Paramagnetic susceptibilities, crystal field Stark energies and hyperfine properties of Eu in europium trifluoromethanesulfonate nonahydrate

Hexagonal single crystals of europium trifluoromethanesulfonate nonahydrate (EuTFMS) have been prepared. The paramagnetic susceptibility perpendicular to the symmetry axis (c-axis, χ_⊥) and the principal magnetic anisotropy (Δχ=χ_||−χ_⊥) were measured in the temperature range of 300-13 and 300-80 K, respectively. The paramagnetic susceptibility parallel to the c-axis (χ_||) was calculated using the values of χ_⊥ and Δχ. χ_|| and χ_⊥ increase slowly with decrease of temperature and below ∼93 K, χ_⊥ is more or less constant. But χ_|| levels off below ∼137 K. The calculated value of the effective magnetic moment (P_eff) of Eu³⁺ in the crystalline environment of EuTFMS decreases with lowering of temperature. The Raman and Fourier transform infrared (FTIR) spectra of EuTFMS were recorded in the wavenumber range of 10-1800 and 370-6000 cm⁻¹, respectively. A good theoretical simulation of the observed magnetic properties including the CF Stark energies of the ground term (⁷F) extracted from the Raman and FTIR spectra of Eu³⁺ in EuTFMS have been achieved using one electron crystal field (CF) analysis. The electronic specific heat and other relevant CF dependent hyperfine properties, viz, nuclear quadrupole splitting and hyperfine specific heat have been computed.     

Development of the Hamiltonian and transition moment operators of symmetric top molecules using the O (3) ⊃ C∞v ⊃ C3v group chain

We present a development of the Hamiltonian, dipole moment, and polarizability operators for XY₃Z molecules. These rovibrational operators are written with the aid of a tensorial formalism derived from the one already used in Dijon and adapted to the XY₃Z symmetric tops in a recent paper [A. El Hilali, V. Boudon, M. Loëte, J. Mol. Spectrosc. 234 (2005) 166-174]. We use the O (3) ⊃ C_∞v ⊃ C_3v group chain. Expressions for the matrix elements are derived for these operators.     

Magnetoresistance hysteresis of bulk textured Bi1.8Pb0.3Sr1.9Ca2Cu3Ox + Ag ceramics and its anisotropy

Magnetoresistance of bulk textured Bi_1.8Pb_0.3Sr_1.9Ca₂Cu₃O_x + Ag ceramics has been studied in the magnetic fields applied parallel and perpendicular to a–b planes of Bi2223 crystallites. Besides well known anisotropy of magnetoresistance of textured superconductors (R_H || c > R_H || a–b), anisotropic hysteresis of R(H) dependences was investigated. Parameters characterizing hysteretic R(H) curves differ for the cases H || c and H || a–b. This behavior is explained within the model of a granular superconductor where the total magnetic induction in the intercrystallite boundaries is superposition of the external field and the magnetic field induced by dipole magnetic moments of neighbor crystallites.     

Crystal field study and magnetic properties of [TbCu6(μ3OH)3(HL)2(L)4](ClO4)2·25H2O (H2L=imino-diacetic acid)

A crystal field (CF) investigation of the magnetic properties of [TbCu₆(μ₃-OH)₃(HL)₂(L)₄](ClO₄)₂·25H₂O (H₂L=imino-diacetic acid) has been carried out. An enhancement of the average magnetic susceptibility (defined by =(χ_||+2χ_⊥)/3, where χ_|| and χ_⊥ are the magnetic susceptibilities parallel and perpendicular to the symmetrical axis of the cluster) with respect to the Tb³⁺ free ion value has been noticed and is attributed to the Tb-Cu interaction. The CF parameters obtained for the system for the first time have been exploited to find the Stark splitting of the ⁷F manifold of Tb³⁺, paramagnetic resonance g-values, and the heat capacity. Two anomalies are obtained in the heat capacity at 40 and 5 K; the peak values are 3.1 and 5.98 J mol⁻¹ K⁻¹, respectively.     

