The far infrared spectrum of 14N16O2

High resolution Fourier transform spectra in the 8–200 cm^-1 spectral region have been used to analyse the pure rotation spectrum of nitrogen dioxide. In this way, the spin rotation levels of the (000) state were accurately measured for K_a up to 14 and N up to 54. Using a hamiltonian which takes the spin-rotation and the hyperfine operators explicitly into account, it has been possible to derive a complete set of molecular parameters (rotational, spin-rotation and hyperfine constants) for the (000) state of ¹⁴N¹⁶O₂ from these experimental data and from the available microwave measurements. Numerous perturbations due to the hyperfine Fermi contact operator were analysed as well as a local resonance [42 0 42, J = 41·5] ? [41 2 40, J = 41·5] due to the electron spin-rotation interaction. Finally, a synthetic spectrum of the (000) ← (000) band of ¹⁴N¹⁶O₂ including all hyperfine transitions has been computed, covering the 0–235 cm^-1 spectral region.     

Reduction of two two-body operators in the effective hyperfine hamiltonian to one-body operators

The two two-body operators representing the effect of far configurations on the contact hyperfine interaction in annl ^N n′s configuration are shown to reduce to one-body operators. In such a configuration the operator for the contact hyperfine field is (a _nlS_nl +a_n,ss_n′s), where a_nl and a_n′s take the same values in all terms of the configuration. A discrepancy between expectation values of these two-body operators deduced from experiment and calculated values is explained.     

Spin eigenfunctions and operators for the Dn groups

An automated procedure for determining symmetry-adapted spin eigenfunctions is developed for the D_n symmetry groups with n equivalent spins for arbitrary size of I and for n=3,…,6. These eigenfunctions are also eigenfunctions of the vector sum of the n equivalent nuclear spins. Generalized hyperfine spin operators are developed that have real matrix elements and that exploit the full symmetry. These spin operators can be combined with operators for other spins and molecular rotation using only real arithmetic.     

Internal rotation and hyperfine coupling interaction in deuterated acetaldehyde

Theoretical and experimental investigations of the hyperfine structure of deuterated acetaldehyde (CD₃COH) are presented. The theoretical approach accounts for the large amplitude internal rotation of the CD₃ group. A hyperfine Hamiltonian, depending on the large amplitude torsional angle, is written taking into account quadrupole hyperfine coupling arising from the three deuterium atoms. Effective hyperfine coupling Hamiltonians are derived for A- and E-type rotation-torsion levels. In the former case, a very symmetrical operator arises in which the hyperfine coupling is the same for all three deuterium atoms. In the latter case the operators are less symmetrical. Hyperfine levels are calculated using symmetry adapted hyperfine wavefunctions in order to build total hyperfine-rotation-torsion wavefunctions satisfying the Pauli exclusion principle. The theoretical approach is used to carry out analyses of six hyperfine patterns which were recorded using a pulsed molecular beam Fourier transform microwave spectrometer. The experimental resolution of this apparatus allows us to resolve individual hyperfine components in many cases. The results of the analysis are consistent with deuterium atoms having an effective quadrupole coupling tensor which, except for appropriate rotations, is quite close to that in CH₃D.     

Spectra,eigenvectors and overlap functions for representation operators ofq-deformed algebras

Operators of representations corresponding to symmetric elements of theq-deformed algebrasU _q (su_1,1),U _q (so_2,1),U _q (so_3,1),U _q (so _n ) and representable by Jacobi matrices are studied. Closures of unbounded symmetric operators of representations of the algebrasU _q (su_1,1) andU _q (so_2,1) are not selfadjoint operators. For representations of the discrete series their deficiency indices are (1,1). Bounded symmetric operators of these representations are trace class operators or have continuous simple spectra. Eigenvectors of some operators of representations are evaluated explicitly. Coefficients of transition to eigenvectors (overlap coefficients) are given in terms ofq-orthogonal polynomials. It is shown how results on eigenvectors and overlap coefficients can be used for obtaining new results in representation theory ofq-deformed algebras.     

