Hyperfine interaction parameters and ground-state wavefunctions of vanadyl ion complexes

Using crystal field approach a theoretical estimate of the ground-state wavefunctions of vanadyl ion doped in various crystals have been made using ESR data and is found to bed _xy in our coordinate system with slight admixture of the excited states ,d _xz andd _yz. The hyperfine interaction parameterP and Fermi contact coupling parameterK have also been estimated for these vanadyl-doped crystals. Results agree with similar studies made earlier.     

Study of EPR parameters and defect structure for two tetragonal impurity centers in MgO:Cr<Superscript>3+</Superscript> and MgO:Mn<Superscript>4+</Superscript> crystals

The electron paramagnetic resonance (EPR) parameters (g-factors g _‖, g _⊥ and zero-field splitting D) of two tetragonal 3d³ impurity centers M_3d-V_Mg and M_3d-Li⁺ (where M_3d = Cr³⁺ or Mn⁴⁺, V_Mg is the Mg²⁺ vacancy) in M_3d-doped MgO crystals are calculated from the high-order perturbation formulas including both the crystal-field (CF) and the charge-transfer (CT) mechanisms for 3d³ ions in the tetragonal symmetry. The calculated results are in reasonable agreement with the experimental values. From the calculations, it can be found that the relative importance of the CT mechanism for EPR parameters increases with increasing valence state of the 3d³ ion. So, for the high-valence 3d ⁿ ions in crystals, a reasonable explanation of EPR parameters should take into account both CF and CT mechanisms. The defect structures (characterized by the displacement ΔR of O²⁻ in the intervening M_3d and V_Mg or Li⁺ at the Mg²⁺ site) for these tetragonal impurity centers are obtained from the calculations. The results are consistent with the expectations based on the electrostatic interactions.     

Studies of local phase transition behavior for Co2+ in CsCaCl3 crystals from EPR data

In this paper, we establish the calculation formulas ofg factorsg _∥,g _⊥ and the hyperfine structure constantsA _∥,A _⊥ for 3d⁷ ions in tetragonal octahedral field from a cluster approach. In these formulas, besides the configuration interaction, the covalency effect due to the admixture between d electrons of 3d⁷ ion and the p electrons of ligands is considered. The parameters used in these formulas (except the core polarization constantsk in the calculation ofA _i) can be obtained from optical spectra of the studied crystal. From these formulas, the local release (or elongation) factork, which is introduced to characterize the release effect of impurity-ligand bond along C₄ axis at the cubic to tetragonal phase transition, is estimated for CsCaCl₃:Co²⁺ crystal by calculating the electronic paramagnetic resonance (EPR) parametersg _i andA _i . These EPR parameters are therefore explained reasonably and the results are discussed.     

Zeeman splitting factor of the Er3+ ion in a crystal field

Numerical computations are presented on the energy levels of the Er³⁺ ion in crystalline fields of cubic, trigonal, tetragonal and orthorhombic symmetry. Zeeman splitting factors were obtained from the level splitting in an additional magnetic field. For the quartet Γ₈ states in cubic symmetry the Zeeman effect is described by an effective Hamiltonian ℋ= gμ_BBJ+ uμ_BBJ³ with the parametersg andu calculated for mixed fourth- and sixth-order potentials. For the eight doublets in the lower symmetry of an axial trigonal or tetragonal crystal field the principalg tensor components g_∥ and g_⊥ were calculated. The results of such calculations for a ground-state doublet can exactly account for the experimental data obtained on around 70 erbium centers in various crystalline hosts. However, sometimes different sets of parameters give comparably good results. An empirical rule of constant trace g_∥ + 2g_⊥ is supported by the calculations. In contrast to analytical treatments the effect of the crystalline field can be followed over a continuous range of the crystal field parameters. This allows one to establish relations on the relative signs of tensor components. It is found that the measured trace of tensors |g_∥| + 2|g_⊥| is not always equal to their real trace g_∥ + 2g_⊥. In an exploratory calculation a nonaxial center was simulated in an orthorhombic field, with calculation of the three principal values g_x, g_y and g_z. A good agreement is obtained for the recently reportedg values of an erbium center in silicon.     