Relationships in Raman intensity theories,in particular the Mayants-Averbukh theory

Brief surveys are given of the Mayants-Averbukh Raman intensity theory, and of the polar tensor Raman intensity theory recently presented by Bogaard and Haines. It was found that these intensity theories in essence are equivalent. In addition, the appearances of the symmetry invariant parameter matrices F_n⁰ of the Mayants-Averbukh theory were derived and tabulated for various symmetries of bond n. These matrices, and a single bond coordinate system, can be used as a convenient alternative to the Mayants-Averbukh treatment of bonds which have some kind of symmetry with respect to the midpoint of the bond. A modification of the Mayants-Averbukh treatment is also suggested. The rotational mode equations of the Mayants-Averbukh theory have been investigated to elecudate the constraints which they impose on Raman intensity theories based on the bond polarizability model. It was found that the valenceoptical theory is in conformity with the rotational modes only if all electrooptical parameters $\text{?α}{}_{\mathrm{ii}}{}^{\mathrm{(n)}}\text{?γ}{}_{\mathrm{p}}$ are neglected, where α_ii⁽ⁿ⁾ (i = 1, 2, 3) are the diagonal components of the polarizability α⁽ⁿ⁾ of bond n, and γ_p is the pth internal angular coordinate. Furthermore, the valence-optical theory was found to be strictly applicable only for cylindrical bond symmetry, C_mv (m ≥ 4). A generalized valence-optical Raman intensity theory, allowing also for non-zero off-diagonal components α_ij⁽ⁿ⁾, was found to be incompatible with the rotational mode equations of the Mayants-Averbukh theory. However, its basic polarizability equation was useful for suggesting a unique interpretation of a set of f parameters (elements of F_n⁰) in terms of components of the anisotropic part of a symmetric bond polarizability.     

Theoretical investigation of ESR spectra and local structure for VO in Ba2Zn(HCOO)6(H2O)

The electron spin resonance spectra (characterized by g factors g_, g_⊥ and hyperfine structure constants A_ and A_⊥) of Ba₂Zn(HCOO)₆(H₂O) (BZFA): VO²⁺ crystal are calculated from high order perturbation formulas. The calculated results are in good agreement with the observed values. The local structure parameters of [VO(H₂O)₅]²⁺ clusters are also obtained from the calculation. The magnitudes of the metal-ligand distances parallel and perpendicular to the C₄-axis are, respectively, R_≈0.163 nm and R_⊥≈0.210 nm. It is shown that the local structure around the V⁴⁺ ion possesses a compressed tetragonal distortion along C₄-axis.     

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.     

Refractive indices, order parameter and principal polarizability of cholesteric liquid crystals and their homogeneous mixtures

Measurements of refractive indices (n_e,n_o) and birefringence (Δn) have been made in solid, cholesteric and isotropic phases of cholesteryl carbonate, cholesteryl stearate and their three homogeneous mixtures of concentration 0.25, 0.50 and 0.77 at varying temperature in the range of 18-35 °C. The results clearly indicates that various transitions are of the first order. For accurate measurement of Δn, a modified wedge method was used. Using n_e and n_o, principal polarizability (α_e,α_o), internal field factor (γ_e,γ_o) and order parameter (S) have been evaluated, and their temperature dependence discussed. The order parameter has been determined by using the isotropic internal field model (Vuks approach) and the anisotropic internal field model (Neugebauer's approach), and both values agree up to average deviation of 0.7%.     

Study of the electron paramagnetic resonance spectra of Zn(antipyrine)2(NO3)2:VO

In this work, a full ligand-field energy matrix (10×10) diagonalization treatment for 3d¹ ions in tetragonal symmetry is developed on the basis of the two-s.o.-coupling-parameter model. Spin Hamiltonian parameters (g factors g_∥, g_⊥ and hyperfine structure constants A_∥, A_⊥) of the tetragonal V⁴⁺ center in Zn(antipyrine)₂(NO₃)₂ are calculated from the complete energy matrix diagonalization method and the perturbation theory method. The calculated results from both methods are not only close to each other but also in good agreement with the experimental values. Furthermore, the compressed defect structure of V⁴⁺ center is discussed.     

