A family of angle-moments proportional to r-n,n = 1,2,…, in free space

The moments M_n(r) ≡ 1/2 ∝^2π₀ dθ sinⁿ θ I(r,θ) of the intensity I(r, θ) in free space surrounding a spherical object emitting radiation with an arbitrary directional dependence are shown to be exactly proportional to r^-(n+1), n = 0, 1,….     

High-resolution study of the bΣ(b0)→XΣ(X10) transition of PI

Emission spectra of the b¹Σ⁺(b0⁺)→X³Σ⁻(X₁0⁺) transition of phosphorus iodide have been measured with a high-resolution Fourier-transform spectrometer. The PI radicals were generated and excited in a fast-flow system by reaction of phosphorus vapor (P_x) with iodine and microwave-discharged oxygen. Four sequences, Δv=0,+1,−1,−2, of the b¹Σ⁺(b0⁺)→X³Σ⁻(X₁0⁺) transition of PI comprising 28 bands were observed. Six bands were measured at high spectral resolution. Vibrational and rotational analyses have yielded accurate spectroscopic constants of the X₁0⁺ and b0⁺ states (in cm⁻¹): X₁0⁺: ω_e=371.296(4), ω_ex_e=1.3302(9), B_e=0.1194117(2), α_B=−0.0005676(7), D_e=4.56(2) ×10⁻⁸; b0⁺: T_e=11136.921(4), ω_e=400.165(6), ω_ex_e=1.345(2), B_e=0.1239237(2), α_B=−0.0005540(2), D_e=4.84(5) × 10⁻⁸, where the numbers in parentheses are the standard deviations of the parameters. No emissions of the b0⁺→X₂1 sub-system nor of the a¹Δ(a2)→X³Σ⁻(X₂1) transition have been observed leaving PI the only group Va halide for which the spin splitting in the X³Σ⁻ ground state is still unknown.     

Rotationally resolved state-to-state photoelectron study of zirconium monoxide cation (ZrO+)

Using two-colour visible (Vis)–ultraviolet (UV) photoionisation and pulsed field ionisation–photoelectron (PFI–PE) methods, we have obtained cleanly rotationally resolved photoelectron spectra for ZrO⁺(X ²Δ_3/2,5/2; v⁺ = 0, 1, and 2). The rotation assignment of these state-to-state Vis–UV–PFI–PE spectra has allowed the unambiguous determination of the ground state term symmetry for ZrO⁺(X) to be ²Δ_3/2, and the adiabatic ionisation energy of ⁹⁰Zr¹⁶O, IE(⁹⁰Zr¹⁶O) = 54,948.3(8) cm^?1 [6.81272(10) eV]. The symmetry of the ionic ZrO⁺(X ²Δ_3/2) ground state determined here disagrees with that reported in previous experiments. The rotational and vibrational constants determined in this experiment for the ionic ⁹⁰Zr¹⁶O⁺(X ²Δ_3/2) ground state are: B_e⁺ = 0.4343(8) cm^?1 and α_e⁺ = 0.0019(5) cm^?1, and ω_e⁺ = 991.2(8) cm^?1 and ω_e⁺x_e⁺ = 3.5(8) cm^?1; and those for the ionic ⁹⁰Zr¹⁶O⁺(X ²Δ_5/2) excited spin-orbit state are: B_e⁺ = 0.4357(6) cm^?1 and α_e⁺ = 0.0022(4) cm^?1, and ω_e⁺ = 991.9(8) cm^?1 and ω_e⁺x_e⁺ = 3.6(8) cm^?1, respectively. Based on the latter B_e⁺ value, the equilibrium bond distances are determined to be r_e⁺ = 1.691(2) Å for ⁹⁰Zr¹⁶O⁺(X ²Δ_3/2) and r_e⁺ = 1.688(1) Å for ⁹⁰Zr¹⁶O⁺(X ²Δ_5/2). The IE(ZrO) along with the spectroscopic constants obtained here are valuable for benchmarking the ab initio quantum chemical calculations for energetic and structural predictions of ZrO/ZrO⁺.     