Influence of structural deformations on the magnetic properties of Jahn-Teller complexes of divalent copper in CaxSr1−x F2 mixed crystals

Crystals of variable constituency Ca_xSr_1−x F₂:Cu (0⩽x⩽0.05, x≅0.5, 1.0⩾x⩾0.95) are investigated by EPR and x-ray structural analysis. The electron-Zeeman, intrinsic hyperfine, and ligand hyperfine interaction parameters are determined; they characterize the magnetic properties of the copper paramagnetic complexes formed in the crystals. Models of the molecular structures of these complexes are discussed, along with the influence of structural deformations and vibronic interactions on their magnetic properties. Fiz. Tverd. Tela (St. Petersburg) 40, 445–451 (March 1998)     

Relaxation times and line widths of isotopically-substituted nitroxides in aqueous solution at X-band

Optimization of nitroxides as probes for EPR imaging requires detailed understanding of spectral properties. Spin lattice relaxation times, spin packet line widths, nuclear hyperfine splitting, and overall lineshapes were characterized for six low molecular weight nitroxides in dilute deoxygenated aqueous solution at X-band. The nitroxides included 6-member, unsaturated 5-member, or saturated 5-member rings, most of which were isotopically labeled. The spectra are near the fast tumbling limit with T₁∼T₂ in the range of 0.50–1.1 μs at ambient temperature. Both spin–lattice relaxation T₁ and spin–spin relaxation T₂ are longer for ¹⁵N- than for ¹⁴N-nitroxides. The dominant contributions to T₁ are modulation of nitrogen hyperfine anisotropy and spin rotation. Dependence of T₁ on nitrogen nuclear spin state m_I was observed for both ¹⁴N and ¹⁵N. Unresolved hydrogen/deuterium hyperfine couplings dominate overall line widths. Lineshapes were simulated by including all nuclear hyperfine couplings and spin packet line widths that agreed with values obtained by electron spin echo. Line widths and relaxation times are predicted to be about the same at 250 MHz as at X-band.     

A theoretical study of the hyperfine fields of Fe and Co in ferromagneticbcc Fe x Co1−x

The hyperfine fields of Fe and Co in the substitutionally disorderedbcc alloy system Fe _x Co_1−x due to the Fermi contact interaction have been studied by means of charge self-consistent cluster Korringa-Kohn-Rostoker-Coherent Potential Approximation- (KKR-CPA) band structure calculations. The contribution to the Fermi contact hyperfine field due to core polarisation was found to be proportional to the local moment for Fe as well as for Co throughout the concentration range. On the other hand, the contributions of the conduction band did not show such a simple behavior, but were found to be dominated by the population of the s-bands for spin up and down. These findings are completely analogous to those obtained in a recent study of the ferromagnetic alloy systems Fe _x Ni_1−x and Fe _x Cr_1−x . To investigate the importance of relativistic effects on the Fermi contact hyperfine fields, the corresponding hyperfine matrix elements have been calculated nonrelativistically as well as fully relativistically. The results of the present work are compared with experiment as well as to theoretical data on related alloy systems.     

Anomalous temperature dependence of the 1.7T magnetic hyperfine field of fluorine in nickel

By means of time-differential perturbed angular distribution (TDPAD) techniques, the magnetic hyperfine field ofF atoms implanted in a ferromagnetic Ni lattice has been measured at temperatures from 80 K to 650 K obtaining, for example, a fieldH ₁(295 K)=+1.72(3)T at room temperature. The temperature dependence of the reduced fieldH ₁(T)/H ₁(0) has been found to deviate up to 38% from that of the reduced magnetization of the Ni host. Comparing this result for the halogenF with other nontransitional impurities in nickel, it seems that such deviations become more pronounced with increasing number of excessp-electrons of the impurity. With a simple two-zone model distinguishing between the hyperfine fields originating in the local and in the more distant undisturbed surrounding of theF impurity, the observed temperature dependence can be explained. In this approach the disturbed magnetization of the inner zone is described by localized Ni moments in the molecular field approximation.A satellite magnetic field of + 9.4T was observed at 80 K only.Supported by the Bundesministerium für Forschung und Technologie     