Dielectric properties of 4′-n-alkyl-4-cyanobiphenyls in their nematic phases

The principal dielectric constants of the pentyl to octyl derivatives of 4′-n-alkyl-4-cyanobiphenyl have been measured as functions of temperature in their nematic and isotropic phases. All the compounds exhibit a strong positive dielectric anisotropy due to the presence of a large dipole moment along the major molecular axis. The principal dielectric constantsε _‖ andε _⊥ as well as the anisotropy Δε decrease with increasing alkyl chain length. The experimental value of (ε_‖+2ε_⊥) decreases with decreasing temperature, and is throughout less than the extrapolated isotropic value, in conformity with the model of antiferroelectric short range order proposed by Madhusudana and Chandrasekhar.     

Coexistence of one-electron- and monoprotonated two-electron-reduced species of the K5[PMo2VW9O40] · 24H2O heteropolyoxometalate identified by EPR

The simulation of the room-temperature experimental electron paramagnetic resonance spectrum of K₅[PMo₂VW₉O₄₀] · 24 H₂O heteropolyoxometalate indicates the presence of equal amounts of a one-electron-reduced species (g _∥ = 1.922,g _⊥ = 1.972,A _∥ = 181 G,A _⊥ = 63 G) and a monoprotonated two-electron-reduced species with mixed-valence V^IV, Mo^V and Mo^VI ions (g _iso = 1.972, ΔB _iso(p-p) = 450 G). Two unprotonated one-electron-reduced isomers are identified in dimethylsulfoxide-H₂O solution of the sample atT = 100 K (g _∥¹ = 1.929,g _⊥¹ = 1.990,A _∥¹ = 179 G,A _⊥¹ = 65 G andg _∥² = 1.918,g _⊥² = 2.000,A _∥² = 187 G,A _⊥² = 80 G, respectively). The values of the in-plane π(V−O) bond π₂² coefficient for the one-electron-reduced species (0.87 at room temperature and 0.83 and 0.74 for the species in frozen solution) suggests the delocalization of the vanadium unpaired electron towards the molybdenum ions via O_b atoms.     

Effect of heavy quark symmetry on the mass difference ofB-system in minimal left right symmetric model

An estimation of the mass difference of system with heavy quark symmetry formalism is presented. The effective Hamiltonian describing the transition (whereh=b forB _d ⁰ -system) is considered in a manifest left right symmetric (MLRS) model along with contribution from neutral Higgs boson. We use the spin and flavor symmetry for heavy quarks to obtain the transition matrix element 〈B _d ⁰ |ℋ_eff(x)| _d ⁰ 〉 in terms of Isgur-Wise function. Assuming thatB _d ⁰ and states are at rest, we find that Isgur-Wise function turns out to be unity. However using the experimental values of ΔM _K and as input, we find thatM _R=835 GeV andM _H⩾2·9 TeV.     

On conformally related pp-waves

Brinkmann [1] has shown that conformally related distinct Ricci flat solutions are pp-waves. Brinkmann’s result has been generalized to include the conformally invariant source terms. It has been shown that [4] if g _ik and _ik (=w ⁻² g _ik ; w: a scalar function), are distinct metrics having the same Einstein tensor, G _ik = _ik , then both represent (generalized) pp-waves and w _i is a null covariantly constant vector of g _ik . Thus pp-waves are the only candidates which yield conformally related nontrivial solutions of G _ik =T _ik = _ik , with T _ik being conformally invariant source. In this paper the functional form of the conformal factor for the conformally related pp-waves/generalized pp-waves has been obtained. It has been shown that the most general pp-wave, conformally related to ds ²=−2du[dv−mdy=Hdu]+P ⁻²[dy ²+dz ²], turns out to be (au+b)⁻² ds ², where a,b are constants. Only in the special case when m=0, H=1, and P=P(y, z), the conformal factor is (au+b)⁻² or (a(u+v)+b)⁻².     

