Axial exchange currents and nucleon spin

We calculate the axial couplings g_A⁸(0) and g_A⁰(0) related to the spin of the nucleon in a constituent quark model. In addition to the standard one-body axial currents, the model includes two-body axial exchange currents. The latter are necessary to satisfy the Partial Conservation of Axial Current (PCAC) condition. For both axial couplings we find significant corrections to the standard quark model prediction. Exchange currents reduce the valence quark contribution to the nucleon spin and afford an interpretation of the missing nucleon spin as orbital angular momentum carried by nonvalence quark degrees of freedom.     

EPR and optical-absorption studies of Cu2+-doped Zn(NH2(CH2)3NHOH)2Ni(CN)4 single crystals

Electron paramagnetic resonance of Cu²⁺-doped catena-trans-bis(N-(2-hydroxyethyl)-ethylenediamine) zinc(II)-tetra-μ-cyanonicelate(II) [Zn(NH₂(CH₂)₃NHOH)₂Ni(CN)₄] single crystals and powder are examined at room temperature. The spectra show the substitution of the Zn²⁺ ion with the Cu²⁺ ion. The crystal field around the Cu²⁺ ion is nearly axial. There is a single paramagnetic site withg _xx=2.073,g _yy=2.060,g _zz=2.248,A _xx=40.5 G,A _yy=50.8 G,A _zz=172.0 G. The ground-state wave function is an admixture of d _x ²−y ² and d _z ² states. The optical-absorption studies show two bands at 320 nm (31250 cm⁻¹) and 614 nm (16286 cm⁻¹) which confirm the axial symmetry. The crystal field parameters and the wave function are determined.     

Electronic absorption spectrum of Ni2+ in lithium potassium sulphate single crystal

Single crystals of nickel-doped lithium potassium sulphate were grown by slow evaporation method at room temperature. From the nature and position of the bands observed, a successful interpretation of all the bands could be made assumingO _h symmetry for the Ni²⁺ ion in the crystal. The bands have been assigned transitions from the ground³A_2g(F) state to the excited³T_2g(F),¹E_g(D),³T_1g(F),¹T_2g(D) and³T_1g(P) states. The crystal field parameters derived areDq=910cm^–1,B=890cm^–1 andC=3560cm^–1.The authors wish to express their thanks to Prof. K. Sreerama Murthy for his constant encouragement throughout this investigation. The authors are also thankful to Prof. Mihir Chowdhury, Indian Association for the cultivation of Science, Calcutta for giving permission to take the spectra.     

Spin-Hamiltonian Parameters and Defect Structure of the Copper (2+) Center in Lithium Borate

The spin-Hamiltonian parameters (the anisotropic g factors g _|| and g _⊥ and the hyperfine structure constants A _|| and A _⊥) for the impurity Cu²⁺ in Li₂B₄O₇ are theoretically investigated using the high-order perturbation formulas of these parameters for a 3d ⁹ ion in tetragonally elongated octahedra. In the calculation formulas, the tetragonal field parameters D_s and D_t are determined from the superposition model, by considering the relative axial elongation of the oxygen octahedron around Cu²⁺ due to the Jahn-Teller effect. Based on the calculations, the relative axial elongation of about 0.21 Å for the tetragonal Cu²⁺ center was found.     

Electronic pair excitations of Mn2+ and Ni2+ in perovskite fluorides: involvement of the 3 T 1g a state of Ni2+