Theoretical calculations of the optical band positions and spin-Hamiltonian parameters for Yb at the tetragonal Y site of KY3F10 crystal

The six optical band positions and six spin-Hamiltonian parameters [g factors g_∥, g_⊥ and hyperfine structure constants A_∥(¹⁷¹Yb³⁺), A_⊥(¹⁷¹Yb³⁺), A_∥(¹⁷³Yb³⁺), A_⊥(¹⁷³Yb³⁺)] for Yb³⁺ ion at the tetragonal Y³⁺ site of KY₃F₁₀ crystal are calculated from a diagonalization (of energy matrix) method. In the method, the Hamiltonian of energy matrix contains the free-ion, crystal-field interaction, Zeeman (or magnetic) interaction and hyperfine interaction terms and so a 14×14 complete energy matrix for 4f¹³ ion in tetragonal crystal-field and under an external magnetic field is constructed. Diagonalizing the energy matrix, these optical and EPR spectral data are calculated together and the calculated results are in reasonable agreement with the experimental values. The signs of hyperfine structure constants A_∥, A_⊥ for the isotopes ¹⁷¹Yb³⁺ and ¹⁷³Yb³⁺ in KY₃F₁₀ are suggested. The results are discussed.     

Lower bounds on the slope parameter

A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t₀ where A(s, t) is the absorptive part of the elastic scattering amplitude and t₀ is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like s^α(t)ln^η(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t₀, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.     

New screening doublets in x-ray satellite spectra

Recent scrutiny of the relevant data available at present on x-ray satellite spectra in theK, L andM regions revealed the existence of two new satellite pairsα″α′ andα″α′ ₃ ′ in theKα satellite group, three pairsα′ ₂ α″,α′ ₂ α^VI andα? α ^IV in theLα satellite group, twoLβ ₂ satellite groups; viz.,β ₂ ^(b) (β ₂ ^I ,β ₂ ^II β ₂ ^(c) ) andβ ₂ ^(c) (β ₂ ^I β ₂ ^II ), two pairsγ′₁ γ′₂ andγ′₁ γ′_2′ in theLγ satellite group and also a pairβ _II β _III in theMβ satellites, which are all found to be governed by the screening doublet relationship,Δ(v/R)^1/2=constant.     

In beam gamma spectroscopy of62Zn

The decay scheme of⁶²Zn has been investigated by studying the yield functions, angular distributions and coincidence relation-ships of theγ-rays emitted in the⁶³Cu(p, 2nγ) and⁶⁰Ni(α, 2nγ) reactions. Spins up to7? were assigned to the observed states. Nuclear Reactions ⁶⁰Ni(α, 2nγ)⁶²Zn,E _α=28–35 MeV and⁶³Cu(p, 2nγ)⁶²Zn,E _p = 22–31 MeV; measuredE _γ,I _γ(θ),I _γ(E _p , andI _γ,E _α-γ coincidences,⁶²Zn deduced decay scheme. Enriched target, Ge(Li) detectors.     

Determination of ratios of emission probabilities of Auger electrons and K-L-shell radiative vacancy transfer probabilities for 17 elements from Mn to Mo at 59.5 keV

The measurements of the K X-ray intensity ratio I(K_β)/I(K_α) for the 17 elements Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, Rb, Sr, Y, Zr, Nb and Mo have been done following ionization by 59.5 keV γ-rays from a ²⁴¹Am point source. Ratios of emission probabilities of Auger electrons and the vacancy transfer coefficients have been extracted in terms of the intensity ratios. It is found that the present results agree well with earlier fitted values and the semi-empirical values.     

