Quantum electrodynamic calculation of interelectron interaction for He-like and Li-like multiply charged ions

Exact quantum-electrodynamic calculations of the interelectron interaction corrections are performed for the 1s _1/22s _1/2 ¹ S ₀, 1s _1/22p _1/2 ³ P ₀, and 1s _1/22s _1/2 ³ S ₁ configurations in He-like ions and for the (1s _1/2)²2s _1/2 and (1s _1/2)²2p _1/2 configurations in Li-like ions for all charges of nuclei 10≤Z≤92. The calculations are performed in the Coulomb calibration. The Coulomb-Coulomb and the Coulomb-Breit parts are calculated exactly, and the Breit-Breit part of the correction is calculated by neglecting the retardation. The calculations are the most exact of those available by now.     

Niveaux d'énergie et spectres de rayons X du rutile

The electronic levels of the complex TiO^?8₆ in the D_2h symmetry are determined according to an extended L. C. A. O. method. The results can explain the X-ray spectra of TiO₂. The absoption L_III and K rays are related to transitions from the 2p_3/2 and 1 s levels to the conduction band levels since the emission L_III and K components are explained by the transitions from the valence band levels to the 2p_3/2 and 1 s states. Interband transitions are related to the components of the optical reflexion spectrum of TiO₂ for the energies 0–20 eV. A comparaison is made with the electronic band structures of SnO₂, TiO₂ and BaTiO₃. At the center of the Brillouin zone, we obtain a forbidden gap of 3,01 eV, the corresponding widths of the valence and conduction band are 4,8 and 2,9 eV.     

Neutron diffraction study of the layered compounds MnPSe3 and FePSe3

In the insulating compounds MnPSe₃ (1) and FePSe₃ (2) the divalent transition metal ions form planar honeycomb lattices. A neutron diffraction study revealed a collinear antiferromagnetic order below T_N = 74 ± 2 K (1) and T_N = 119 ± 1 K (2) with the corresponding wavevectors k = [000] (1) and $\text{k = [}\text{1}\text{2}\text{0}\text{1}\text{2}\text{]}$ (2). In MnPSe₃ the magnetic moments (m₀ = 4.74 μ_B) lie within the basal plane and in FePSe₃ (m₀ = 4.9 μ_B) they are pointing along the c-axis. The collinear structures are determined by the dominating intralayer interactions between first (J₁), second (J₂) and third neighbours (J₃) which in MnPSe₃ are all antiferromagnetic whereas in FePSe₃J₁ is ferromagnetic and J₂ and J₃ are antiferromagnetic.     

Spectroscopy of XY2Z2 (C2v) Molecules: A Tensorial Formalism Adapted to the O(3)⊃Td⊃C2v Chain. Application to the Ground State of SO2F2

A tensorial formalism adapted to the case of quasi-spherical XY₂Z₂ asymmetric tops such as SO₂F₂ has been developed as an extension of the usual one for the tetrahedral molecules. We use the O(3)⊃T_d⊃C_2v group chain. All the coupling coefficients and formulas for the computation of matrix elements are given for this chain. Such relations are then deduced in the C_2v group itself. We also present a development of the Hamiltonian, dipole moment, and polarizability operators for the molecules under consideration using this formalism. These operators are involved in the calculation of the energies and intensities of rovibrational transitions and are essential for spectrum simulations. Expressions for the matrix elements are derived for these operators. A first application to the ground state of SO₂F₂ is presented. Programs for spectrum simulation and fit using these methods are freely available at the URL http://www.u-bourgogne.fr/LPUB/c2vTDS.html.     