Crystals of KZnF₃ and KMgF₃ doped with Mn²⁺ and Ni²⁺ were used to study the spectroscopic properties of Mn²⁺-F^--Ni²⁺ pairs. Pair transitions to the doubly excited states ⁴ E_g ^a , ⁴ A _1g (Mn)³ T _1g ^a (Ni) and ⁴ E_g ^b (Mn)³ T _1g ^a (Ni) were observed. The participation of the spin-allowed ³ A _2g →³ T _1g ^a excitation on Ni²⁺ in the pair transition is explained by spin-orbit mixing between ³ T _1g ^a and ¹ E_g . The prominent electronic origins are assigned to the double spin-flip transitions ⁶ A _1g (Mn)³ A _2g (Ni) →⁴ E_gu(Mn)³ T _1g ^a (Γ₃)v(Ni) and ⁴ A _1g (Mn)³ T _1g ^a (Γ₃)v(Ni). The former lie at lower energy and are more intense than the corresponding ⁶ A _1g (Mn)³ A _2g (Ni) →⁴ E_gv(Mn)³ T _1g ^a (Γ₃)u(Ni) transitions involving two orbital jumps. The well-resolved vibronic structure is composed of three basic vibrations of ～ 150 cm^-1, ～ 294 cm^-1 and ～ 508 cm^-1 in the KZnF₃ host.     

Optical absorption spectrum of Ni2+ ions doped in sodium potassium sulphate single crystal

Single crystals of nickel-doped sodium potassium sulphate were grown by slow evaporation method at room temperature. From the nature and position of the bands observed, a successful interpretation of all the observed bands could be made assuming the octahedral symmetry for the Ni^{2 +} ion in the crystal. The bands have been ascribed to transitions from the ground³A_2g(F) state to the excited³T_2g(F),¹E_g(D),³T_1g(F),¹T_2g(D) and³T_1g(P) states. The experimental and calculated energies are in good agreement. The crystal field parameters derived areDq= =880 cm^–1,B= 900cm^–1 andC=3600 cm^–1.One of the authors, Sujatha John expresses her thanks to the Secretary and the Principal, R. B. V. R. Reddy College, Hyderabad for according her permission to pursue the M. Phil. course.     

Vibrational spectrum of perfluoroethane

We have obtained IR absorption spectra of a C₂F₆ gas and a C₂F₆ cryosolution in Xe (T = 163 K) in the fundamental and overtone ranges. We have interpreted 28 bands of ¹²C¹²CF₆ and three bands of ¹³C¹²CF₆. In the spectral ranges that correspond to vibrations that are combinations with ν₁, ν₇, and ν₅, we observe multiplets, which we attribute to interactions of the type of Fermi resonances between the states ν₁(A _1g ) ∼ ν₆(A _1g ), ν₇(E _g ) ∼ ν₆ + ν₁₁(E _g ) ∼ 2ν₈(E _g ), ν₅(A _2u ) ∼ ν₈ + ν ₁₁(A _2u ). We reveal an anomalous intensity distribution in the spectrum of an asymmetric isotopologue. For the basic and isotopic configurations of perfluoroethane, we calculate the coefficients of shapes of vibrations and the intensities of absorption bands. We reveal that the behavior of the groups ¹²CF₃ and ¹³CF₃ is indifferent to the excitation of doubly degenerate stretching vibrations ν₇(E _g ) and ν₁₀(Eu).     

Investigation of the local structure of Cu2+ ions doped in alkali lead tetraborate glasses by their electron paramagnetic resonance and optical spectra

The local structure of the Cu²⁺ centers in alkali lead tetraborate glasses was theoretically studied based on the optical spectra data and high-order perturbation formulas of the spin Hamiltonian parameters (electron paramagnetic resonance g factors g_∥, g_⊥ and hyperfine structure constants A_∥, A_⊥) for a 3d⁹ ion in a tetragonally elongated octahedron. In these formulas, the relative axial elongation of the ligand O^2? octahedron around the Cu²⁺ due to the Jahn–Teller effect is taken into account by considering the contributions to the g factors from the tetragonal distortion which is characterized by the tetragonal crystal-field parameters Ds and Dt. From the calculations, the ligand O^2? octahedral around Cu²⁺ is determined to suffer about 19.2% relative elongation along the C₄ axis of the alkali lead tetraborate glass system, and a negative sign for A_∥ and a positive sign for A_⊥ for these Cu²⁺ centers are suggested in the discussion.     