Decoupling experiments for the study of electric and magnetic hyperfine interactions in ferromagnetic compounds

The decoupling experiments involving the time-differential perturbed angular correlation (TDPAC) of the 133–482 keV γ-γ cascade in the presence of an external magnetic field applied along the quantization axis have been performed to measure the electric quadrupole and the magnetic hyperfine interactions experienced by the¹⁸¹Ta nuclei at Hf sites in the pseudobinary compounds HfFe_2-xSi_x, withx=0.1 andx=0.3. The hyperfine magnetic fields measured at 298 K areH _hf=133.1±12.0 kG in the cubic (C15) Laves phase compound HfFe_1.9Si_0.1 andH _hf=76.8±7.0 kG in the hexagonal (C14) Laves phase compound HfFe_1.7Si_0.3. The decoupling technique has also been used to obtain a —ve sign for the hyperfine field experienced by¹⁸¹Ta nuclei at the Ti or Hf sites in the Heusler compound Co₂Ti_0.8Hf_0.2Sn and a+ve sign for the hyperfine field at Zr sites in the cubic (C15) Laves phase compound ZrFe₂.     

On the reduction of the Dirac equation to non-relativistic form: the dipole-dipole interaction in the hydrogen atom

Finite nucleus models are used in the calculation of the dipole-dipole part of the second-order hyperfine energy in the ground state of the hydrogen atom. The results are used as a guide to bring the non-relativistic calculation for a point nucleus into agreement with the relativistic calculation. This necessitates the introduction of delta function operators in the dipole-dipole operator and the zeroth-order hamiltonian. It is concluded that the reduction of the Dirac equation to non-relativistic form is valid for the hyperfine interaction up to order mc ²α⁶.     

Absolute sign of the Mu* hyperfine parameters in diamond

Standard μSR experiments in diamond have shown that the relative sign of the hyperfine parameters of the anisotropic Mu^* state is negative (A _‖/A _⊥<0). We report an experimental determination of theabsolute sign of the Mu^* hyperfine parameters by studying the transferred muon polarization during the thermally-activated transition from the isotropic Mu state to Mu^*. The results demonstrate that the isotropic part of the Mu^* hyperfine interaction is negative. In a nitrogen-poor diamond, both the Mu disappearance rate and the enhancement of the Mu^* signals are well-described by a single Arrhenius law.     

Consequences of relativity for the hyperfine interactions — with applications to transition metals

The strong influence of relativity on the hyperfine interaction is demonstrated by non-, scalar andfully relativistic calculations for solid transition metal systems. By calculations of hyperfine fields andof the nuclear spin lattice relaxation rate of Ag in Ag _x Pt_1–x it is shown that scalar relativistic calculations, which neglect the influence of spin-orbit coupling, seem to be sufficient to account for relativistic effects in many cases. To account properly for the symmetry-breaking caused by spin-orbit coupling, which is reflected by many hyperfine interaction properties, a fully relativistic approach is demanded. The corresponding formalism in the framework of the KKR-GF (Korringa-Kohn-Rostoker-Green's function) method of band structure calculation for magnetic solids is outlined. As applications results for the hyperfine fields of pure transition metals andalloys are presented.     

Effects of nitrogen and vanadium on the57Fe hyperfine field of RFe12−x V x N y (R=Y,Nd)

Magnetization and⁵⁷Fe Mössbauer measurements were carried out on RFe_12–x V _x N _y compounds (R=Y and Nd,x=1.7 and 2.2) and the effects of nitrogen and vanadium atoms on the⁵⁷Fe hyperfine fields at the different iron crystallographic sites were investigated. The hyperfine field decreases with increasing number of vanadium neighbour atoms at all the iron sites. The hyperfine field is strongly enhanced in the nitrogen composition withy>1 where the compound tends to transform into an amorphous-like solid. The iron moment deduced from the hyperfine field increases more upon nitrogenation for the 8i-site than for the other sites, and exceeds the moment of bcc iron.     

