ESR Spin Trapping of the Reaction Between Urate and Peroxynitrite: the Hydrogen Adduct

Under basic conditions, the hydrogen adduct of the spin traps N-t-butyl-phenylnitrone (PBN) and α-(4-pyridyl-1-oxide)-N-t-butylnitrone (POBN) is formed as a major product in the reaction between the urate anion or dianion and peroxynitrite. It shows a characteristic nine-line spectrum with an intensity pattern of (1:2:1:1:2:1:1:2:1) and hyperfine splitting constants of a(H) = 10.68 G (two magnetically equivalent protons) and a(N) = 16.64 G. The hydrogen adduct of PBN also forms in the absence of urate. In this case, its formation is proposed to follow the non-traditional “inverted spin trapping” mechanism, followed by electron transfer between spin traps and the PBN–OH (or POBN–OH) adduct or one of its decomposition products. The H adduct formation is amplified when uric acid and peroxynitrite are present. Different yields of H adducts obtained from various spin traps supported the inverted spin trapping mechanism and can be rationalized by the relative redox potential of the spin traps.     

Quantum tetrahedra and simplicial spin networks

A new link between tetrahedra and the group SU(2) is pointed out: by associating to each face of a tetrahedron an irreducible unitary SU(2) representation and by imposing that the faces close, the concept of the quantum tetrahedron is seen to emerge. The Hilbert space of the quantum tetrahedron is introduced and it is shown that, due to an uncertainty relation, the “geometry of the tetrahedron” exists only in the sense of “mean geometry”.A kinematical model of quantum gauge theory is also proposed, which shares the advantages of the loop representation approach in handling in a simple way gauge- and diff-invariances at a quantum level, but is completely combinatorial. The concept of quantum tetrahedron finds a natural application in this model, giving a possible interpretation of SU(2) spin networks in terms of geometrical objects.     

Classical mechanics on the GL(n, ℝ) group and Euler-Calogero-Sutherland model

Relations between free motion on the GL ⁺(n, ?) group manifold and the dynamics of an n-particle system with spin degrees of freedom on a line interacting with a pairwise 1/sinh² x “potential” (Euler-Calogero-Sutherland model) are discussed within a Hamiltonian reduction. Two kinds of reductions of the degrees of freedom are considered: that which is due to continuous invariance and that which is due to discrete symmetry. It is shown that, upon projecting onto the corresponding invariant manifolds, the resulting Hamiltonian system represents the Euler-Calogero-Sutherland model in both cases.     

Reformulation of general relativity as a gauge theory

The starting point is a spinor affine space-time. At each point, two-component spinors and a basis in spinor space, called “spin frame,” are introduced. Spinor affine connections are assumed to exist, but their values need not be known. A metric tensor is not introduced. Global and local gauge transformations of spin frames are defined with GL(2) as the gauge group. Gauge potentials B_μ are introduced and corresponding fields F_μν are defined in analogy with the Yang-Mills case. Gravitational field equations are derived from an action principle. Incases of physical interest SL(2, C) is taken as the gauge group, instead of GL(2). In the special case of metric space-times the theory is identical with general relativity in the Newman-Penrose formalism. Linear combinations of B_μ are generalized spin coefficients, and linear combinations of F_μν are generalized Weyl and Ricci tensors and Ricci scalar. The present approach is compared with other formulations of gravitation as a gauge field.     

X-ray photoelectron spectra of iron complexes: Correlation of iron 2p satellite intensity with complex spin state

Metal and ligand core-level spectra have been obtained for 36 iron complexes which possess a variety of ligands including carbonyl, nitrosyl, triphenylphosphine,o-phenylenebis(dimethylarsine), halides and pseudohalides. Formal metal oxidation states range from ? 1 to + 3, and complex spin states represented in the series include 0, $\text{1}\text{2}$, $\text{3}\text{2}$, 2 and $\text{5}\text{2}$. A clear correlation between complex spin state and satellite intensity in the Fe 2p spectra is found. The satellite intensities observed experimentally are in approximate quantitative accord with those predicted by a “spin flipping” model. Although the present analysis does not provide a definitive choice between the “sudden approximation” and “spin flipping” models, the agreement between experimental satellite intensities and the intensities predicted by the “spin flipping” model suggests that such a mechanism can be important in the satellite process.     

