Shell Correction Method Research Articles

Trianionic gold clusters

Using Penning-trap experiments and a shell-correction method incorporating ellipsoidal shape deformations, we investigate the formation and stability patterns of trianionic gold clusters. Theory and ex- periment are in remarkable agreement concerning appearance sizes and electronic shell eects. In contrast to multiply cationic clusters, decay of the trianionic gold clusters occurs primarily via electron autodetach- ment and tunneling through a Coulomb barrier, rather than via ssion. PACS. 36.40.Wa Charged clusters { 36.40.Qv Stability and fragmentation of clusters { 36.40.Cg Electronic and magnetic properties of clusters

Multiply charged metal cluster anions.

Formation and stability patterns of silver dianionic and gold trianionic clusters are investigated with Penning-trap experiments and a shell-correction method including shape deformations. The theoretical predictions pertaining to the appearance sizes and electronic shell effects are in remarkable agreement with the experiments. Decay of the multiply anionic clusters occurs predominantly by electron tunneling through a Coulomb barrier rather than via fission, leading to appearance sizes unrelated to those of multiply cationic clusters.

Semiclassical density functional theory: Strutinsky energy corrections in quantum dots

We develop a semiclassical density functional theory in the context of quantum dots. Coulomb blockade conductance oscillations have been measured in several experiments using nanostructured quantum dots. The statistical properties of these oscillations remain puzzling, however, particularly the statistics of spacings between conductance peaks. To explore the role that residual interactions may play in the spacing statistics, we consider many-body systems that include electron-electron interactions through an explicit density functional. First, we develop an approximate series expansion for obtaining the ground state using the idea of the Strutinsky shell correction method. Next, we relate the second-order semiclassical corrections to the screened Coulomb potential. Finally, we investigate the validity of the approximation method by numerical calculation of a one-dimensional model system, and show the relative magnitudes of the successive terms as a function of particle number.

Decay channels and appearance sizes of doubly anionic gold and silver clusters

Second electron affinities of Au_N and Ag_N clusters and the dissociation energies for fission of the Au_N^{2-} and Ag_N^{2-} dianions are calculated using the finite-temperature shell-correction method and allowing for triaxial deformations. Dianionic clusters with N > 2 are found to be energetically stable against fission, leaving electron autodetachment as the dominant decay process. The second electron affinities exhibit pronounced shell effects in excellent agreement with measured abundance spectra for Au_N^{2-} (N < 30), with appearance sizes N=12 for gold dianionic clusters and N=24 for silver dianionic clusters.

Spheroidal shell model for fission of doubly charged silver clusters

Fission of doubly charged silver clusters ${\mathrm{Ag}}_{n}^{2+}$ is studied in the size range of $12&lt;~n&lt;~22.$ It is assumed that two fragment clusters are in contact at the transition state. The shape of each fragment is an energetically optimized spheroid. The energy barrier for various fission channels is calculated by using the shell correction method. This simple model closely reproduces the fragment size distribution measured by Katakuse et al. It is confirmed that the shell effects govern the distribution of fission fragments, while the liquid droplet model cannot explain the distribution. In particular, the even-odd oscillations observed in the distribution are found to be due to deformations of fragment clusters. Competition between fission and evaporation is discussed.

Staggering in Rotor Hamiltonians Without C4 Symmetry

After a brief review of the negative results of the microscopic study, of both the Strutinsky shell correction method and Hartree-Fock approximation, for the C4 symmetry in nuclei, a proposed rotor Hamiltonian to simulate both the microscopic results and the staggering effect is investigated and the staggering resulting from the rotor Hamiltonians without C4 symmetry can be found.

On charged mesoscopic metallic bubbles

We investigate the existence of stable charged metallic bubbles using the shell correction method. We find that for a given mesoscopic system of n atoms of a given metal and q less n (positive) elementary charges, a metallic bubble turns out to have a lower total energy than a compact spherical cluster, whenever the charge number q is larger than acritical charge number q_c. For a magic number (n-q) of free electrons, the spherical metallic bubble may become stable against fission.