Influence of anisotropy on the dispersion of surface plasmon-phonon polaritons in silicon carbide

Surface plasmon-phonon polaritons (SPPP’s) of types 3 and 4 are investigated in doped anisotropic single crystals of hexagonal silicon carbide (6H-SiC) in the orientation corresponding to K⊥C and xy⊥C. It is shown that a dispersion dependence of the type-3 SPPP’s bounded by K appears in 6H-SiC when the plasmon frequency increases to ν _p⊥⩾350 cm⁻¹. At ν _p⊥⩾400 cm⁻¹, ν _s(K) exists for type-4 SPPP’s in the frequency range Ω _∥ ⁺ <ν< _⊥ ⁺ . When the concentration of free charge carriers is increased, the dispersion curves are displaced toward higher frequencies. The conditions for the existence of type-3 and type-4 SPPP’s in 6H-SiC are determined. Fiz. Tverd. Tela (St. Petersburg) 40, 636–639 (April 1998)     

ESR of V4+ in α-RbTiOPO4 single crystals

We have recorded and investigated the ESR spectrum of vanadium-doped α-RbTiOPO₄ single crystals in the temperature interval 77–300 K. Two types of structurally distinct centers, V1 and V2, with a 4:1 ratio of the peak intensities were observed. The angular dependences of the resonance magnetic fields are described by a spin Hamiltonian corresponding to axial symmetry with the parameters g _∥1=1.9305, g _⊥1=1.9565, A _∥1=−168.2×10⁻⁴cm⁻¹, and A _⊥1=−54.3×10⁻⁴cm⁻¹ for V1 centers and g _∥2=1.9340, g _⊥2=1.9523, A _∥2=−169.0×10⁻⁴cm⁻¹, and A _⊥2=−55.2×10⁻⁴cm⁻¹ for V2 centers. A model of a paramagnetic center is proposed: The vanadium ions replace titanium ions in two structurally distinct positions Ti1 and Ti2 (V1 and V2 centers, respectively). The possibility that a VO²⁺ ion forms when α-RbTiOPO₄ crystals and crystals of the KTP group (KTiOPO₄, NaTiOPO₄, α-and β-LiTiOPO₄), studied earlier, are doped with vanadium is discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 534–536 (March 1998)     

Electron paramagnetic resonance of NH 3 + radical in potassium sulphate

Room temperature EPR spectra of (NH₄)₂SO₄ doped K₂SO₄ monocrystals irradiated with x-rays show the presence of NH₃ ⁺ radicals. The EPR parameters areg ‖=2.0037 andg ⊥ = 2.0068;¹⁴NA _XX=13.75;A _YY=24.5;A _ZZ=25.5 gauss;¹HA _XX=A _YY=22 andA _ZZ=25 gauss. From the¹⁴N and¹H coupling constants it has been inferred that at room temperature the planar NH₃ ⁺ radical undergoes rotation about theC ₃ axis which corroborates with the equivalence of the protons, but the radical itself is in an asymmetric crystal field environment. The 77K spectra indicate a considerable reduction in the motion of the radical with the free motion almost completely stopped. Part of Ph.D. work of the second author     

Θ+-Pentaquark parity from associative baryon production in πd collisions, π ± + d → Θ+ + Σ±

We derive, in model-independent way, the spin structure of the matrix element for the reaction of associative Θ⁺-pentaquark production, π ^± + d → Θ⁺ + Σ^±, in the threshold region and in collinear kinematics. The expressions for the polarization observables in this reaction are found assuming spin 1/2 and different parities for Θ⁺. We have proved that such a reaction can be used for a model-independent determination of the P parity of Θ⁺ only by measuring the Θ⁺ polarization. Other polarization observables, such as the dependence of the Σ^± polarization on the vector and tensor deuteron polarizations, are insensitive to the Θ⁺ parity under the considered kinematical conditions. The linear and quadratic relations between polarization observables in (Θ⁺ is unpolarized) do not depend on the parity of the Θ⁺ pentaquark. The analysis performed for this reaction is also applicable without any modification to the reaction K ⁺ + d → Θ⁺ + p. Using the pole model for the reaction mechanism, we estimated the value of the cross section for the reaction K ⁺ + d → Θ⁺ + p near the threshold. The text was submitted by the authors in English.     

