The Branching Rules for SU(2N)⊃(SU(N)⊃O(N)⊃O(3))⊗SU(2) and the Highest Weight States for SU(N) and O(N)

Simple analytical recurrent formulae of the branching rules for group chain SU(2N)⊃(SU(N)⊃O(N)⊃O(3))⊗SU(2) are obtained. The highest weight states for the irreducible representations [2^al^b] or {nS} of group SU(N) and for the irreducible representations (2^α1^β) or (υS) of group O(N) are constructed respectively     

Reduction Factors for O(N)⊃O(NK-1)

In terms of the concept of irreducible tensor basis and the properties of irreducible tensor operator, we give, by mathematical induction, the irreducible representations of O(N) for (m_1Nm_2N...m_[N/2]N) and all reduction factors of O(N)⊃O(N-1) for (1 0...0)⊗(m_1Nm_2N...m_[N/2]N)     

Spinor Representation Reduction Factors for O(N) ⊃ O(N - 1)

In this paper, the spinor irreducible representations of O (N) for (σ 1/2 1/2 ± 1/2) with some O (N) U-functions, are obtained by the building-up process.     

Fabrication, morphology, and photoluminescence properties of GaN nanowires and nanorods by ammoniating Ga2O3/V films on Si(1 1 1)

GaN nanowires and nanorods have been successfully synthesized on Si(1 1 1) substrates by magnetron sputtering through ammoniating Ga₂O₃/V films at 900 °C in a quartz tube. X-ray diffraction (XRD), scanning electron microscopy (SEM), high-resolution transmission electron microscopy (HRTEM), X-ray photoelectron spectroscopy (XPS), and photoluminescence (PL) spectrum were carried out to characterize the structure, morphology, and photoluminescence properties of GaN sample. The results show that the GaN nanowires and nanorods with pure hexagonal wurtzite structure have good emission properties. The growth direction of nanostructures is perpendicular to the fringes of (1 0 1) plane. The growth mechanism is also briefly discussed.     

Piezoresponse imaging and local characterization of ferroelectric domains in Pb(Zn1/3Nb2/3)O3–7%PbTiO3 single crystals

Ferroelectric domain structures of (001)‐oriented Pb(Zn_1/3Nb_2/3)O₃–7%PbTiO₃ (PZN‐7%PT) single crystals were visualized and characterized by piezoresponse force microscopy (PFM). Locally regular domain configurations are found to be possibly related to the stable macroscopic properties in the PZN‐7%PT single crystals. Nanoscale piezoresponse hysteresis loops measured by PFM tip revealed no evidence of local domain switching behavior in the PZN‐7%PT single crystal. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Atypical grain growth for (2 1 1) CdTe films deposited on surface reconstructed (1 0 0) SrTiO3 substrates

The (1 0 0) SrTiO₃ substrate has emerged as the oxide substrate of choice for the deposition of a wide variety of materials. The substrate's unavoidable miscut leads to a step-terrace morphology when heated to high temperatures. This morphological transition is accompanied by an atomic scale repositioning of the uppermost terrace atoms, the nature of which is strongly dependent on the substrate temperature and ambient atmosphere used. Here, we report the deposition of CdTe films on the as-received and reconstructed surfaces of (1 0 0) SrTiO₃. The as-received substrate gives rise to a [1 1 1] CdTe film with four equally distributed in-plane grain orientations. The surface reconstruction, on the other hand, gives rise to an unprecedented reorientation of the film's grain structure. For this case, a [2 1 1] CdTe film emerges having twelve unevenly distributed in-plane orientations. We attribute the film's grain structure to an atomic scale surface reconstruction, with the anisotropic distribution of grain-types arising from a preferential formation due to the step edges.     

Stark broadening of isolated lines: calculation of the diagonal multiplet factor for complex configurations (n1l1 n n2l2 m n3l3 p)

Owing to the increasing sensitivity of detectors, accurate line profiles are needed for accurate stellar atmospheres modelling and for laboratory and technological plasmas as well. So, Stark broadening parameters of isolated lines of complex atoms and ions within the impact and quasistatic approximation are needed, even if the atomic abundance of the considered element is low. Angular factors of the diagonal line strength entering the quadrupole term appearing in the semi-classical expression of the width of line broadened by electron or ion perturbers, are needed. The aim of this paper is to extend the previous calculations of this diagonal multiplet factor which were obtained for configurations of the type lⁿ and l₁ ⁿl₂ ^m to more complex configurations in LS coupling. To study the Stark broadening of isolated lines in the impact and quasistatic approximation, we use the semi-classical-perturbation treatment, including both dipole and quadrupole contribution in the expansion of the electrostatic interaction between the optical electron and the perturber. We also use the Fano-Racah algebra. Angular factors of the diagonal line strength entering the quadrupole term appearing in the semi-classical expression of the width of line broadened by electron or ion perturbers, are calculated. New diagonal multiplet factor formulae for more complicated configurations such as (n₁l₁ ⁿ(L_nS_n)n₂l₂ ^m(L_mS_m)n₃l₃ ^p(L_pS_p)) are provided. These formulae can enter the computer Stark semi-classical perturbation codes.     