The dependence of the radiative transition probability of donor-acceptor pairs on pair separation

The probability W(R) for radiative donor-acceptor pair transitions is generally assumed to decrease exponentially with increasing pair separation R, with a characteristic length a. When one centre in the pair is deep and strongly localized and the other one is shallow, a equals half the Bohr radius of the shallower centre. For pairs in GaP involving two shallow centres we have previously reported that a exceeds half this Bohr radius, and have suggested this to be due to the spatial extent of the deeper centre. In the present paper we investigate this point, both experimentally, and by considering Novotny's calculations — for direct transitions — on the R-dependence of W(R), in which the Bohr radii of both donor and acceptor are parameters. According to these calculations, W(R) is not exponential in the case of two shallow centres. In a limited range of R, W(R) is approximately exponential, however, and theoretical “effective values” of a can be obtained. These effective values are compared with experimental data on a for the pair series S_P-Si_P, S_P-Cd_Ga, S_P-Zn_Ga and S_P-C_P in the indirect semiconductor GaP; a amounts to ∽ 5.4, 7.0, 7.7 and 9.1 Å, respectively. The comparison shows that the difference found between the experimental a and half the Bohr radius of the less localized centre in the pair can indeed be explained by the influence on a of the spatial extent of the more localized centre. This findings implies a non-exponential W(R) for pairs with two shallow centres. This conclusion depends critically on the values used for the Bohr radii of the acceptors, however. These are not accurately known, due to insufficient knowledge of m¹_h, one of the quantities needed in calculating the radii. We used m¹_h = 0.36 m₀ to 0.40 m₀, corresponding to the normally used hydrogen-model energy of 40–45 meV. An alternative explanation for the experimental values of a is that in reality m¹_h is significantly lower than the 0.36 m₀ to 0.40 m₀ used, leading to larger acceptor Bohr radii and, in the extreme case, to no influence on a of the more localized centre and to an exponential W(R). In order to decide between the two possible explanations, additional experiments are presented. These include an accurate comparison of a between S_P-C_P and O_P-C_P as well as between S_P-Zn_Ga and O_P-Zn_Ga pairs. This is done by analysing the intergral band decay and time-resolved spectra of these pairs. The conclusions for all pairs mentioned are: (i) The Bohr radius of the acceptors involved is significantly larger than calculated from an effective-mass energy of 40–45 meV; they correspond to a hydrogen-model energy of 28 meV (m¹_h = 0.25 m₀). (ii) There is in first approximation no influence on the shape of W(R) of the spatial extent of the more localized centre. (iii) The experimental results are well described by an exponential W(R) with a equal to half the Bohr radius of the less localized centre of the pair.     

The Condition of Applicability for the Extended Boundary Conditions Method for Small Multilayer Particles

We have examined an analog to the extended boundary conditions method (EBCM) with the standard spherical basis, which is popular in light scattering theory, with respect to its applicability to the solution of an electrostatic problem that arises for multilayer scatterers the sizes of which are smaller compared to the wavelength of the incident radiation. It has been found that, in the case of two or more layers, to determine the polarizability and other optical characteristics of particles in the far-field zone, the parameters of the surfaces of layers should obey the condition max{σ₁^(j)} < min{σ₂^(j)}. In this case, appearing infinite systems of linear equations for expansion coefficients of unknown fields have a unique solution, which can be found by the reduction method. For nonspheroidal particles, this condition is related to the convergence radii of expansions of regular and irregular fields outside and inside of the particle, including its shells—R₁^(j) = σ₁^(j) and R₂^(j) = σ₂^(j). In other words, a spherical shell should exist in which expansions of all regular and irregular fields converge simultaneously. This condition is a natural generalization of the result for homogeneous particles, for which such a condition is imposed only on expansions of the “scattered” and internal fields—R₁ < R₂. For spheroidal multilayer particles, which should be singled out into a separate class, the EBCM applicability condition is written as max{σ₁⁽¹⁾, σ₁⁽²⁾, …, σ₁^(J?1), σ₁^(J)} < min{σ₂⁽¹⁾, σ₂⁽²⁾, …, σ₂^(J?1)} and parameters σ₂^(j) of the surfaces of shells are not related to corresponding convergence radii R₂^j of irregular fields. Numerical calculations for two-layer spheroids and pseudospheroids have confirmed completely theoretical inferences. Apart from the EBCM algorithm, an approximate formula has been proposed for the calculation of the polarizability of two-layer particles, in which the polarizability of a two-layer particle is interpreted as a linear combination of the polarizabilities of homogeneous particles that consist of the materials of the shell and core proportionally to their volumes. The range of applicability of this formula is wider than that for the EBCM, and the calculation error is smaller than 1%.     