A molecular cluster model of the Vo. center in paratellurite

A RHF-SCF electronic structure calculation has been performed by means of the MELD program package for a cluster model of the V_o^.-center, a basic radiation-induced defect in paratellurite identified recently by ESR as an oxygen vacancy defect with a net positive charge. A “perfect” Te₂O₇H₆ cluster has been constructed with an effective core potential and an STO-3G valence basis set complemented by a single Gaussian d-function on Te. The charge distribution inside this cluster has been optimized by adjusting positions and nuclear charges of the peripheral “hydrogens”. A Mulliken analysis of a Te₂O₆H₆ defect cluster derived from the perfect one by removing an O⁻ ion and relaxing both Te's showed that the unpaired spin is primarily concentrated on the Te nearest to the oxygen vacancy with appreciable spin densities on nearby atoms and a substantially modified distribution of the surplus charge. The open-shell wave function has also been employed to derive hyperfine constants, taking into account relativistic corrections in independently calculated values of |;ψ_5s(0)|² and 〈r⁻³〉_5p for the Te atom, but neglecting core polarization. The calculated spin populations and hyperfine parameters account for all major features of the ESR spectra.     

Photoelectron spectroscopic assignment of symmetry to the ground state and first excited state of the 1,4-cyclohexadiene radical cation

The empirical correlation of the photoelectron spectra of 1,4-cyclohexadiene (molecule 4), 1, 4, 5, 8-tetrahydronaphthalene (molecule 5), 1, 4, 5, 6, 9, 1 0-hexahydroanthracene (molecule 6), and 1, 4, 5, 6, 7, 10, 11, 12-octahydronaphthacene (molecules 6) proves that the electronic ground state of these molecules is ²B_1u, assuming that they have D_2h symmetry. In particular this confirms previous predictions for 1,4-cyclohexadiene (molecule 4), for which the “inverted” orbital sequence 2b_1u(π) above lb_3g(π) had been proposed under the assumption that hyperconjugative “through-bond” interaction dominates the “through-space” interaction of the two semi-localized π-orbitals.     

Topological bootstrap theory of hadrons

A topological framework is constructed for anS-matrix bootstrap theory of particles. Each component of anS-matrix topological expansion is associated with a pair of intersecting “quantum” and “classical” surfaces whose complexity exhibits an entropy property. The bounded classical surface embeds graphs that carry the direct observables — energymomentum, spin and electric charge. The closed quantum surface carries a triangulation whose orientations represent internal quantum numbers — which turn out to be baryon number, lepton number and flavor. A form of “color” automatically appears. All strong-interaction components of the expansion are generated through “Landau connected sums” from “zeroentropy” surface pairs — which are self generating. Elementary particles correspond to triangulated areas on the quantum surface; consistency at zero entropy determines allowed hadrondisks on quantum spheres together with the associated quantum numbers. Elementary topological hadrons turn out to include mesons, baryons and baryoniums, with quarks appearing as “peripheral triangles” (along the perimenters of hadron disks) whose attachments correspond to a total of 8 flavors as well as spin. Individual quarks do not carry momentum and cannot be hadrons; quark confinement is automatic. Also appearing within hadron disks are “core triangles” that carry baryon number and electric charge but no flavor or spin. Hadron disks have quantum numbers that accord with the lowestmass physically-observed mesons and baryons. The relation of topological theory to QCD is discussed.     

Magnetic moments of composite fermions

There have been a considerable number of papers proposing composite models for leptons and quarks. Recently, Glück and Lipkin have stated that reproducing the observed magnetic moments of these fermions presents a serious difficulty for these composite models. We show for a renormalizable theory that, in contrast to Glück's and Lipkin's nonrelativistic arguments, a deeply bound system (with heavy constituent particle masses m_c) of (total) spin $\text{1}\text{2}$, charge e and mass m has the magnetic moment $\text{(e/2m) [1 +}\text{“usual” (QED + QCD + weak) corrections +O}\text{(m/m}{}_{\mathrm{<mtext>c</mtext>}}\text{)}\text{“new” bindng corrections]}$. Although there remains the considerable dynamical problem of obtaining “light” bound fermions from heavy constituents, there is no separate, additional magnetic moment difficulty.     

Orientational dynamics of superfluid 3He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies $\text{ω ?}\text{Δ(T)}\text{h}\text{?}$ irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ ? 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω ～ Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

The quantum inverse scattering method for Hubbard-like models

This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of the classical “covering” Hubbard model within the algebraic Bethe ansatz framework. The fundamental commutation rules exhibit a hidden 6-vertex symmetry which plays a crucial role in the whole algebraic construction. Next we apply this formalism to study the SU(2) highest weights properties of the eigenvectors and the solution of a related coupled spin model with twisted boundary conditions. The machinery developed in this paper is applicable to many other models, and as an example we present the algebraic solution of the Bariev XY coupled model.     