Molecular Dynamics in Shape Space and Femtosecond Vibrational Spectroscopy of Metal Clusters

We introduce a method of molecular dynamics in shape space aimed at metal clusters. The ionic degrees of freedom are described via a dynamically deformable jellium with inertia parameters derived from an incompressible, irrotational flow. The shell correction method is used to calculate the electronic potential energy surface underlying the dynamics. Our finite temperature simulations of Ag_14 and its ions, following the negative to neutral to positive scheme, demonstrate the potential of pump and probe ultrashort laser pulses as a spectroscopy of cluster shape vibrations.

Energetics, forces, and quantized conductance in jellium-modeled metallic nanowires

Energetics and quantized conductance in jellium modeled nanowires are investigated using the local density functional based shell correction method, extending our previous study of uniform in shape wires [C. Yannouleas and U. Landman, J. Phys. Chem. B 101, 5780 (1997)] to wires containing a variable shaped constricted region. The energetics of the wire (sodium) as a function of the length of the volume conserving, adiabatically shaped constriction leads to formation of self selecting magic wire configurations. The variations in the energy result in oscillations in the force required to elongate the wire and are directly correlated with the stepwise variations of the conductance of the nanowire in units of 2e^2/h. The oscillatory patterns in the energetics and forces, and the correlated stepwise variation in the conductance are shown, numerically and through a semiclassical analysis, to be dominated by the quantized spectrum of the transverse states at the narrowmost part of the constriction in the wire.

Comment on “Density functional theory study of some structural and energetic properties of small lithium clusters” [J. Chem. Phys. 105, 9933 (1996)

The Ionization Potentials of small LiN clusters are calculated with a Shell Correction Method. They are used to illustrate that, within the jellium approximation, deformed cluster shapes provide an adequate description of the observed systematic size dependence of the properties of simple metal clusters. Such deformation effects were overlooked in the analysis of Gardet et al.

On Mesoscopic Forces and Quantized Conductance in Model Metallic Nanowires

Energetics and conductance in jellium-modeled nanowires are investigated using the local-density-functional-based shell correction method. In analogy with studies of other finite-size fermion systems, e.g., simple metal clusters or 3He clusters, we find that the energetics of the wire as a function of its radius (transverse reduced dimension) leads to formation of self-selecting magic wire configurations (MWCs, i.e., discrete sequence of wire radii with enhanced stability), originating from quantization of the electronic spectrum, namely formation of subbands that are the analogs of electronic shells in clusters. These variations in the energy result in oscillations in the force required to affect a transition from one MWC of the nanowire to another and are correlated directly with stepwise variations of the quantized conductance of the nanowire in units of 2e2/h.

Shapes and shells in nuclear structure

Preface 1. Introduction 2. Charge and matter distribution in nuclei 3. The semi-empirical mass formula and nuclear stability 4. Nuclear fission and the liquid-drop model 5. Shell structure and magic numbers 6. The nuclear one-particle potential in the spherical case 7. The magnetic dipole moment and electric quadrupole moment for nuclei with closed shells +/- one nucleon 8. Single-particle orbitals in deformed nuclei 9. The shell correction method and the nuclear deformation energy 10. The barrier penetration problem - fission and alpha-decay 11. Rotational bands - the particle-rotor model 12. Fast nuclear rotation - the cranking model 13. The nucleon-nucleon two-body interaction 14. The pairing interaction Solutions to exercises.

POTENTIAL-ENERGY SURFACES OF SODIUM CLUSTERS WITH QUADRUPOLE, HEXADECAPOLE, AND TRIAXIAL DEFORMATIONS

Combining a modified Nilsson-Clemenger model with the shell-correction method, the potential-energy surfaces of sodium clusters with sizes of up to N = 200 atoms are calculated, including nonaxial deformations. For spherical clusters, the model potential is fitted to the single-particle spectra obtained from microscopically self-consistent Kohn-Sham calculations using the jellium model and the localdensity approximation. Employing the Strutinsky shell-correction method, the surface energy of the jellium model is renormalized to its experimental value. The ground-state shapes are determined by simultaneous minimization of the deformation energies for quadrupole, hexadecapole, and triaxial cluster deformations.