The level structure of69Ge

Theγ-ray decay of the states in⁶⁹Ge has been studied using the reaction⁶⁶Zn(α, nγ)⁶⁹Ge atE _α =13 and 19 MeV. The level scheme and spin assignments were established by means of coincidence measurements, angular distributions and excitation functions. 27 new levels could be found or confirmed. It is suggested that⁶⁹Ge is a further example for the weak coupling phenomenon in the medium mass nuclei. Nuclear Reactions: ⁶⁶Zn(α, nγ)⁶⁹Ge,E _α =13–22 MeV, measuredE _γ ,I _γ ,I _γ (θ),E _γ =f(E _α ),γ-γ coincidences,⁶⁹Ge deduced levels,J, enriched target.     

Dynamic model for alpha particle emission during fission

We investigate the motion of anα-particle in the average time depencent potentialV(R _α ,t) of a fissioning nucleus. The emission process is treated quantum mechanically via a numerical solution of the one-body Schroedinger equation withV(R _α ,t). This solution yields the distribution of initial conditions for classical trajectories describing theα-particles outside the Coulomb barrier. The time and shape dependence ofV(R _α,t) is shown to have significant influence on the observable angle and energy distribution of theα-particles emitted during fission.     

Helium burning of22Ne

The²²Ne(α, γ)²⁶Mg and²²Ne(α, n)²⁵Mg reactions were investigated forE _α(lab) from 0.71 to 2.25 MeV. Neon gas enriched to 99% in²²Ne was recirculated in a differentially pumped gas target system of the extended type. Theγ-ray transitions were observed with Ge(Li) detectors and the neutrons with³He ionization chambers. A previously known resonance at E_R(lab)=2.05 MeV was verified and 15 new resonances were found in the energy range covered, with the lowest at E_R(lab)=0.83 MeV. Information on resonance energies, widths, strengths,γ-ray branching ratios, as well asJ ^π assignments, is reported. The energy range investigated corresponds to the important temperature range ofT ₉ from 0.3 to 1.4 (10⁹ K), for which the astrophysical rates were determined for both reactions. The results show that the ratios of the rates for²²Ne(α, n)²⁵Mg and²²Ne(α, γ)²⁶Mg are significantly smaller than the previously adopted values, e.g., by at least a factor of 60 nearT ₉=0.65. Thus, the²²Ne(α, n)²⁵Mg reaction will likely play a smaller role as a neutron source fors-process nucleosynthesis, than has frequently been assumed.     

EPR parameters and local lattice structure study of V ions in CdCl2 and CsMgCl3 crystals

The local lattice structure and EPR parameters (D, g_‖, g_⊥) have been studied systematically on the basis of the complete energy matrix for a d³ configuration ion in a trigonal ligand field. By simulating the calculated optical and EPR spectra data to the experimental results, the local distortion parameters (ΔR, Δθ) are determined for V²⁺ ions in CdCl₂ and CsMgCl₃ crystals, respectively. The results show that the local lattice structure of CdCl₂:V²⁺ system exhibits a compression distortion (ΔR=−0.0868 Å) while that of CsMgCl₃:V²⁺ system exists an elongation distortion (ΔR=0.0165 Å). The different distortion may be ascribed to the fact that the radius of V²⁺ ion is smaller than that of Cd²⁺ ion or larger than that of Mg²⁺ ion. Moreover, the relationships between EPR parameter D and local structure parameters (R, θ) as well as the orbital reduction factor k and g‐factors (g_‖, g_⊥) are discussed.