Elastic constants of 2H-MoS2 and 2H-NbSe2 extracted from measured dispersion curves and linear compressibilities

Recent neutron data on the dispersion curves and X-ray measurements of the linear compressibilities of the 2H polytypes of MoS₂ and NbSe₂ have been used to obtain approximate values of the five independent elastic constants of these materials. In the case of NbSe₂ sufficient information is available to over-determine the elastic constants and the results are self consistent within estimated uncertainties, although the uncertainties are especially large for c₃₃ and c₁₁. Additional related considerations such as Debye temperatures and model calculations of c₃₃, and c₄₄ are also made. It is found that there is significant and unexplained disagreement between the value of the low temperature specific heat Debye temperature of NbSe₂ and the value determined on the basis of the elastic constants, but that the model predictions of c₃₃ and c₄₄ are in satisfactory agreement with the values extracted from the neutron data for both MoS₂, and NbSe₂.     

Studies of lattice dynamics in 2HTaS2 by Raman scattering

Raman spectra are presented in the high and low temperature phases of 2H-TaS₂. In the normal phase at 380 K one A_1g- and two E_2g-modes have been observed at 400, 27 and 286 cm^-1, respectively. In the charge density wave state two extra peaks appear with strong scattering intensity in E_2g- symmetry and weak in A_1g-symmetry. The E_2g peak grows and hardens toward 50 cm^-1 with decreasing temperature. The temperature dependence is very similar to the E_2g-mode in 2H-TaSe₂ of similar 3a₀ × 3a₀ superstructure. Other peaks observed in 2H-TaSe₂ in the commensurate phase are not observed. This suggests the incommensurability of the charge density wave state in 2H-TaS₂.     

Topology of spin Hamiltonian and crystal field tensors for Mn2+ in ZnSeO4·6H2O crystal

The expansion of the {B ₂} and {B ₄} tensors of the spin Hamiltonian (SH) for Mn²⁺ (⁶S-state) is performed in terms of the irreducible tensor products {V _{L 1} ?V _{L 2}}₂ and {V _{L 1} ?V _{L 2}}₄ of the crystal field (CF) tensors {V _{L 1}} and {V _{L 2}}. The EPR spectra of Mn²⁺ in the ZnSeO₄·6H₂O crystal are studied and the SH tensors {B ₂} and {B ₄} are calculated. The tensors {V ₄?V ₄}₂ and {V ₄?V ₄}₄ are computed using the point-charge model (PCM) of the [Zn(H₂O)₆] complex with the C₂ symmetry and are compared with the SH tensors {B ₂} and {B ₄}, respectively. The correct signs of the elements and the pseudo-symmety axes of the tensors are obtained both for the {B ₂} tensor and {V ₄?V ₄}₂ and for the {B ₄} tensor and {V ₄?V ₄}₄. It is concluded that the irreducible tensor products {V ₄?V ₄}₂ and {V ₄?V ₄}₄ provide the predominant contribution respectively to the SH tensors {B ₂} and {B ₄} of Mn²⁺.     

All-optical soliton switching for the asymmetric fiber couplers

Coupled nonlinear Schrödinger (CNLS) equations for the fiber couplers with asymmetric self-phase modulation (SPM) and cross-phase modulation (XPM) are studied. With symbolic computation, one- and two-soliton solutions are obtained for the constant- and variable-coefficient CNLS equations. Switching dynamics of the solitons is discussed, and effects of the second-order group-velocity dispersion β ₂, SPM coefficient σ ₁, XPM coefficient σ ₂ and Kerr nonlinear intensity γ on the all-optical switching properties are studied, while other coefficients in those equations are seen not to affect the all-optical switching properties. For the constant-coefficient CNLS equations, we find that |β ₂| is proportional to the optical switching speed, and the optical extinction ratios increase with the decrease of σ ₁/σ ₂ and increase of |β ₂| and γ. A numerical simulation by the split-step Fourier and Runge-Kutta methods is presented on the constant-coefficient CNLS equations to analyse the stability of the one- and two-solitons with the random initial perturbations. For the variable-coefficient CNLS equations, effects of σ ₁/σ ₂, β ₂(z) = a ₂ e ^bz and γ(z) = a ₃ e ^bz on the optical switching are analyzed (where a ₂, a ₃ and b are all constants, and z gives the direction of propagation in the fiber couplers): optical switching speed increases with the increase of |a ₂| and decrease of |b|, and optical extinction ratios increase with the increase of |a ₂| and decrease of σ ₁/σ ₂ and |a ₃|.     