High resolution MCD spectroscopy of transition metal ions in fluoride crystals

Measurements of the MCD spectra of Ni²⁺ in KMgF₃ and KZnF₃ have confirmed and extended previous assignments of spin-orbit structure based on similarities of vibrational patterns. The measurements also reveal the presence of a ¹ A _1g (¹ G) state which interacts strongly with the ³ T _1g ^b (³ P) state. The MCD spectra of the tetragonal crystals K₃Ni₂F₇ and K₂NiF₄ have been measured for the transitions ³ A _2g →³ T _1g ^a , ¹ E_g . The spectrum of K₃Ni₂F₇ is characterized by the appearance of electric dipole zero phonon lines, consistent with the C _4v site symmetry of the Ni²⁺ in the paramagnetic phase. An analysis of the MCD spectrum allows a positive assignment of six of the seven states (from ³ T _1g ^a and ¹ E_g ) to which transitions are allowed by symmetry in the axial spectrum. A complete tetragonal crystal-field analysis has been made which shows that the distortion is an axial compression of the fluoride octahedron. The absorption spectrum of K₂NiF₄ shows much less vibrational structure, but the MCD spectrum allows a definitive assignment of six states (from ³ T _1g ^a and ¹ E_g ) through a _2u vibrations in the usual vibronic mechanism. False origins based on e_u phonons have not been identified. The tetragonal field is larger than for K₃Ni₂F₇ and corresponds to an axial compression, in agreement with the known crystal structure.     

Magnetic circular dichroism of the first spin-forbidden transition in 2[Cr(en)3Cl3] . KCl . 6H2O

The longitudinal Zeeman effect of the ² E ←⁴ A ₂ transition of the Cr⁺³ ion in single crystals of 2[Cr(en)₃Cl₃] . KCl . 6H₂O has been measured using circularly polarized light as a function of magnetic field strength between 0 and 160 kgauss at ～80 K. The g factor for the ground state was determined to be g _‖(⁴ A ₂) = 2·01±0·05, in agreement with the E.S.R.-determined value. The ratio between the excited state g values and that of the ground state was determined; using the value g _‖(⁴ A ₂) = 1·99, the g factors g _‖(2) = 2·61±0·04 and g _‖() = 1·47±0·04 were obtained.     

Single-Crystal EPR Identification of a Low Hyperfine Value and Interstitial Position of Copper Impurity in Diaquabis[malonato(1-)-κ2O,O′] Zinc(II)

Electron paramagnetic resonance studies have been carried out at 300 K on the Cu(II)-doped [Zn(C₃H₂O₄)₂(H₂O)₂] system in single-crystal and powder forms in order to rationalize the low parallel ⁶³Cu hyperfine value. Angular variation of the hyperfine resonances in the three orthogonal planes shows the presence of only one magnetic site with g and A values equal to g _zz = 2.455, g _yy = 2.121, g _xx = 2.105 and A _zz = 160.9 · 10⁻⁴ cm⁻¹, A _yy = 12.5 · 10⁻⁴ cm⁻¹, A _xx = 7.35 · 10⁻⁴ cm⁻¹. The crystal structure of the host lattice is isostructural with the corresponding cobalt complex and contains two molecules per unit cell. The low magnitude of A _zz value for the complex is rationalized in terms of an admixture of the ground state with the excited state and delocalization of the unpaired spin density onto the ligands. In addition, the highest hyperfine value obtained from the single-crystal data (160.9 · 10⁻⁴ cm⁻¹) is considerably larger than that obtained from the powder spectrum (138 · 10⁻⁴ cm⁻¹). Authors' address: P. Sambasiva Rao, Department of Chemistry, Pondicherry University, Pondicherry 605014, India     

Radiative properties of α-ZnAl2S4:V spinel type single crystals

The absorption and luminescent properties of α-ZnAI₂S₄:V spinel type crystals in the temperature range 10-300 K are investigated. The spectra are assigned to the electronic transitions of trivalent vanadium ions located in octahedral sites. It is shown that at low temperatures the three main components of the revealed IR luminescence spectra are caused by the ¹A_1g(¹G)→¹E_g(¹D), ¹T_2g(¹D), ³T_2g(³F)→³T_1g(³F), and ¹E_g(¹D)→³T_1g(³F) transitions. The observed dependencies of the emission components intensities on temperature are explained assuming that there is a phonon assisted tunnelling between ³T_2g(³F) and ¹E_g(¹D) states. On temperature rise, the ³T_2g(³F)→³T_1g(³F) vibronic transitions suppress other emission channels, which leads to the enhancement of the integral luminescence intensity and to the broadening of the spectrum centred at λ=1.4 μm.     