Interaction de l'oxygène aux basses pressions avec la solution solide niobium-oxygène à haute température: II. Désorption d'oxydes

Interations between oxygen under low pressure and a niobium-oxygen solid solution at high temperature (2200 >T > 1800 K) have been studied. Evidence was found of the validity of a model where the rates of oxide desorption (Z_NbOx) are related to superficial coverage θ : Z_NbOx = K_NbOxθ^x. It is shown experimentally that it is possible to derive from this model an expression which relates flux to bulk concentration C : Z_NbOx = K_NbOxC^x From the equivalence of these two expressions it results that: (1) the enthalpy of transfer (ΔH_SV between the surface and the bulk of solid solution, and (2) the bond energy (x) of the superficial oxygen atoms, have the same dependence on superficial coverage θ (i.e. influence of the interactions between adsorbed oxygen atoms on both X and ΔH_SV is the same). So, X and Δ_SV are theoretically in the form: ΔH_SV = ΔH_SV(0) ? αθ and X = x(0) ? αθ. In fact, there is a discrepancy beiween experimental values which is discussed.     

On the transfer of line radiation in random magnetic fields

An analysis is made of the influence of a magnetic field of constant magnitude but with random orientations, described by the spherical coordinates θ and φ, on the polarization transfer in spectral lines. The assumption that the statistical properties of the field are determined by the one- and two-point probability densities P₁(x, θ, φ) and P₂(x₁, θ₁, φ₁; x₂, θ₂, φ₂) where x is the coordinate along the ray, implies that the variations of θ and φ can be considered as being due to a Markovian process in x. The expectation values of the Stokes parameters 〈Iγ〉, γ = 1, …4, are calculated functions of x or the optical depth τ. The formalism includes the limiting cases of infinite and zero correlation length. Assuming an artificial triplet and simple conditions, the results suggest that isotropic magnetic fields of the type considered have no influence on the polarization characteristics during the transfer.     

A measurement of Kevγ+ decay

The decay K⁺ → e⁺vγ has been observed. In a counter experiment at CERN, 56 events of this type have been identified by detection of a γ with an energy > 100 MeV and of an e⁺ with an energy between 236 MeV and the maximum e⁺ energy, 247 MeV. The angle between γ and e⁺ was > 120°. Thus, the experiment was sensitive only to the structure decay (SD) term proportional to the squared sum of vector- and axialvector amplitudes, |ν_K + a_K|², corresponding to the emission of right handed γ. We find Δ₊(SD)/Δ(K_e2) = 1.05_?0.30^+0.25 and Δ_(SD) < 85 (90% CL). Δ₊ is in agreement with theoretical predictions.     

Dispersion polaritons on metallized surfaces of optically uniaxial crystals

We have constructed a theory of dispersion polaritons (localized electromagnetic waves) on arbitrarily oriented metallized surfaces of optically uniaxial crystals. The domain of existence of polaritons is defined by the following inequalities for permittivities ε_o and ε_e of the crystal and the angle θ between the optical axis and the surface: ?ε_etan²θ < ε_o < 0. Thus, polaritons exist only in the range of wave frequencies ω ensuring negative values of ε_o(ω) for ε_e > 0. The frequency boundaries of this region are specified for the case when the ε_o(ω) dependence corresponds to the model of a single polar excitation. The azimuthal orientation φ of the optical axis projection onto the surface does not appear in the criterion for polariton existence, but affects (together with angle θ) its main dispersion characteristics, such as the refractive index and partial wave localization parameters. This effect is analytically described in detail. Anomalies in the behavior of polariton parameters are studied in the vicinity of the boundaries of the domain of its existence, where the wave fields are especially sensitive to variations in the angles θ and φ. It is shown that a polariton in the plane of propagation (sagittal plane) passing through the optical axis is transformed into a one-partial bulk wave satisfying the boundary conditions. Accordingly, the wave branch under investigation for close orientations (when the optical axis forms a small angle with the sagittal plane) describes deeply penetrating (quasi-bulk) polaritons.     

The ground state of two-dimensional electrons in a nonuniform magnetic field

An exact solution to the Schrödinger equation for the ground state of two-dimensional Pauli electrons in a nonuniform transverse magnetic field H is presented for two cases. In the first case, the field H depends on a single variable, H = H(y), while in the second case, the field is axially symmetric, H = H(ρ), ρ²=x ²+y ². The electron density distributions n = n(y) and n = n(ρ) that correspond to a completely filled lower level are found. For quasiuniform fields of fixed sign, the functions n(y) and n(ρ) are locally related to the magnetic field: n(y) = H(y)/?₀ and n(ρ) = H(ρ)/?₀, where ?₀ = hc/|e| is a magnetic flux quantum. Magnetic fields are considered that are periodic, singular, and bounded in the plane xy. Finite electron objects in a nonuniform magnetic field are analyzed.     

