Spin-Hamiltonian parameters,defect model and defect structure for the tetragonal Mo5+ center in x-ray-irradiated α-ZnMoO4 crystals

ABSTRACT

The spin-Hamiltonian parameters (g factors g_i, hyperfine structure constants A_i (⁹⁵Mo⁵⁺) and A_i (⁹⁷Mo⁵⁺), i?=?// and ⊥) assigned to the tetragonal Mo⁵⁺ (4d¹) tetrahedral center in α-ZnMoO₄ crystal caused by a Mo⁶⁺(1) ion trapping an electron after x-ray irradiation are calculated from the high-order perturbation formulas resting on the two-mechanism model. The model takes account of both the effects of crystal-field (CF) mechanism concerning the CF excited states in the CF theory and that of the charge-transfer (CT) mechanism related to CT excited states. The calculated results are reasonably consistent with the experimental values, confirming this assignment (or defect model). The calculations also indicate that the effect of CT mechanism cannot be neglected. The defect structure (particularly, the angular distortion) and signs of constants A_i (⁹⁵Mo⁵⁺) and A_i (⁹⁷Mo⁵⁺) of this Mo⁵⁺ defect center are also decided from the calculations. The outcomes are discussed.     

A new basis set for molecular wavefunctions

A new basis set is proposed for molecular self-consistent field and configuration interaction calculations. Expansion functions are proposed in the form sin (r _A · p) exp (-ar_A ²) and cos (r _A · p) exp (-ar _A ²) and it is suggested that they are used as an alternative to the gaussian basis set x_A ⁱy_A ^jz_A ^k exp (-ar _A ²).

It is shown how the new basis can have the same effects, for suitable vectors p, as the gaussian basis. It is further shown that all the one and two-electron integrals in the new basis are evaluable in terms of exponentials, square roots and the complex error function erf (z). First calculations, using the new basis, are presented in LiH, HF and H₂O.     

Eigenvalues of Laplacian with Constant Magnetic Field on Non-Compact Hyperbolic Surfaces with Finite Area

We consider a magnetic Laplacian −Δ _A = (id + A)^* (id + A) on a non-compact hyperbolic surface M with finite area. A is a real one-form and the magnetic field dA is constant in each cusp. When the harmonic component of A satisfies some quantified condition, the spectrum of −Δ _A is discrete. In this case, we prove that the counting function of the eigenvalues of −Δ _A satisfies the classical Weyl formula, even when dA=0.     

Temperature dependence of ion-induced auger electron emission from (111) silicon: I. Experiments

Abstract

Measurements of both secondary electron emission coefficient γ and SiL₂₃ Auger yield ρ_A obtained from (111) Si target bombarded by high fluence of noble gas ions were performed. For Si irradiated at room temperature at doses more than 10¹⁷ ions per cm², monotonous increasing variation of γ and ρ_A versus incidence angle i was observed. For Si irradiated at a temperature more than a critical value, γ(i) and ρ_A(i) curves exhibited, superimposed to monotonous variation, some minima when the ion beam penetrates the crystal along low index directions. In the range 20–650°C, the Auger yield temperature dependence showed a sharp variation around a critical value depending on the ion mass for a given incident energy. These results are linked to an amorphous-crystalline phase transition.     

A<Subscript>4</Subscript> symmetry and lepton masses and mixing

Stimulated by Ma’s idea, which explains the tribimaximal neutrino mixing by assuming an A₄ flavor symmetry, a lepton mass matrix model is investigated. A Frogatt–Nielsen-type model is assumed, and the flavor structures of the masses and mixing are caused by the VEVs of SU(2)_L singlet scalars φ_i ^u and φ_i ^d (i=1,2,3), which are assigned to 3 and (1 ,1 ’,1 ”) of A₄, respectively. Possible charged lepton and neutrino mass spectra and mixing are investigated.     

