Solitary Solvable Groups

A subgroup H of a group G is a solitary subgroup of G if G does not contain another isomorphic copy of H. Combining together the concepts of solitary subgroups and solvable groups, we define (normal) solitary solvable groups and (normal) strongly solitary solvable groups. We derive several results that hold for these groups and we discuss classes of groups that, under certain hypotheses, are (normal) solitary solvable and (normal) strongly solitary solvable. We also derive several results about p-groups that are solitary solvable.     

Ion bunch stacking in a Penning trap after purification in an electrostatic mirror trap

The success of many measurements in analytical mass spectrometry as well as in precision mass determinations for atomic and nuclear physics is handicapped when the ion sources deliver “contaminations”, i.e., unwanted ions of masses similar to those of the ions of interest. In particular, in ion-trapping devices, large amounts of contaminant ions result in significant systematic errors—if the measurements are possible at all. We present a solution for such cases: The ions from a quasi-continuous source are bunched in a linear radio-frequency-quadrupole ion trap, separated by a multi-reflection time-of-flight section followed by a Bradbury–Nielsen gate, and then captured in a Penning trap. Buffer-gas cooling is used to damp the ion motion in the latter, which allows a repeated opening of the Penning trap for a stacking of mass-selected ion bunches. Proof-of-principle demonstrations have been performed with the ISOLTRAP setup at ISOLDE/CERN, both with ¹³³Cs⁺ ions from an off-line ion source and by application to an on-line beam of ¹⁷⁹Lu⁺ ions contaminated with ¹⁶³Dy¹⁶O⁺ ions. In addition, an optimization of the experimental procedure is given, in particular for the number of ion bunches captured as a function of the ions’ lifetimes and the parameters of the experiment .     

Quantum anticentrifugal potential in a bent waveguide

We show the existence of an anticentrifugal force for a quantum particle in a bent waveguide. This effect may be observed in interference experiments which are sensitive to the additional phase of the wavefunction gained in the bent regions and can find application in distinguishing between straight and bent geometries.     

Influence of the environment on equilibrium properties of Au-Pd clusters

The question of the influence of the environment on the structure and thermodynamic state of a bimetallic cluster is examined, using Metropolis Monte Carlo methods. An embedded atom model is used to estimate metal energies. The environment is modeled at a generic level as a rigid matrix which atoms interact with the atoms of an embedded Au-Pd cuboctahedral cluster via a Lennard Jones (LJ) potential. The high sensitivity of the cluster properties on its environment is demonstrated by scaling the LJ potential. It is found that the strength of the interfacial interactions completely determines surface segregation. Full segregation with either Au or Pd at the surface favors the occurrence of stable alloy phases in the cluster core while the subsurface layer acts as a buffer accommodating both the induced surface segregation and the inner composition constrained by phase stability. Cluster surface disorder induced by an amorphous matrix limits interface segregation and phase stability in the cluster core, even when the interfacial interaction strength is weak. The contrast between the epitaxial and amorphous matrix cases over a wide range of interface energies suggests the importance in the thermodynamic properties of the cluster core of the interfacial atomic arrangement in the matrix.     

Detailed ab initio first-principles study of the magnetic anisotropy in a family of trigonal pyramidal iron(II) pyrrolide complexes

A theoretical, computational, and conceptual framework for the interpretation and prediction of the magnetic anisotropy of transition metal complexes with orbitally degenerate or orbitally nearly degenerate ground states is explored. The treatment is based on complete active space self-consistent field (CASSCF) wave functions in conjunction with N-electron valence perturbation theory (NEVPT2) and quasidegenerate perturbation theory (QDPT) for treatment of magnetic field- and spin-dependent relativistic effects. The methodology is applied to a series of Fe(II) complexes in ligand fields of almost trigonal pyramidal symmetry as provided by several variants of the tris-pyrrolylmethyl amine ligand (tpa). These systems have recently attracted much attention as mononuclear single-molecule magnet (SMM) complexes. This study aims to establish how the ligand field can be fine tuned in order to maximize the magnetic anisotropy barrier. In trigonal ligand fields high-spin Fe(II) complexes adopt an orbitally degenerate (5)E ground state with strong in-state spin-orbit coupling (SOC). We study the competing effects of SOC and the (5)E?ε multimode Jahn-Teller effect as a function of the peripheral substituents on the tpa ligand. These subtle distortions were found to have a significant effect on the magnetic anisotropy. Using a rigorous treatment of all spin multiplets arising from the triplet and quintet states in the d(6) configuration the parameters of the effective spin-Hamiltonian (SH) approach were predicted from first principles. Being based on a nonperturbative approach we investigate under which conditions the SH approach is valid and what terms need to be retained. It is demonstrated that already tiny geometric distortions observed in the crystal structures of four structurally and magnetically well-documented systems, reported recently, i.e., [Fe(tpa(R))](-) (R = tert-butyl, Tbu (1), mesityl, Mes (2), phenyl, Ph (3), and 2,6-difluorophenyl, Dfp (4), are enough to lead to five lowest and thermally accessible spin sublevels described sufficiently well by S = 2 SH provided that it is extended with one fourth order anisotropy term. Using this most elementary parametrization that is consistent with the actual physics, the reported magnetization data for the target systems were reinterpreted and found to be in good agreement with the ab initio results. The multiplet energies from the ab initio calculations have been fitted with remarkable consistency using a ligand field (angular overlap) model (ab initio ligand field, AILFT). This allows for determination of bonding parameters and quantitatively demonstrates the correlation between increasingly negative D values and changes in the σ-bond strength induced by the peripheral ligands. In fact, the sigma-bonding capacity (and hence the Lewis basicity) of the ligand decreases along the series 1 > 2 > 3 > 4.     

Luminescence properties of thin films prepared by laser ablation of Nd-doped potassium gadolinium tungstate

Optically active thin films on Si substrates have been produced by laser ablation of a Nd-doped potassium gadolinium tungstate (Nd:KGW) single crystal. Films grown at low oxygen pressures (<0.6 mbar) are potassium-deficient and appear to be mainly disordered. They show a poor photoluminescence (PL) performance that improves upon annealing in air at temperatures in the range 700–1000 °C. Films grown at high oxygen pressure (1 mbar) show instead good stoichiometry and the presence of a dominant textured gadolinium-tungstate phase compared to KGW. These films have low absorption, a refractive index close to that of bulk KGW and good PL performance, the emission lifetimes being longer (τ>150 μs) under certain conditions than those measured in the single-crystal material. Received: 25 July 2001 / Accepted: 26 July 2001 / Published online: 17 October 2001     

Qubits from tight knots, bent nano-bars and nano-tubes

We propose a novel mechanism for creating a qubit based on a tight trefoil knot, that is an electron nano-waveguide system so small as to be quantum coherent with respect to curvature-induced effects. To establish tight trefoil knots as legitimate candidates for qubits, we propose an effective curvature-induced potential that produces the two-level system and identify the tunnel coupling between the two local states. The proposed two-level system is geometrical in nature and is macroscopic of origin. It also represents new and peculiar property of the trefoil knot. We also propose a different realization of a qubit based on twisted nano-bars and nano-tubes.