, as well as values for the satellite and receiver instrumental biases. Root‐mean‐square (RMS) residuals of 2–3 TEC units are observed over the 20°–80° latitude band. Various systematic errors affecting the TEC estimates are discussed. The capability of using these global maps to produce ionospheric calibrations for sites at which no GPS data are available is also investigated.

Simplified alpha +4n model for the 8He nucleus.

A simple five-body cluster orbital shell model approximation is proposed to describe the ground state wave function of the [sup 8]He neutron-halo nucleus. The spatial angular correlations, the geometry of the system, the [alpha]-particle, and the valence neutron momentum distribution are calculated analytically. With a single free parameter the model is able to reproduce the experimental geometry of [sup 8]He as well as the experimental transverse momentum distribution of the [sup 6]He nucleus from [sup 8]He fragmentation on a carbon target, at high energy.

Momentum distributions of a 9Li fragment arising from the ( 11Li, 9Li) reaction and neutron correlations

The inclusive momentum distribution of a 9Li fragment arising from the ( 11Li, 9Li) reaction on light target nuclei at an incident energy of 800 MeV/nucleon is calculated within the Glauber theory. Both the reaction dynamics and the two-neutron correlation in the 11Li ground-state wave function is taken into account. The momentum distribution is found to reflect precisely the motion of the halo neutrons and affected little by the reaction dynamics. Some simple wave functions are employed to investigate the sensitivity of the momentum distribution to the structure of the halo neutrons. Neither the simple shell model nor the di-neutron cluster model alone reproduces the measured distribution. A linear combination of the shell-model and di-neutron cluster-model wave functions is found to reproduce the measured distribution, where the interference between them plays the important role in producing both narrow and wide components of the distribution.

A simple shell model interpretation of the evolution of structure in pre-collective nuclei

The evolution of structure in pre-collective nuclei from oxygen to actinides is studied in terms of the structural signature R 4 2 ≡ E(4 + 1) E(2 + 1) in singly magic nuclei. A simple physical interpretation of these empirical trends is discussed in terms and illustrated with schematic shell model calculations. The basic idea does not depend on details of the calculations but rather invokes only very general features of nuclear shell structure and the fact that the nuclear force is short-range and attractive.

Calculation of the strain derivatives of the static dielectric constant within the framework of the exchange charge model using different short range potential forms

A program has been developed to calculate up to third order volume and pressure derivatives of the static dielectric constant within the framework of the exchange charge model and the simple shell model. Salts with NaCl and CsCl structures are considered using seven different forms for the overlap potential. The higher order derivatives of the short-range potential with respect to the interionic distance, overlap potential parameters, force constants and their volume derivatives are also calculated with this program, among other quantities of interest.

Metallic character of small metal aggregates as a function of their atomic structure

The electronic properties of small clusters are investigated by various techniques as a function of their atomic structure. In alkali clusters, most electronic properties may be understood in terms of a very simple electronic shell model. In divalent metal clusters, a transition occurs as a function of the size from the Van der Waals structure to the metallic one. This transition has been characterized in mercury. In trivalent metal clusters, a different behaviour has been found for aluminium and indium clusters. This difference could be due to a solid-like structure for aluminium and a liquid-like structure for indium in our experimental conditions.