EPR parameters and defect structure of the tetrahedral Ti3+ defect center in beryl crystal

The EPR parameters (g factors g _i and hyperfine structure constants A _i , where i=x, y, z) of Ti³⁺ ion at the tetrahedral Si⁴⁺ site of beryl crystals are calculated within the rhombic symmetry approximation from the high-order perturbation formulas based on the two-spin-orbit (SO)-parameter model. In these formulas both the contribution due to the SO coupling parameter of the central 3d¹ ion and that of ligand ions are considered. From the calculations, the defect structure of the Ti³⁺ defect center in beryl crystal is estimated and the EPR parameters g _x , g _y , g _z and A _y are reasonably explained. The values of the parameters A _x and A _z (which were not reported) are suggested and remain to be checked by the further experimental studies.     

Incommensurate phase in the layered hexagonal crystal Cs3Bi2I9

An incommensurate phase is observed in a Cs₃Bi₂I₉ crystal, which belongs to the family of layered A₃B₂X₉ structures. Data from ¹²⁷I NQR and x-ray powder diffraction patterns show that the second-order normal phase—incommensurate phase transition at T _i=220 K is accompanied by a P6₃/mmc↔P2₁/m symmetry change and takes place at the center of the Brillouin zone. The nature of the instability leading to the appearance of this little-studied form of incommensurability is discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 1105–1108 (June 1997)     

On the physical interpretation of Heywood and Redhead's algebraic impossibility theorem

Heywood and Redhead's 1983 algebraic (Kochen-Specker type) impossibility proof, which establishes the inconsistency of a broad class of contextualized local realistic theories, assumes two locality conditions and two auxiliary assumptions. One of those auxiliary conditions, FUNC^*, has been called a physically unmotivated,ad hoc formal constraint.In this paper, we derive Heywood and Redhead's auxiliary conditions from physical assumptions. This allows us to analyze which classes of hidden-variables theories escape the Heywood-Redhead contradiction. By doing so, we hope to clarify the physical and philosophical ramifications of the Heywood-Redhead proof. Most current hidden-variables theories, it turns out, violate Heywood and Redhead's auxiliary conditions.1. See Redhead [1], pp. 133–136, for a complete discussion.2. Arthur Fine first pointed out the implicit reliance on FUNC^*, and proved FUNC^* to be both consistent with and independent of the Value Rule.3. LetA=_ia_i P _i andB=_jb_j P_j be spectral resolutions ofA andB. Then <A,B> is the observable associated with maximal operatorR=_ijf_ij P _iP_j, where f_ij=F(a_i,b_j), and where function F is 1:1.4. Heywood and Redhead's versions of these conditions employ equivalence-class notation to specify the ontological context. {<D,E>}={R} refers to the equivalence class of all possible <D,E> formed by using different F functions (cf. Footnote 3). Clearly, such notation assumes that ifR andR are two distinct commuting maximal operators formed as described in Fn. 3 fromD andE using two different F(d_i,e_j) functions, then [Q]^t _(R)(R)=[Q]^t _(R)(R), so that [Q]^t _{R}(R) is uniquely defined.Heywood and Redhead never rely upon this assumption in their proof, however. It is easily checked that a Heywood-Redhead contradiction follows from my non-equivalence class versions of OLOC, ELOC, VR, and FUNC^*. Therefore, I will not use equivalence class notation.5. Here I denote by µ_R the composite state of all the apparatuses needed to measure R. So µ_R may represent the state of more than one device.6 This is because in a hidden-variables framework, quantum mechanical probabilities are a weighted average of the underlying hidden-variables probabilities.7. This argument resembles a proof given by Fine [8].8. Recall from theorem 1 that ifQ=f(R), then for all quantum states , P_(t)(Qf(r), R=r)=0.     