Hyperfine-structure studies of the 1s<Superscript>2</Superscript>2snp (n=2, 3) <Superscript>3</Superscript>P states for the beryllium isoelectronic sequence

The hyperfine structure parameters of the 1s²2snp (n=2, 3) ³P states for the beryllium isoelectronic sequence from Z= 4 to 10 are calculated with the full-core plus correlation (FCPC) wave functions. For the 1s²2s2p ³P state of the beryllium atom, the calculated fine structure parameters are in good agreement with the latest theoretical and experimental data in the literature. It is shown that hyperfine constants of the low-lying excited states for the beryllium atom can be calculated accurately using this theoretical method. For 1s²2snp (n=2, 3) ³P states of the beryllium isoelectronic sequence, our predictions may provide valuable reference data for other theoretical calculations and experimental measurements in future.     

Control of Charge Transfer Phase Transition in Iron Mixed-Valence System (n-C n H2n+1)4N[FeIIFeIII(dto)3] (n=3–6; dto = C2O2S2)

The spin flop behaviour of low anisotropy Mn ions within the mixed halide (⁵⁴Mn)Mn(Br _x Cl_1−x )₂·4H₂O is shown to be interpolative with that of the two terminal compounds, in striking contrast with the dynamics of nuclear spin lattice relaxation.     

Screening constant by unit nuclear charge calculations for (n s2)1Se, (np2)1De and (N s n p)1P○ excited states of He-like systems

Screening Constant by Unit Nuclear Charge (SCUNC) is a new analytical method suitable for the treatment of the properties of He-like systems. In this paper, the possibilities of the method are demonstrated for calculating in the framework of semi-empirical procedure, total energies, total electron-electron interaction energies and excitation energies for (ns²)¹S^e, (np²)¹D^e and (Nsnp)¹P° doubly excited states of He-like ions. The proposed semi-empirical scheme, leads to accurate results in good agreement as well as with available other theoretical results than experimental data.     

Facile Synthesis of Gd(OH)3‐Doped Fe3O4 Nanoparticles for Dual‐Mode T1‐ and T2‐Weighted Magnetic Resonance Imaging Applications

The facile hydrothermal synthesis of polyethyleneimine (PEI)‐coated iron oxide (Fe₃O₄) nanoparticles (NPs) doped with Gd(OH)₃ (Fe₃O₄‐Gd(OH)₃‐PEI NPs) for dual mode T₁‐ and T₂‐weighted magnetic resonance (MR) imaging applications is reported. In this approach, Fe₃O₄‐Gd(OH)₃‐PEI NPs are synthesized via a hydrothermal method in the presence of branched PEI and Gd(III) ions. The PEI coating onto the particle surfaces enables further modification of poly(ethylene glycol) (PEG) in order to render the particles with good water dispersibility and improved biocompatibility. The formed Fe₃O₄‐Gd(OH)₃‐PEI‐PEG NPs have a Gd/Fe molar ratio of 0.25:1 and a mean particle size of 14.4 nm and display a relatively high r₂ (151.37 × 10^?3m ^?1 s^?1) and r₁ (5.63 × 10^?3m ^?1 s^?1) relaxivity, affording their uses as a unique contrast agent for T₁‐ and T₂‐weighted MR imaging of rat livers after mesenteric vein injection of the particles and the mouse liver after intravenous injection of the particles, respectively. The developed Fe₃O₄‐Gd(OH)₃‐PEI‐PEG NPs may hold great promise to be used as a contrast agent for dual mode T₁‐ and T₂‐weighted self‐confirmation MR imaging of different biological systems.     

Cross-sections for the formation of isomeric pair Ge through (n, 2n), (n, p) and (n, α) reactions measured over 13.73 MeV to 14.77 MeV and calculated from near threshold to 20 MeV neutron energies

The cross-sections for formation of isomeric pair, ⁷⁵Ge^m(σ_m) and ⁷⁵Ge^g(σ_g), through ⁷⁶Ge(n, 2n), ⁷⁵As(n, p) and ⁷⁸Se(n, α) reactions were measured at 13.73 MeV, 14.42 MeV and 14.77 MeV neutrons and also estimated using EMPIRE-II and TALYS codes over neutron energies from near threshold to 20 MeV. For each (n, 2n), (n, p) and (n, α) reaction, the cross-section initially increases with neutron energy, but starts decreasing as the neutron energy exceeds the respective threshold of (n, 3n), (n, pn) and (n, αn) reactions. The higher values of σ_m relative to σ_g reveal that the transitions of the excited ⁷⁵Ge from higher energy levels to metastable state (7⁺/2) are favored as compared to unstable ground state (1⁻/2). The present values of cross sections for formation of ⁷⁵Ge^m,g through (n, 2n) and (n, α) reactions are lower, and that of (n, p) reaction are higher compared to most of the corresponding literature cross-sections.