Semi-spheroidal Quantum Harmonic Oscillator

A new single-particle shell model is derived by solving the Schr\"odinger equation for a semi-spheroidal potential well. Only the negative parity states of the $Z(z)$ component of the wave function are allowed, so that new magic numbers are obtained for oblate semi-spheroids, semi-sphere and prolate semi-spheroids. The semi-spherical magic numbers are identical with those obtained at the oblate spheroidal superdeformed shape: 2, 6, 14, 26, 44, 68, 100, 140, ... The superdeformed prolate magic numbers of the semi-spheroidal shape are identical with those obtained at the spherical shape of the spheroidal harmonic oscillator: 2, 8, 20, 40, 70, 112, 168 ...Comment: 4 pages, 3 figures, 1 tabl

Classical Analysis of Phenomenological Potentials for Metallic Clusters

The classical trajectories of single particle motion in a Wodds-Saxon and a modified Nilsson potential are studied for axial quadrupole deformation. Both cases give rise to chaotic behaviour when the deformation in the Woods-Saxon and the l**2 term in the modified Nilsson potential are turned on. Important similarities, in particular with regard to the shortest periodic orbits, have been found.Comment: 9 pages LaTex + 4 figures available via e-mail requests from the authors, to appear in Phys.Rev.Let

Orbital Magnetic Dipole Mode in Deformed Clusters: A Fully Microscopic Analysis

The orbital M1 collective mode predicted for deformed clusters in a schematic model is studied in a self-consistent random-phase-approximation approach which fully exploits the shell structure of the clusters. The microscopic mechanism of the excitation is clarified and the close correlation with E2 mode established. The study shows that the M1 strength of the mode is fragmented over a large energy interval. In spite of that, the fraction remaining at low energy, well below the overwhelming dipole plasmon resonance, is comparable to the strength predicted in the schematic model. The importance of this result in view of future experiments is stressed.Comment: 10 pages, 3 Postscript figures, uses revte

Semiclassical analysis of the lowest-order multipole deformations of simple metal clusters

We use a perturbative semiclassical trace formula to calculate the three lowest-order multipole (quadrupole \eps_2, octupole \eps_3, and hexadecapole \eps_4) deformations of simple metal clusters with $90 \le N \le 550$ atoms in their ground states. The self-consistent mean field of the valence electrons is modeled by an axially deformed cavity and the oscillating part of the total energy is calculated semiclassically using the shortest periodic orbits. The average energy is obtained from a liquid-drop model adjusted to the empirical bulk and surface properties of the sodium metal. We obtain good qualitative agreement with the results of quantum-mechanical calculations using Strutinsky's shell-correction method.Comment: LaTeX file (v2) 6 figures, to be published in Phys. Lett.

The 3-Dimensional q-Deformed Harmonic Oscillator and Magic Numbers of Alkali Metal Clusters

Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3) > SOq(3) symmetry are compared to experimental data for alkali metal clusters, as well as to theoretical predictions of jellium models, Woods--Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. The 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of alkali metal clusters.Comment: 13 pages, LaTe

Deformed Harmonic Oscillators for Metal Clusters: Analytic Properties and Supershells

The analytic properties of Nilsson's Modified Oscillator (MO), which was first introduced in nuclear structure, and of the recently introduced, based on quantum algebraic techniques, 3-dimensional q-deformed harmonic oscillator (3-dim q-HO) with Uq(3) > SOq(3) symmetry, which is known to reproduce correctly in terms of only one parameter the magic numbers of alkali clusters up to 1500 (the expected limit of validity for theories based on the filling of electronic shells), are considered. Exact expressions for the total energy of closed shells are determined and compared among them. Furthermore, the systematics of the appearance of supershells in the spectra of the two oscillators is considered, showing that the 3-dim q-HO correctly predicts the first supershell closure in alkali clusters without use of any extra parameter.Comment: 25 pages LaTeX plus 21 postscript figure

Electronic-structure-induced deformations of liquid metal clusters

Ab initio molecular dynamics is used to study deformations of sodium clusters at temperatures $500\cdots 1100$ K. Open-shell Na$_{14}$ cluster has two shape isomers, prolate and oblate, in the liquid state. The deformation is stabilized by opening a gap at the Fermi level. The closed-shell Na$_8$ remains magic also at the liquid state.Comment: REVTex, 11 pages, no figures, figures (2) available upon request (e-mail to hakkinen at jyfl.jyu.fi), submitted to Phys. Rev.

Electric multipole plasmons in deformed sodium clusters

The random-phase-approximation (RPA) method with separable residual forces (SRPA) is proposed for the description of multipole electric oscillations of valence electrons in deformed alkali metal clusters. Both the deformed mean field and residual interaction are derived self-consistently from the Kohn-Sham functional. SRPA drastically simplifies the computational effort which is urgent if not decisive for deformed systems. The method is applied to the description of dipole, quadrupole and octupole plasmons in deformed sodium clusters of a moderate size. We demonstrate that, in clusters with the size N>50, Landau damping successfully competes with deformation splitting and even becomes decisive in forming the width and gross structure of the dipole plasmon. Besides, the plasmon is generated by excitations from both ground state and shape isomers. In such clusters familiar experimental estimates for deformation splitting of dipole plasmon are useless.Comment: 27 pages, 10 figure

Scissors modes in triaxial metal clusters

We study the scissors mode (orbital M1 excitations) in small Na clusters, triaxial metal clusters ${\rm Na}_{12}$ and ${\rm Na}_{16}$ and the close-to-spherical ${{\rm Na}_9}^+$, all described in DFT with detailed ionic background. The scissors modes built on spin-saturated ground and spin-polarized isomeric states are analyzed in virtue of both macroscopic collective and microscopic shell-model treatments. It is shown that the mutual destruction of Coulomb and the exchange-correlation parts of the residual interaction makes the collective shift small and the net effect can depend on details of the actual excited state. The crosstalk with dipole and spin-dipole modes is studied in detail. In particular, a strong crosstalk with spin-dipole negative-parity mode is found in the case of spin-polarized states. Triaxiality and ionic structure considerably complicate the scissors response, mainly at expense of stronger fragmentation of the strength. Nevertheless, even in these complicated cases the scissors mode is mainly determined by the global deformation. The detailed ionic structure destroys the spherical symmetry and can cause finite M1 response (transverse optical mode) even in clusters with zero global deformation. But its strength turns out to be much smaller than for the genuine scissors modes in deformed systems.Comment: 17 pages, 5 figure