On the problem of whether the transition probability plays a role in describing secondary-photon yields

The yields of secondary photons, i.e. photons emitted from sputtered excited states, have been described variously as being proportional to either P(?_i) b_fi or P(?_i) v_fiA_fi. Here P( the function giving the probability of a sputtered particle having excitation energy ?_i, b_fi is the branching ratio, v_fi is the photon frequency, and A_fi is the transition probability. In an attempt to clarify the role of A_fi we have compared experimental yields from bombarded Li, Zn, Cd, Sc, and Ti with tabulated plasma yields and obtained results which suggest that A_fi does not enter, in the case of secondary photons, as a simple multiplier of P(?_i). This is not really surprising, as secondary photons are emitted by isolated atoms whereas the use of the factor A(_fi) assumes thermodynamic equilibrium during decay, as in a plasma. In further experiments, yields were measured versus distance in front of the target. Introducing the decay rate constant, γ_i = ΣA_fi, one finds that for γ_i exceeding 0.4 × 10⁸ s^?1 the signals fall by a factor of 10 within 1.5 mm, for γi of (0.02?0.2) × 10⁸ s^?1 they fall by such a factor within 3–10 mm, and for γi of (0.0004–0.004) × 10⁸ s^?1 significant decay occurs beyond the reach of the detector. This shows that A_fi does indeed play a role in describing photon yields whenever γ_i is sufficiently small, namely in the somewhat complicated relation describing the spatial distribution of the photon emission. Nevertheless, in most situations the use of A_fi is unjustified.     

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.     

Mathematical Modelling of the Role of Intra- and Extracellular Activity of Carbonic Anhydrase and Membrane Permeabilities of HCO3, H2O and CO2 in 18O Exchange

Abstract

Numerical simulation of ¹⁸O exchange between CO₂, H₂O and HCO₃ ^? explains the ratio mass 46/mass 44 (=C¹⁸O¹⁶O/C¹⁶O₂) measured by mass spectrometry to approximately 1% relative mean difference. In the presence of intact red blood cells the reaction takes place extra- and intracellularly at different reaction rates. Because CO₂ hydration/dehydration is accelerated intracellularly by carbonic anhydrase, a difference in intra- and extracellular concentration of labelled reactants occurs. The ensuing transfer of reactants across the cell membrane depends on their membrane permeabilities which are approximately P_{CO 2} ? 2 cm/s, P_{H 2 O} ? 0.002 cm/s and P_{HCO 3} ? 0.00015 cm/s (values from the literature). We found that the numerical simulation is affected most by P_{HCO 3} . The influence of the other permeabilities is at least ten times less. Therefore within the range of normal literature values, P_{HCO 3} is the only permeability that has a rate limiting effect on ¹⁸O exchange. This is why, in turn, P_{HCO 3} can be derived from an experimentally determined time course of mass 46/mass 44 by a fitting procedure. Another crucial parameter that can be estimated from the experimental results is the intraerythrocytic carbonic anhydrase activity A_i .     

Harness Processes and Non-Homogeneous Crystals

We consider the Harmonic crystal, a measure on with Hamiltonian H(x)=∑ _i,j J _i,j (x(i)−x(j))²+h∑ _i (x(i)−d(i))², where x, d are configurations, x(i), d(i)∈ℝ, i,j∈ℤ ^d . The configuration d is given and considered as observations. The ‘couplings’ J _i,j are finite range. We use a version of the harness process to explicitly construct the unique infinite volume measure at finite temperature and to find the unique ground state configuration m corresponding to the Hamiltonian.     

Gauge invariance of the Euler-Lagrange expressions

We prove, for a Lagrangian density L(g_ij;A _i ⁱ ;A _i ^j ), that the gauge invariance of the Euler-Lagrange expressionsE ⁱ (L) implies the existence of a gauge-invariant scalar densityL ₁, such thatE ⁱ (L) =E ⁱ (L₁). We then prove the uniqueness of the Yang-Mills field equations.     