Spin forbidden transitions in the Ka = 0 subband of NO2 in the λ = 592.5 nm region

In a high resolution laser excitation spectrum of NO₂, lines were recorded which do not follow the selection rule ΔN = ΔJ = ΔF of “spin allowed” transitions. Line positions and intensities of these “spin forbidden” lines were investigated for all rotational lines up to N″ = 12 of the K_a = 0 subband around λ = 592.5 nm. While the observed line intensities of “spin allowed” transitions can be well described by the J-coupling scheme, neither the J- nor the G-coupling scheme sufficiently describes the “spin forbidden” transitions. The observations can be fitted satisfactorily by perturbation theory, in which the Fermi interaction in ²A₁ is treated as the perturber. This looks similar to a superposition of J and G scheme in the ²A₁ ground state.     

Analyticity for one-dimensional systems with long-range superstable interactions

We consider unbounded spin systems and classical continuous particle systems in one dimension. We assume that the interaction is described by a superstable two-body potential with a decay at large distances at least asr ^?2(lnr)^?(2+ε), ε > 0. We prove the analyticity of the free energy and of the correlations as functions of the interaction parameters. This is done by using a “renormalization group technique” to transform the original model into another, physically equivalent, model which is in the high-temperature (small-coupling) region.     

Baxter’s Q-operators and Operatorial Bäcklund Flow for Quantum (Super)-Spin Chains

We propose the operatorial Baxter’s TQ-relations in a general form of the operatorial Bäcklund flow describing the nesting process for the inhomogeneous rational gl(K|M) quantum (super)spin chains with twisted periodic boundary conditions. The full set of Q-operators and T-operators on all levels of nesting is explicitly defined. The results are based on a generalization of the identities among the group characters and their group co-derivatives with respect to the twist matrix, found by one of the authors Kazakov and Vieira (JHEP 0810:050, 2008). Our formalism, based on this new “master” identity, allows a systematic and rather straightforward derivation of the whole set of nested Bethe ansatz equations for the spectrum of quantum integrable spin chains, starting from the R-matrix.     

Supercompositeness from superstrings

String Unified Models based on the k = 1 level of the Kac-Moody Algebra, predict the existence of “exotic” new states which carry fractional electric charges. We analyse the possibility of considering these “exotics” as preonic matter which can be used to form the families and the gauge group breaking higgs scalars. It is proposed that such a formation may occur provided that these states transform non-trivially under a non-Abelian gauge group with a relatively large rank in order to confine them at a sufficiently large scale. Such a situation is natural in string derived unified models, since the role of the confining group can be played by (part of) the Hidden symmetry. As an example, we present a string derived toy model based on the SU(4) × SU(2) _L × SU(2) _R Pati-Salam gauge group.     

Nuclear inelastic scattering study of a dinuclear iron(II) complex showing a direct spin transition

The results of the nuclear inelastic scattering (NIS)/nuclear resonance vibrational spectroscopy (NRVS) for the powder spectra of dimeric [Fe ₂L₅(NCS) ₄] (L = N-salicylidene-4-amino-1,2,4-triazole) complex are presented. This system is spin crossover (SCO) material tagged with a fluorophore that can sense or “feel” the SCO signal ripping through the molecular network and thereby providing an opportunity to register the SCO transition. The spectra have been measured for the low-spin and high-spin phases of the complex. The high-spin isomer reveals one broad band above 200 cm ^?1, while the low-spin one displays two intense bands in the range from 390 to 430 cm ^?1, accompanied by a number of weaker bands below this area and one at ca. 490 cm ^?1. A normal coordinate analysis based on density functional calculations yields the assignment of the spin marker bands to particular molecular modes. In addition the vibrational contribution to the spin transition has been estimated     

Coherent Exchange Cluster Approach for two-dimensional disordered Heisenberg-spin system

The Coherent Exchange Cluster Approach, developed within two proceeding papers, is applied to dilute quasi two-dimensional Heisenberg spin-systems, consisting of one magnetic and one nonmagnetic alloying component. The level density of spin wave excitations is discussed for concentrations of the magnetic component, which are larger than the critical value, where all excitations become localized. The propagation of the excitations through the disordered system is described by an effective Heisenberg-Hamiltonian with a complex and energy-dependent exchange integral \(\tilde J\) (E). This quantity is determined by the postulate, that the most important matrix elements of the scatteringT-matrix should vanish after averaging over the possible configurations of a scattering cluster, consisting of a central lattice site and its four nearest neighbours. Numerical results are obtained both for the “dilute bond” and “site” problems, respectively; in both cases, the results agree rather well with existing computer simulations for 30 × 30 spin arrays. For the “site” problem, it is necessary to introduce a coherent single ion anisotropy field in addition to the coherent exchange integral: Results in agreement with the analyticity requirements are obtained by a careful choice of the additional selfconsistency equation.