Calculation of the influence of the wind effect and collision-induced velocity changes on the H2O-molecule absorption-line profiles upon broadening by monatomic gases

The influence exerted on the H₂O-molecule absorption line profiles in the H₂O-He, H₂O-Ar, and H₂O-Kr systems by two factors—the dependence of broadening coefficient γ on velocity ν _a of the absorbing H₂O molecule (wind effect) and the collision-induced change in the H₂O molecule velocity—is studied. Three H₂O molecule absorption lines of the ν ₂ band, which are formed by transitions from energy levels with different rotational quantum numbers J and K _a , are chosen for investigations.     

Infrared-microwave double resonance of 12CH3OH with a CO2 laser

The Stark effect of the 2₂ ← 2₁(E₁), 2₁ ← 3₀(E₁) microwave transitions in the ground state and the 2₂ ← 2₁(E₁) microwave transition in the first excited CO stretching vibrational state are measured by means of infrared-microwave double resonance with the ^qQ₁(2)E₁ infrared transition as the pump transition in the range of 1000 to 2300 V/cm. The dipole moments μ_a and μ_b as well as the off-diagonal rotational constant D_ab are determined for both the ground and the excited states. The frequency of the ^qQ₁(2)E₁ infrared transition is found to be lower by 128 ± 2 MHz than that of the P(34) CO₂ laser.     

Optical absorption spectra and energy levels of Er3+ ions in glassy lithium tetraborate matrix

The optical absorption spectra of Er:Li₂B₄O₇ glasses are studied in the range 200–800 nm. The lines corresponding to the direct f-f parity-forbidden intraconfigurational transitions from the ground ⁴ I _15/2 state to the levels of the excited ⁴ F _9/2, ⁴ S _3/2, ² H _9/2, ² H _11/2, ⁴ F _7/2, ⁴ F _5/2, ⁴ F _3/2, ² H _9/2, ⁴ G _11/2, ⁴ D _3/2, ⁴ D _1/2, and ² D _3/2 states are found.     

Europium valency in EuCu2−x Fe x Si2, EuCu2Si2−x Ge x,EuCu2−x Si2+x and EuNi2−x Si2+x

Mössbauer spectroscopy, X-ray photoemission spectroscopy and magnetization studies of EuCu_2?x Fe _x Si₂, EuCu₂Si_2?x Ge _x , EuCu_2?x Si_2+x , and EuNi_2?x Si_2+x have been performed. In EuFe₂Si₂ and EuNi₂Si₂ the Eu ion is trivalent, in EuCu₂Si₂ it is of intermediate valency. In all systems withx=0, many inequivalent Eu sites of intermediate valency are formed. In EuCu_2?x Fe _x Si₂, the average valency of Eu moves nonmonotonically toward Eu³⁺. In EuCu₂Si_2?x Ge _x , EuCu_2?x Si_2+x and EuNi_2?x Si_2+x , the Eu average valency moves quickly towards Eu²⁺. In all three systems, whenx=1, all Eu ions are already stable divalent. The systems EuCuSi₃ and EuNiSi₃ order magnetically at 40 K and 34 K, and exhibit hyperfine fields of 323 kOe and 458 kOe, respectively. XPS and Mössbauer isomer shift determinations of the average Eu valence as a function of temperature in EuCu_1.5Fe_0.5Si₂ are in good agreement. The experimental observations concerning the Eu valencies can not be explained solely in terms of the local volume available to the Eu ion; the nature of chemical environment plays a dominant role.     