Prediction of Re ɛ fromK 13 decays in an extended cabibbo model

With the help of an extended Cabibbo model for the weak hadronic vector current which includes the 10 and ¯10 representations to account for possibleΔS=-ΔQ transitions, a prediction is made for the quantity (1-¦x¦²)/¦1?x¦² wherex=A(K⁰→π^üe^?¯v)/A(¯K⁰→π^üe^?¯v) using the experimental branching ratio Γ(K^?→ π⁰e^?¯v/Γ(K _L ⁰ →π^üe^?¯v). From the known charge asymmetry in the decay of the long lived kaon one then obtains Re?.     

A rigorous replica trick approach to Anderson localization in one dimension

LetH=?Δ+V onl ²(?), whereV(x),x∈?, are i.i.d.r.v.'s, and letG _L (x,y;E+iη)= 〈x|(H _L?(E+iη))^?1|y〉, whereH _L denotes the operatorH restricted to {?L, ?L+1,...,L} with Dirichlet boundary conditions. We use a supersymmetric replica trick to prove that $$E(|G_L (0,x; E + i\eta )|^2 ) \leqq K\eta ^{ - 2} \exp \{ - m|\log \eta |^{ - \sigma } |x|\} $$ for somem>0, σ>0,K<∞, uniformly inL andE. This estimate, together with the usual necessary estimate on the density of states, implies zero conductivity and gives exponential localization by the Fröhlich, Martinelli, Scoppola, and Spencer method.     

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

Electric moments of the first excited state of 18O

The static quadrupole moment Q_2⁺ and the B(E2; 0⁺ → 2⁺) value of the first excited state of ¹⁸O at e_x = 1.982 MeV have been determined using the reorientation effect in Coulomb excitation. Surface-barrier detectors at laboratory angles of 90° and 174° were used to detect ¹⁸O ions elastically and inelastically scattered from ²⁰⁸Pb. At both angles, we determined experimentally the maximum bombarding energies at which nuclear interference effects were negligible. It is found that Q_⁺ = ?0.023 ± 0.021 e · b (?0.052 ± 0.021 e · b) for destructive (constructive) interference from higher states. This result is in good agreement with theoretical expectation. For the transition moment we find B(E2; 0⁺ → 2⁺) = 0.00390 ± 0.00018 e² · b² (0.00371 ± 0.00018 e² · b²) for destructive (constructive) interference.     

Simple model for spin-crisis

Starting from the additive quarkSU(6) model and taking into account the pion and kaon (η) emission during the initial stage of evolution (fromq ²～m _quark ² toq ²～1 GeV²) we convert the main fraction of the proton spin into the orbital momentum of the pseudoscalar mesons. The results are in a good agreement with the experimental data. We get ∫g ₁(x)dx=0.152 for proton and +0.007 for the Λ hyperon (i.e. the quarks carry out only about 39% of the Λ spin). In the same model we explain the violation of the Gottfried sum rule ?∫(F ₂ ^p(x)?F ₂ ⁿ(x))dx=0.23 due to the charged meson exchanges at the beginning of the evolution. The Gribov-Lipatov relation between the polarized structure functions in DIS ande ⁺ e ^?-annihilation is discussed. It gives the possibility to study the spin structure of Λ hyperon produced through the decay of the jet originated by a polarized quark ine ⁺ e ^?-annihilation or in DIS.     

Nonisotropic L-conversion-electron — X-ray directional correlations in160Dy

The directional correlations betweenL-conversion electrons andL x-rays have been measured. The electrons were emitted in the 86.78keV 2⁺→0⁺ transition in¹⁶⁰Dy, in the decay of¹⁶⁰Tb. The experimental results areA ₂₂(e _L -x _Li )=0.085 (22),A ₂₂(e _L -x _Lα )=0.0066 (29),A ₂₂(e _L -x _Lβ )=0.0000 (27), andA ₂₂(e _L -x _Lγ )=0.0096 78). These results are in disagreement with published theoretical values. It is suggested that the discrepancy is due to a phase inconsistency in the internal conversion matrix elements and there is good agreement withA ₂₂ values calculated in this work.     

Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems

From measurements of the decrease in the heat (enthalpy) of transition in the solid phase using differential scanning calorimetry, the apparent molar heats of solution, slope ΔH_t/x, the partial molar heats of solution at infinite dilution, χ, and the heats of solution, ΔH_s^°, of Tl⁺ in CsNO₃ crystal and Cs⁺ in TlNO₃ crystal and Rb⁺ in CsNO₃ crystal and Cs⁺ in RbNO₃ crystal along with their recovered lattice energies, ΔH_L^°, are reported. ΔH_s^° of Tl⁺ and Rb⁺ in CsNO₃ crystal are each found to be negligible or zero representing an ideal solid solution, i.e. ΔH_mix=0. The complete phase diagrams of the TlNO₃-CsNO₃ and RbNO₃-CsNO₃ systems with details of the sub-solidus regions are included. The properties of Tl_(1−x)Cs_xNO₃ and Rb_(1−x)Cs_xNO₃ compositions are discussed in terms of a ‘mixed crystal’ or ‘crystalline solid solution’ in relation to parallel compositions of Tl_(1−x)Rb_xNO₃.     

Electric quadrupole moments of the first excited states of 194Pt, 196Pt and 198Pt

Coulomb excitation of ^{194, 196, 198}Pt by ⁴He, ¹²C and ¹⁶O projectiles has been used to determine the static electric quadrupole moments Q(2₁⁺) of the first excited states of ^194,196,198Pt, together with values of B(E2; 0₁⁺ → 2₁⁺). It is clearly established that Q(2₁⁺) is positive for each nucleus, having values of 0.48 (14)e · b and 0.66 (12)e · b for ¹⁹⁴Pt and ¹⁹⁶Pt, respectively, and 0.42 (12)e · b or 0.54 (12)e · b for ¹⁹⁸Pt, depending on whether the interference term P₄(2₂⁺) is positive or negative. Results obtained for B(E2; 0₁⁺ → 2₁⁺) are 1.661 (11)e² · b², 1.382 (6)e² · b² and 1.090 (7)e² · b² for ^{194, 196, 198}Pt respectively. The results are compared with the predictions of various nuclear models.     

Phonon properties of vanadium-substituted lanthanum niobate derived from heat-capacity measurements

We have measured the 3–400 K heat capacity of vanadium-substituted lanthanum niobate LaNb_1−x,V_xO₄ (0 < x⩽0.35) to determine how the relevant averaged properties, or moments, of the phonon spectrum 〈ωⁿ〉 relate to certain other lattice properties of these compounds, most noteworthy of which is a large decrease in the paraelastic-ferroelastic transformation temperature T_c with x. The pertinent moments, represented by their corresponding Debye temperatures, are θ_D(−3) corresponding to the lowest frequency modes; θ_D(0) associated with the geometric mean frequency of the entire spectrum; and θ_D (2) identified with the high-frequency modes that are sampled at the upper end of the temperature range. We find that θ_D(−3) falls rapidly with x and this effect can be correlated with the comparably sharp drop in T_c. There is little effect of composition on θ_D(0) and θ_D (2) because the phonons that govern soft-mode behavior represent only a small fraction of the mode population. In the vicinity of T_c the temperature dependences of the free energies of the tetragonal and monoclinic phases are so similar that the discontinuity in C_p is immeasurably small.     

A simple solution to the strongCP-problem

We suggest soft breaking of Peccei-Quinn symmetry as a simple solution to the strongCP problem without the presence of the axion. In the context of theSU(2) _L ×U(1) model, it is shown how settingθ _tree=0 keeps θ calculable and, furthermore, extremely small: θ?10^?16. Unlike in the case of the axion the model is free from the cosmological domain wall problem. Possible extension of this idea to grand unification is discussed.     

Spectral line parameters in the (3 ← 0) overtone band of the HI molecule and line-mixing in the band head

The linestrengths, self-pressure broadening and shifting coefficients have been measured for P₃ (10)- R₃ (12) lines in the second overtone band of hydrogen iodide. A dipole moment function in terms of the reduced nuclear displacement x = (R − R_e)/R_e is obtained using rotationless dipole matrix elements determined by the Herman-Wallis analysis of the (1, 2, 3 ← 0) HI bands: μ (x) = 0.4471(5) − 0.0770(2)x + 0.547(3)x² − 1.93(2)x³, in a full agreement with the function proposed previously [J. Mol. Spectrosc. 223 (2004) 67]. A close match is demonstrated of the results of most recent relativistic calculations [Phys. Chem. Chem. Phys. 6 (2004) 3779] with the spectroscopically derived electric dipole parameters for HI. Line-mixing in the band head is observed, the self-pressure shifting and broadening coefficients for the (3 ← 0) band lines are determined.