Coexistence of one-electron- and monoprotonated two-electron-reduced species of the K5[PMo2VW9O40] · 24H2O heteropolyoxometalate identified by EPR

The simulation of the room-temperature experimental electron paramagnetic resonance spectrum of K₅[PMo₂VW₉O₄₀] · 24 H₂O heteropolyoxometalate indicates the presence of equal amounts of a one-electron-reduced species (g _∥ = 1.922,g _⊥ = 1.972,A _∥ = 181 G,A _⊥ = 63 G) and a monoprotonated two-electron-reduced species with mixed-valence V^IV, Mo^V and Mo^VI ions (g _iso = 1.972, ΔB _iso(p-p) = 450 G). Two unprotonated one-electron-reduced isomers are identified in dimethylsulfoxide-H₂O solution of the sample atT = 100 K (g _∥¹ = 1.929,g _⊥¹ = 1.990,A _∥¹ = 179 G,A _⊥¹ = 65 G andg _∥² = 1.918,g _⊥² = 2.000,A _∥² = 187 G,A _⊥² = 80 G, respectively). The values of the in-plane π(V−O) bond π₂² coefficient for the one-electron-reduced species (0.87 at room temperature and 0.83 and 0.74 for the species in frozen solution) suggests the delocalization of the vanadium unpaired electron towards the molybdenum ions via O_b atoms.     

Rotational analysis of the 0–9, 0–10 and 0–11 bands of theA 2II u -X 2II g band system of (16O18O)+

High-resolution spectra of the 0–9, 0–10 and 0–11 bands of theA ²II _u —X ²II _g system of (¹⁶O¹⁸O)⁺ ion have been studied for their rotational structure. This study enables a direct determination of the Λ-doubling parameters of theA ²II _u andX ²II _g states. The model of ‘pure precession’ explains, though not entirely, the Λ-doubling of theX ²II _a state as arising out of its interaction with theB ² Σ _g ⁻ state. The Λ-doubling in theA ²II _u state was found insignificant.     

Classical and quantum duality in Jordanian quantizations

We prove that for the first order coboundary deformation of a Lie bialgebra (g, g₁ ^*) (g, g₁ ^* + g₂ ^*) one can always get the quantized Lie bialgebra A(g, g₂ ^*) as a limit of the sequence of quantizations of the type A(g, g₁ ^*).     

Electromagnetic form factors of nucleons in a relativistic square-root potential model of independent quarks

The nucleon electromagnetic form factorsG _E ^P (q²),G _M ^P (q²) and the axial-vector form factor G_A(q²) are studied in a relativistic model of independent quarks confined by an equally mixed scalar-vector square root potentialV _q(r)=1/2(1+γ ⁰)(ar ^1/2+ν ₀) taking into account the appropriate centre-of-mass corrections. The respective root-mean-square radii associated withG _E ^P (q²) and G _A (q²) come out as [〈r ²〉 _E ^P ]^1/2=0.86 fm and 〈r _A ² 〉^1/2=0.88 fm. Restoration of chiral symmetry in this model is discussed to derive the pion-nucleon form factorG _πNN(q²) and consequently the pion-nucleon coupling constant is obtained asg _πNN(q²)=12.81 as compared tog _πNN(q²)_exp⋍13.     