Effect of CO and H adsorption on the compositional structure of binary nanoalloys via DFT modeling

Theoretical methods (DFT/B3LYP and MP2) have been used to optimize the geometries of the Al _x Sb _y (x + y = 3, 5) clusters and their anions. Single point energy computations at CCSD(T) level have also been performed using the optimized B3LYP and MP2 structures. The basis sets used for Al and Sb atoms are 6-311+G(2d) and LANL2DZdp ECP, respectively. Harmonic vibrational frequency computations were carried out to confirm the nature of the stationary points. We report the structural and spectroscopic parameters of the named clusters. We also report the relative energy of the clusters, the vertical electron detachment energy, the adiabatic electron detachment energy and the adiabatic electron affinity. The most stable structures at the CCSD(T)//MP2 level are, the D _∞h linear structure (AlSb₂) and the C _2v V-bent structure (AlSb ₂ ^? ), the C _2v V-bent structure (Al₂Sb and its anion), the C _2v edge-capped tetrahedron (Al₂Sb₃ and its anion), the C _2v trigonal bipyramidal structure (Al₃Sb₂ and its anion), the C _4v square pyramidal (AlSb₄) and a C _2v ground structure for its anion, the C _2v planar trapezoidal structure (Al₄Sb) and the C _2v edge-capped tetrahedron (Al₄Sb^?). The adiabatic electron affinities calculated at the CCSD(T)//MP2 level are 2.17 eV (AlSb₂), 2.17 eV (Al₂Sb), 2.38 eV (Al₂Sb₃), 2.76 eV (Al₃Sb₂), 2.21 eV (AlSb₄) and 2.03 eV (Al₄Sb). The findings of this research are analysed, discussed and compared with the analogous picnogenides clusters.     

Oscillator strength of electron-type color centers in KCl single crystals irradiated with electrons and protons

The absorption spectra of KCl single crystals irradiated with electrons and protons at energies of 15 and 100 keV and a particle flux ranging from 5×10¹² to 10¹⁵ cm^?2 are investigated. The absorption bands attributed to simple (F, F _a, K) and complex (M, R ₂, R ₄, N) color centers are identified in the spectra. The correlation dependences of the absorption coefficients for M, R ₂, and R ₄ centers on the absorption coefficient of F centers and the correlation dependences of the absorption coefficients for R ₂ and R ₄ centers on the absorption coefficient of M centers are established. The oscillator strengths are calculated for M, R ₂, and R ₄ color centers.     

Rotational analysis of visible bands of nitrogen dioxide using polarization spectroscopy

Polarization labeling spectroscopy is used to simplify the visible absorption spectrum of NO₂. State-selected spectra of the ²B₂-²A₁ transition in the range 16 600–17 000 and 17 350–17 850 cm^?1 are developed using a narrow-band pump operated (1) near 545 nm, where the pumped transitions also belong to the ²B₂ system, and (2) near 436 nm on a selected transition of the ²B₁-²A₁ (Douglas-Huber) band system. Rotational analyses are given for the K_a = 0 and K_a = 1 subbands of 11 vibronic bands and limited observations reported for the K_a = 0 or 1 manifold of a further 8 bands. Polarization-labeling experiments within the ²B₁-²A₁ band system are also described.     

Concurrent changes of crystallographic and Mössbauer effect parameters at the high-spin(5T2) ⤥ low-spin(1A1) transition in compounds of iron (II)

Distinct and different X-ray diffraction patterns are found for the ⁵T₂ and ¹A₁ phases at the high-spin(⁵T₂) ? low-spin(¹A₁) transition in Fe(bt)₂(NCS)₂ (I) and Fe(phy)₂(ClO₄)₂ (II) (bt = 2,2′-bi-2-thiazoline; phy = 1,10-phenanthroline-2-carbaldehydephenylhydrazone). The peak profiles show the same temperature dependence and the same hysteresis behaviour as the ⁵T₂ and ¹A₁ fractions determined on the basis of Mössbauer effect or magnetism. At the transition temperature T_c, both phases are coexistent.     