Ellipsometric spectroscopy of the ZnO nonpolar(1\bar 100) surface

Ellipsometric spectroscopy has been performed on nonpolar ZnO surfaces in the spectral range 1.5 eV<ħω<4.0 eV. Absolute measurements with two different crystal orientations in air allow the determination of the optical constantsn _∥,k _∥ andn _⊥,k _⊥ for light polarized parallel and perpendicular to thec-axis. The ellipsometric angles Δ and ψ are changed remarkably on ultrahigh vacuum cleaved surfaces near the band gap energy of ∼3.4eV when oxygen or atomic hydrogen is adsorbed or when the crystal is annealed. This observation is interpreted in terms of a field effect on the optical constants in the space charge layer.     

Superhyperfine Structure of EPR Spectra in LiLuF<Subscript>4</Subscript>:U<Superscript>3+</Superscript> and LiYF<Subscript>4</Subscript>:Yb<Superscript>3+</Superscript> Single Crystals

Electron paramagnetic resonance (EPR) spectra of doped paramagnetic crystals LiLuF₄:U³⁺ and LiYF₄:Yb³⁺ have been investigated at a frequency of about 9.42 GHz in the temperature range of 10–20 K. The U³⁺ ion spectrum is characterized by g-factors g _∥ = 1.228 and g _⊥ = 2.516, and contains the hyperfine structure due to the ²³⁵U isotope with nuclear spin I = 7/2 and natural abundance of 0.71%. The observed hyperfine interaction constants are A _∥ = 81 G and A _⊥ = 83.8 G. Moreover, the spectrum reveals the well-resolved superhyperfine structure (SHFS) due to two groups of four fluorine ions forming the nearest surrounding of the U³⁺ ion. This SHFS contains up to nine components with the spacing between components being about 12.7 G. The SHFS is observed also in the EPR spectrum of the LiYF₄:Yb³⁺ crystal; up to 17 components with spacing of about 3.7 G may be traced. Some parameters of the effective Hamiltonian of the SHF interaction are estimated, the contribution of covalent bonding of f-electrons with ligands into these parameters is discussed. Authors' address: Igor N. Kurkin, Kazan State University, Kremlevskaya ulitsa 18, Kazan 420008, Russian Federation     

Probing meson spectral functions with double differential dilepton spectra in heavy-ion collisions

The double differential dilepton spectrum d/(d ² d _⊥ ²) at fixed transverse mass M _⊥ allows a direct access to the vector meson spectral functions. Within a fireball model the sensitivity of d/(d ² d _⊥ ²) against variations of both the in-medium properties of mesons and the dynamics of the fireball is investigated. In contrast to the integrated invariant-mass spectrum d/d ², in the spectrum d/(d ² d _⊥ ²) with fixed M _⊥ the ω signal is clearly seen as bump riding on the ρ background even in case of strong in-medium modifications.[3mm] Received: 16 November 2000 / Accepted: 16 January 2001     

a 0 + (980)-resonance production in the reaction pp → dπ + η close to the K\bar K threshold

The reaction pp → dπ ⁺ η has been measured at a beam energy of T _p = 2.65 GeV (p _p = 3.46 GeV/c) using the ANKE spectrometer at COSY-Julich. The missing-mass distribution of the detected dπ ⁺ pairs exhibits a peak around the η mass on top of a strong background of multipion pp → dπ ⁺(nπ) events. The differential cross section d ⁴ σ/dΩ_d dΩ _π ⁺ dp _d dp _π ⁺ for the reaction pp → dπ ⁺ η has been determined model independently for two regions of phase space. Employing a dynamical model for the a ₀ ⁺ production allows one then to deduce a total cross section of σ(pp → da ₀ ⁺ → dπ ⁺ η) = 1.1 ± 0.3_stat ± 0.7_syst μb for the production of π ⁺ η via the scalar a ₀ ⁺ (980) resonance and σ(pp → dπ ⁺ η) = 3.5 ± 0.3_stat ± 1.0_syst μb for the nonresonant production. Using the same model as for the interpretation of recent results from ANKE for the reaction , the ratio of the total cross sections is , which is in agreement with branching ratios in the literature. The text was submitted by the authors in English.     