Generalized q-Hermite Polynomials

We consider two operators A and A ⁺ in a Hilbert space of functions on the exponential lattice , where 0<q<1. The operators are formal adjoints of each other and depend on a real parameter . We show how these operators lead to an essentially unique symmetric ground state ψ₀ and that A and A ⁺ are ladder operators for the sequence . The sequence (ψ _n /ψ₀) is shown to be a family of orthogonal polynomials, which we identify as symmetrized q-Laguerre polynomials. We obtain in this way a new proof of the orthogonality for these polynomials. When γ=0 the polynomials are the discrete q-Hermite polynomials of type II, studied in several papers on q-quantum mechanics. Received: 6 December 1999 / Accepted: 21 May 2001     

Hyperfine patterns of infrared absorption lines of Ho3+ C4v centres in CaF2

Hyperfine structure is observed on several infrared transitions to the ⁵I₇ and ⁵I₆ multiplets of the Ho³⁺ C_4v centre in CaF₂. Particularly complex and detailed hyperfine structures are observed for transitions to the Y₃ level of the ⁵I₇ multiplet, which include the appearance of ΔI_z ≠ 0 transitions. The hyperfine lines of this level are satisfactorily accounted for by strong mixing of close-lying levels of this multiplet by the perpendicular hyperfine interaction, which leads to relaxation of the ΔI_z = 0 selection rule and a redistribution of the hyperfine intensities over many transitions. An excellent correspondence is found between the measured and simulated spectra.     

Electron Paramagnetic Resonance,Optical Spectra and DC Conductivity Studies of Vanadyl Doped Bi2O3 · BaO · B2O3 Glasses

Glasses with composition xBi₂O₃ ·(0.30 - x)BaO · 0.70B₂O₃ have been prepared in the range (0.00 ≤ x ≤ 0.15) containing 2.0 mol% of V₂O₅. Electron paramagnetic resonance (EPR), optical transmission and absorption spectra and DC conductivity of these glasses have been studied. The spin Hamiltonian parameters (SHP) of VO²⁺ ions, dipolar hyperfine coupling parameter P, Fermi contact interaction parameter K, and molecular orbital coefficients (α² and γ²) have been calculated. The SHP arc related with the theoretical optical basicity. A_th. The position of the absorption edge and the values of the optical band gap have also been reported. The effect of addition of Bi₂O₃ on the DC conductivity has also been studied.     

Concerning the shift of nonlinear optical resonances in a magnetic field

The shift of components of the magnetic hyperfine structure (MHS) of a vibrational-rotational molecular transition in a weak magnetic field is explored. The numerical data are given for the methane transition at λ=3.39 μm [theF ₂ ⁽²⁾ component of theP(7) line of thev ₃ band]. The shift of the line contour due to the magnetic field is found when the MHS components overlap.     

Study of the amorphous Fe100−x B x and (Fe70Co30)100−x B x powder prepared by borohydride reduction

The amorphous fine particles of Fe_100−x B _x (20.7≤x≤36.5) and (Fe₇₀Co₃₀)_100−x B _x (26.9≤x≤40.2) were prepared by borohydride reduction. The amorphous state of the samples was identified with both X-ray and electron diffraction measurements. With increasing boron content, the average hyperfine magnetic fields decrease. Comparing the hyperfine parameters of the glassy powder with those of the ribbons having the same compositions, the average hyperfine fields and the isomer shifts are different. The differences may be due to the amorphous polymorphism which is produced by the different preparation methods. Project is partly supported by the National Natural Science Foundation of China.