High-resolution infrared study of 1,1-ethylene-D2 in the 2000- to 1200-cm−1 region

The infrared spectrum of H₂CCD₂ was investigated in the region 2000-1200 cm^?1 at a resolution of ～0.05 cm^?1. Complete analyses of four type-A bands are reported-the CC stretch, ν₂, the CH₂ deformation, ν₁₂, and the overtones of the CD₂ and CH₂ wagging fundamentals, 2ν₇ and 2ν₈. Localized perturbations are identified and taken into account in the analyses, enabling the perturbing vibrational levels to be located accurately and the interaction parameters to be determined. In the case of ν₁₂, Fermi resonance with 2ν₁₀ has a global effect, and causes a bandhead to be formed in the K_a subband series.     

Fourth-order spin Hamiltonian terms for Fe2+ in rutile structure antiferromagnet FeF2

The paper deals with the spectroscopic and magnetic properties of Fe²⁺ ions in FeF₂. The microscopic spin Hamiltonian theory for Fe²⁺ in crystalline environments with second-kind orthorhombic symmetry is considered. Explicit formulas for the parameters B₀⁽²⁾(D),B₂⁽²⁾(E), g_x, g_y, g_z and, for the first time in the literature, the fourth-order parameters B₀⁽⁴⁾, B₂⁽⁴⁾ and B₄⁽⁴⁾, are derived. Using semi-empirical data for the ⁵D-term energy levels of Fe²⁺ ion in FeF₂, the pressure dependence of the parameters B_q^(k) in the region from 0 to 133 kbar is discussed. The relative role of the fourth-order parameters with respect to the second-order ones is found to increase strongly with pressure (e.g. in the region studied, D increases only by a factor of 3, whereas B₀⁽⁴⁾ increases by a factor of nearly 20). The magnetocrystalline anisotropy of FeF₂; is considered in the strong anisotropy model taking into account the fourth-order spin Hamiltonian terms. The uniaxial anisotropy constants K₁ and K₂ are derived theoretically and their pressure dependence is discussed quantitatively. The theory and numerical results of this paper are useful with regard to Fe²⁺ in other isomorphic fluorides, namely: MgF₂, ZnF₂, VF₂ and MnF₂. It is found that the fourth-order spin Hamiltonian parameters are accessible to experimental detection from spectroscopic studies on Fe²⁺ in non-magnetic fluorides and magnetic studies on Fe²⁺ : MnF₂ and FeF₂, preferably under high pressure.     

Field dependence of uniform magnon energies in lamellar CoCl2 and CoBr2 by AFMR experiments

AFMR experiments in the frequency range 77<v<600 GHz and in the magnetic field range 0<H<75 kG on antiferromagnetic CoCl₂ and CoBr₂ single crystals at 4.2 K are reported. The waves propagate along the c axis of the crystals and the steady magnetic field is in the plane of the layers, which is also the easy plane of the spins.The influence of a rotation of the field in the easy magnetization plane is investigated, showing the existence of antiferromagnetic domains.The results of the field dependence of uniform magnon energies are reported in detail for the two compounds CoCl₂ and CoBr₂. In CoBr₂, the two magnon modes at zero field are non degenerate, their frequencies are v₁(0) = 60 GHzandv₂(0) = 675 GHz, and the field required for saturation is H_s⊥ = 74.2 kG.     

Absorption spectroscopic study of the conduction band of titanium dichalcogenides

The L _{2, 3} spectra of titanium in the layered compound TiSe₂ and intercalated compounds Fe_1/2TiSe₂, Cr_1/3TiSe₂, and Fe_1/4TiTe₂ are studied. Theoretical calculations of the electronic structure of these compounds are performed. The experimental data and calculations suggest that the intercalation of the Cr and Fe atoms into the TiSe₂ matrix brings about a partial filling of the Ti 3d states and the spin polarization of the Cr 3d and Fe 3d states. Chemical bonds are formed through the hybridization of the d orbitals of intercalated atoms with the Ti 3d-Se 4p states of the matrix.