The absorption and magnetic circular dichroism of spectra of Cs2NaPrCl6

The room temperature absorption and magnetic circular dichroism spectra and the absorption spectrum at liquid helium (liquid He) temperature have been measured for Cs₂NaPrCl₆. At room temperature the crystal is cubic and the Pr³⁺ sites have O _h symmetry. All terms above 15 000 cm^-1, except ¹S₀, have been assigned and a previous assignment in PrCl₆ ^3- has been shown to be incorrect. The transition at 20 631 cm^-1 is assigned to ³H₄(A _1g ) →³P₁(T _1g ), in contradiction to previous assignments of Pr³⁺ spectra in other systems. A rich vibrational structure was observed in every transition. Vibrations have been assigned using the site group approximation and there is substantial agreement with the vibrational assignments in Cs₂NaEuCl₆. A crystal phase transition takes place between room temperature and liquid nitrogen temperature and the O _h forbidden transitions, A _1g →E_g and T _2g , are observed. At lower temperatures many additional lines are observed but it is unclear presently whether they are due to lower symmetry or a breakdown of the site group approximation.     

EPR and Optical Absorption Studies of Cu2+-Doped Bis(l-Asparaginato)Mg(II)

The electron paramagnetic resonance study of Cu²⁺-doped bis(l-asparaginato)Mg(II) is performed at room temperature. Two magnetically non-equivalent sites for Cu²⁺ are observed. The spin-Hamiltonian parameters evaluated by fitting spectra to the crystalline field of rhombic symmetry are as follows: g _x  = 2.0420 ± 0.0002, g _y  = 2.0808 ± 0.0002, g _z  = 2.3600 ± 0.0002, A _x  = (99 ± 2) × 10⁻⁴ cm⁻¹, A _y  = (108 ± 2) × 10⁻⁴ cm⁻¹, A _z  = (140 ± 2) × 10⁻⁴ cm⁻¹. The ground state wave function of Cu²⁺ is also determined. The g-anisotropy is estimated and compared with the experimental value. Further, with the help of optical study the nature of bonding of a metal ion with different ligands in the complex is discussed.     

EPR of Cu2+-doped tris-sarcosine calcium chloride

The EPR study of the Cu²⁺-doped tris-sarcosine calcium chloride (TSCC) at room temperature is reported. Two magnetically inequivalent sites for Cu²⁺ were observed. The rhombic spin Hamiltonian parameters are determined by fitting the EPR spectra for two centres: Cu²⁺(I) g₁ = 2.0276, g₂ = 2.0517, g₃ = 2.4019, A₁ = 82, A₂ = 128, A₃ = 152 [G] and Cu²⁺(II) g₁ = 2.0231, g₂ = 2.0368, g₃ = 2.5294, A₁ = 76, A₂ = 92, A₃ = 156 [G]. The ground state wave function is also determined. The g-anisotropy is evaluated and compared with the experimental value. Further, the optical study of the crystal at room temperature is carried out and the nature of bonding in the complex is discussed.     

Electron-vibration effects in Cs2SiF6 : Mn4+

We report a study of the ⁴ A _2g →² T _1g absorption band of Mn⁴⁺ in Cs₂SiF₆. The band shows several lines or groups of lines associated with transitions from the ⁴ A _2g ground state to the spin-orbit components (² T _1g )Γ₈ and (² T _1g )Γ₆ coupled to the three odd-parity vibrations v ₆(t _2u ), v ₄(t _1u ) and v ₃(t _1u ). The absorptions associated with the (² T _1g )Γ₈ electronic state have structure whereas those associated with the (² T _1g )Γ₆ do not. It is shown that the structure is a consequence of splitting of the Γ₈ × v vibronic multiplets by electron-vibration interaction. The intensity of the ⁴ A _2g →(² T _1g )Γ _i + v_j vibronic transitions are expressed in terms of a small number of parameters; two parameters for v(t _1u ) modes and three for v(t _2u ) modes. Plausible but not good fits to the low temperature Zeeman data and vibronic splitting patterns are obtained. The excitation spectrum of the Cs₂SiF₆ : Mn⁴⁺ in the region of the ⁴ A _2g →² E_g and ⁴ A _2g →² T _1g is recorded using a c.w. dye laser. This reveals numerous weaker lines involving combinational modes and even-parity modes v₅ (t _2g ), v ₂(e_g ) and v ₁(a _1g ). Several interesting electron-vibrational effects are observed. These are illustrated and discussed qualitatively.