B→K*ℓ+ℓ- decay in soft-collinear effective theory

We study the rare B decay B→K^*ℓ⁺ℓ^- using soft-collinear effective theory (SCET). At leading power in 1/m_b, a factorization formula is obtained valid to all orders in α_s. For phenomenological application, we calculate the decay amplitude including order α_s corrections, and resum the logarithms by evolving the matching coefficients from the hard scale down to the scale . The branching ratio for B→K^*ℓ⁺ℓ^- is uncertain due to the imprecise knowledge of the soft form factors ζ_⊥(q²) and ζ_∥(q²). Constraining the soft form factor ζ_⊥(q²=0) from data on B→K^*γ yields ζ_⊥(q²=0)=0.32±0.02. Using this input, together with the light-cone sum rules to determine the q²-dependence of ζ_⊥(q²) and the other soft form factor ζ_∥(q²), we estimate the partially integrated branching ratio in the range 1 GeV²≤q²≤7 GeV² to be (2.92^+0.67 _-0.61)×10^-7. We discuss how to reduce the form factor related uncertainty by combining data on B→ρ(→ππ)ℓν_ℓ and B→K^*(→Kπ)ℓ⁺ℓ^-. The forward-backward asymmetry is less sensitive to the input parameters. In particular, for the zero-point of the forward-backward asymmetry in the standard model, we get q₀ ²=(4.07^+0.16 _-0.13) GeV². The scale dependence of q₀ ² is discussed in detail. PACS 13.25.Hw, 12.39.St, 12.38.Bx     

Superhyperfine structure of the EPR spectra of Nd<Superscript>3+</Superscript> and U<Superscript>3+</Superscript> ions in Li<Emphasis Type="Italic">R</Emphasis>F<Subscript>4</Subscript> (<Emphasis Type="Italic">R</Emphasis> = Y,Lu, Tm) double fluorides

The superhyperfine structure of the EPR spectra of impurity Nd³⁺ and U³⁺ ions in LiYF₄, LiLuF₄, and LiTmF₄ double-fluoride single crystals has been observed and discussed. In LiYF₄: Nd (g _| = 1.987, g _⊥ = 2.554) and LiTmF₄: Nd, the superhyperfine structure is observed at the orientation of the external magnetic field B in parallel to the c axis of the crystals and consists of nine components with a splitting of ∼15.4 MHz. In LiYF₄: U (g _| = 1.149, g _⊥ = 2.508) and LiLuF₄: U, the superhyperfine structure is observed at both B | c and B ⊥ c and consists of nine and eleven components, respectively, with a splitting of ∼21.5MHz. It should be noted that the resolution of the superhyperfine structure of the EPR spectrum of LiLuF₄: U³⁺ becomes significantly higher with a deviation from the orientation B ⊥ c.     

Higgs boson production in pp andp\bar p collisionscollisions

The associated production of Higgs particles andZ (W) bosons inpp and collisions is studied. The total cross-section of the processpp →HXl ⁺ l ⁻ is estimated.     

Improved tau polarisation measurement

Using 22 pb⁻¹ of data collected at LEP in 1992 on the peak of the Z resonance, the ALEPH collaboration has measured the polarisation of the tau leptons decaying into ,πν, ρν and a₁ ν from their individual decay product distributions. The measurement of the tau polarisation as a function of the production polar angle yields the two parametersN _τ andN _e, where, in terms of the axial and vector couplingsg _Al andg _Vl,N _l=2g _Vl g_Al/(g _Vl ² +g _Al ² ). This analysis follows to a large extent the methods devised for the 1990 and 1991 data but with improvements which bring a better understanding of the systematic uncertainties. Combining the 1992 measurements with our previously published results yieldsN _τ=0.136±0.012±0.009 andN _e=0.129±0.016±0.005. Assuminge−τ universality, the measurements imply an effective weak mixing angle of sin ² θ _W ^eff =0.2332±0.0014. Deceased