Spectral decomposition of an elementary 3-fermion 2-body operator

The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator 3P²_g∧I¹A³∑_{1≤i≤j≤3}P²_g(i, j)A³ acting on a 3-particle antisymmetric finite-dimensional Hilbert space have been found. Here P_g² denotes the projection operator onto a 2-particle antisymmetric function g², while A³ denotes the 3-particle antisymmetrizing operator.     

Theoretical research on the spin-Hamiltonian parameters of the square-planar CuS46− clusters in Cu(II)–dithiophosphonate complexes

The spin-Hamiltonian parameters (g-factors g_//, g_⊥ and hyperfine structure constants A_//, A_⊥) of the square-planar CuS^{6 ?}₄ clusters in Cu(II)–bis [4-ethoxphenyl-O-alkyl]-dithiophosphonate complexes are computed with the high-order perturbation formulas based on the two-mechanism model. The model includes the contributions to spin-Hamiltonian parameters from the vastly-utilised crystal-field (CF) mechanism concerning the CF excited states and the generally-omitted charge-transfer (CT) mechanism due to CT excited states. The energy levels of CF and CT excited states needed in the calculation are obtained from the observed optical spectra. The calculated results are in rational accordance with the experimental values. The signs of constants A_// and A_⊥ are suggested and the reasons of the very small g-shifts |?g_i| (= | g_i ? g_e |, where g_e ≈ 2.0023 and i = // or ⊥) are discussed.     

Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.     

Investigations of the optical spectra and spin-Hamiltonian parameters for the rhombic Yb centers in garnets

Two complete diagonalization (of energy matrix) methods (CDM-I and CDM-II) are used to calculate the six optical spectral band positions and nine spin-Hamiltonian (SH) parameters (g factors g_i and hyperfine structure constants ¹⁷¹A_i, ¹⁷³A_i, where i=x, y, z) for Yb³⁺ ions in the rhombic dodecahedral sites of garnets Y₃Al₅O₁₂, Lu₃Al₅O₁₂ and Y₃Ga₅O₁₂. In CDM-I, the Hamiltonian concerning energy matrix does not contain the Zeeman and hyperfine interaction terms, whereas in CDM-II, it does. So, in CDM-I, the SH parameters are obtained by first-order perturbation method or the equivalence between SH and Zeeman term (or hyperfine interaction term) and in CDM-II, the SH parameters and optical spectral band positions are calculated together. The results obtained from both methods are not only close to each other, but also in reasonable agreement with the observed values. So the second-order perturbation formulas of SH parameters developed recently are incorrect and unnecessary.     

Investigation of the intershell higher order resonant recombination and polarization of X-ray emission of B-like silicon ions

K-shell dielectronic, trielectronic, and quadruelectronic recombination and polarization of X-ray emission have been studied for the highly charged Si⁹⁺ ions in the initial ground state ²P_1/2 and the metastable state ²P_3/2 using the Flexible Atomic Code. It is found that the resonant recombination cross section from the long-lived metastable state is comparable in magnitude with that of the ground state, so it is important for plasma diagnostics. For Si⁹⁺(²P_1/2), trielectronic recombination contributions of nearly 25% to the total resonant recombination strength are predicted, which is less than previous calculations. We compare the degree of linear polarization for the eleven dominant resonant recombination satellite lines from the initial parent Si⁹⁺(²P_1/2) and Si⁹⁺(²P_3/2) ions. For the same X-ray lines, large variations of polarization are found between ²P_1/2 and ²P_3/2, which can be employed to diagnose formation mechanisms of intermediate resonance states and corresponding X-ray lines.     

The configuration of the benzylradical

4. Conclusions

Provided reliable values for the inertia factors, A_j , are available, the Newton-Raphson approach to the analysis of (v(T)_n.q.r.)_P provides a direct convergent method of deriving the Einstein temperatures and, in theory, the α _j and n_j terms associated with the volume dependence of the ?_j modes.

A preliminary study of v(T)_P for [P³⁵Cl₄]⁺[FeCl₄]^- provides evidence of a torsional mode, at 40·4 cm^-1, which modulates the electric field gradient.