SHAPES AND FREE ENERGIES OF MOLTEN SODIUM CLUSTERS

The shell-correction method is formulated to calculate the shapes and free energies of hot alkali clusters. The equilibrium shapes of Na clusters with mass 50–700 are calculated by minimizing simultaneously with respect to two deformation parameters. For T=700°K strong deviations from spheroidal shape including reflection asymmetric shapes are found to survive in the center of the open shells. The second derivative of calculated free energy correlates with the derivative of the experimental cluster abundances, showing prominent spikes related to the change between spherical and deformed shape.

THEORETICAL STUDY OF FISSION OF SIMPLE METAL CLUSTERS USING A JELLIUM MODEL

Fission of simple metal clusters is investigated using a jellium model which allows axial symmetrical deformations and fission. The Kohn-Sham equations for the jellium model are solved by the discrete-variable representation method where the zeros of the sine functions and the zeros of the 0th order Bessel functions are used for the basis for z-coordinate and ρ-coordinate, respectively. The comparison between the jellium model results and the shell-correction method results is made.

MAGNETIC PROPERTIES OF SODIUM CLUSTERS

Axial and triaxial shapes of Na clusters are determined by means of the shell-correction method.1 The orbital paramagnetism and the diamagnetism of small Na clusters are calculated. Odd axial clusters may have substantial orbital paramagnetic moments, which are quenched for triaxial shapes. Even clusters show diamagnetism, which is maximal for spherical and attenuated for deformed shape.

Fission of metal clusters: A comparison of jellium model calculations and shell correction method calculations

We investigate the fission process Ag2+23 → Ag+12 + Ag+11 in order to compare total energies that calculated by the shell correction method and jellium models. A cavity potential and a Woods-Saxon-type potential are used as the shell potential for the shell correction method, with which the single-particle energy levels are calculated. Shell corrections are obtained by using the Balian-Bloch formula and by smoothing the discrete energy levels in the shell potentials. The jellium model calculations are performed in the framework of the local spin density functional approximation. The conventional jellium model and stabilized jellium model are used. Although the qualitative agreement between the shell correction method calculations and the stabilized jellium calculations is very good, an improvement of the liquid drop energy will be necessary for the satisfactory quantitative agreement. © 1996 John Wiley & Sons, Inc.

Fission of metal clusters: A comparison of jellium model calculations and shell correction method calculations

We investigate the fission process Ag2+23 Ag+12 + Ag+11 in order to compare total energies that calculated by the shell correction method and jellium models. A cavity potential and a Woods-Saxon-type potential are used as the shell potential for the shell correction method, with which the single-particle energy levels are calculated. Shell corrections are obtained by using the Balian-Bloch formula and by smoothing the discrete energy levels in the shell potentials. The jellium model calculations are performed in the framework of the local spin density functional approximation. The conventional jellium model and stabilized jellium model are used. Although the qualitative agreement between the shell correction method calculations and the stabilized jellium calculations is very good, an improvement of the liquid drop energy will be necessary for the satisfactory quantitative agreement. © 1996 John Wiley & Sons, Inc.

General axial shapes of sodium clusters

AbstractThe shell correction method is applied to calculate the shapes and binding energies of Na clusters. The axial equilibrium shapes are calculated by minimizing five deformation parameters simultaneously. Strong deviations from spheroidal shapes including reflection asymmetric ones are found. The influence of cluster deformation on the separation energies and ionization potentials and on the splitting of the photo ‐ resonance are compared with the available experimental data. The N‐dependence of the cluster shape and its relation to the N‐ and Z‐dependences of the nuclear shape is discussed.

Fission of metal clusters: A comparison of jellium model calculations and shell correction method calculations

Fission of metal clusters: A comparison of jellium model calculations and shell correction method calculations