Contribution Of Orbital Angular Momentum Research Articles

Linear and Nonlinear Two-Coordinate Vanadium Complexes: Synthesis, Characterization, and Magnetic Properties of V(II) Amides

The synthesis and characterization of the first stable two-coordinate vanadium complexes are described. The vanadium(II) primary amido derivative V{N(H)Ar(iPr6)}2 [Ar(iPr6) = C6H3-2,6-(C6H2-2,4,6-iPr3)2] (1) was synthesized via the reaction of LiN(H)Ar(iPr6) with the V(III) complex VCl3·2NMe3 or the V(II) salt [V2Cl3(THF)6](+)I(-) in a 2:1 and 4:1 stoichiometry, respectively. Reaction of the less crowded LiN(H)Ar(Me6) with [V2Cl3(THF)6](+)I(-) afforded V{N(H)Ar(Me6)}2 [Ar(Me6) = C6H3-2,6-(C6H2-2,4,6-Me3)2] (2), which has a nonlinear [N-V-N = 123.47(9)°] vanadium coordination. Magnetometry studies showed that V{N(H)Ar(iPr6)}2 and V{N(H)Ar(Me6)}2 have ambient temperature magnetic moments of 3.41 and 2.77 μB, respectively, which are consistent with a high-spin d(3) electron configuration. These values suggest a significant spin orbital angular momentum contribution that leads to a magnetic moment that is lower than their spin-only value of 3.87 μB. DFT calculations showed that the major absorptions in their UV-vis spectra were due to ligand to metal charge transfer transitions. Exposure of the reaction mixture for 2 to dry O2 resulted in the formation of the diamagnetic V(V) oxocluster [V{N(H)Ar(Me6)}2]2(μ-O-Li-O)2 (3).

Magnetic phase transition and relaxation effects in lithium iron phosphate

AbstractWe report the observation of a para‐antiferromagnetic transition at ∼50 K in lithium iron phosphate, LiFePO4 through DC magnetic susceptibility and Mössbauer spectroscopy. The ferrous ion Fe2+ (3d6, 5D) in LiFePO4 exhibits relaxation effects with a relaxation frequency ∼1.076 × 107 s−1 at 300 K. The temperature dependence of the frequency suggests the origin of the relaxation is of the spin–lattice type. The quadrupole splitting at low temperatures indicates that the excited orbital states mix strongly to the orbital doublet ground state via spin–orbit coupling. Modified molecular field model analysis yields a saturation value for hyperfine field Bhf ∼ 125 kOe. The anomaly in susceptibility and Mössbauer parameters below 27 K may be ascribed to a contribution of orbital angular momentum. The high value of the asymmetry parameter η (∼0.8) of the electric field gradient obtained in the antiferromagnetic regime indicates a strongly distorted octahedral oxygen neighborhood for the ferrous sites.

Generalized parton distributions of the photon with helicity flip

We present a calculation of the generalized parton distributions (GPDs) of the photon when the helicity of the initial photon is different from the final photon. We calculate the GPDs using overlaps of photon light-front wave functions (LFWFs) at leading order in electromagnetic coupling α and zeroth order in the strong coupling αs, when the momentum transfer is purely in the transverse direction. These involve a contribution of orbital angular momentum of two units in the LFWFs. We express these GPDs in the impact parameter space.

Proton Spin Structure from Measurable Parton Distributions

We present a systematic study of the proton spin structure in terms of measurable parton distributions. For a transversely polarized proton, we derive a polarization sum rule from the leading generalized parton distributions appearing in hard exclusive processes. For a longitudinally polarized proton, we obtain a helicity decomposition from well-known quark and gluon helicity distributions and orbital angular-momentum contributions. The latter are shown to be related to measurable subleading generalized parton distributions and quantum-phase space Wigner distributions.

Meson-loop contributions in the quark model

We present a review of some recent results obtained in the unquenched quark model for baryons. The effects of sea quarks are taken into account in an explicit form via a QCD-inspired creation mechanism of the quark-antiquark pairs. In this approach, the contribution of the quark-antiquark pairs can be studied for any inital baryon and for any flavor of the qq̄ pairs (uū, dd̄ and ss̄). It is shown that, whereas the inclusion of qq̄ pairs (or meson loops) does not affect the baryon magnetic moments, it immediately leads to an excess of d̄ over ū in the proton and introduces a sizeable contribution of orbital angular momentum to the spin of the proton. The contribution of ss̄ pairs to the magnetic moment and the radius of the proton is found to be small, in agreement with the latest experimental results and recent lattice calculations.

Synthesis, Structural, and Magnetic Characterization of Linear and Bent Geometry Cobalt(II) and Nickel(II) Amido Complexes: Evidence of Very Large Spin–Orbit Coupling Effects in Rigorously Linear Coordinated Co2+

The complexes M(II){N(H)Ar(Pr(i)(6))}(2) (M = Co, 1 or Ni, 2; Ar(Pr(i)(6)) = C(6)H(3)-2,6(C(6)H(2)-2,4,6-Pr(i)(3))(2)), which have rigorously linear, N-M-N = 180°, metal coordination, and M(II){N(H)Ar(Me(6))}(2) (M = Co, 3 or Ni, 4; Ar(Me(6)) = C(6)H(3)-2,6(C(6)H(2)-2,4,6-Me(3))(2)), which have bent, N-Co-N = 144.1(4)°, and N-Ni-N = 154.60(14)°, metal coordination, were synthesized and characterized to study the effects of the metal coordination geometries on their magnetic properties. The magnetometry studies show that the linear cobalt(II) species 1 has a very high ambient temperature moment of about 6.2 μ(B) (cf. spin only value = 3.87 μ(B)) whereas the bent cobalt species 3 had a lower μ(B) value of about 4.7 μ(B). In contrast, both the linear and the bent nickel complexes 2 and 4 have magnetic moments near 3.0 μ(B) at ambient temperatures, which is close to the spin only value of 2.83 μ(B). The studies suggest that in the linear cobalt species 1 there is a very strong enhanced spin orbital coupling which leads to magnetic moments that broach the free ion value of 6.63 μ(B) probably as a result of the relatively weak ligand field and its rigorously linear coordination. For the linear nickel species 2, however, the expected strong first order orbital angular momentum contribution does not occur (cf. free ion value 5.6 μ(B)) possibly because of π bonding effects involving the nitrogen p orbitals and the d(xz) and d(yz) orbitals (whose degeneracy is lifted in the C(2h) local symmetry of the Ni{N(H)C(ipso)}(2) array) which quench the orbital angular momentum.

Spin structure of the nucleon: QCD evolution, lattice results and models

The question how the spin of the nucleon is distributed among its quark and gluon constituents is still a subject of intense investigations. Lattice QCD has progressed to provide information about spin fractions and orbital angular momentum contributions for up- and down-quarks in the proton, at a typical scale \mu^2~4 GeV^2. On the other hand, chiral quark models have traditionally been used for orientation at low momentum scales. In the comparison of such model calculations with experiment or lattice QCD, fixing the model scale and the treatment of scale evolution are essential. In this paper, we present a refined model calculation and a QCD evolution of lattice results up to next-to-next-to-leading order. We compare this approach with the Myhrer-Thomas scenario for resolving the proton spin puzzle.

Spin and flavor content of octet baryons

We discuss the spin and flavor content of the proton in an unquenched quark model. It is shown that the inclusion of hadron loops leads automatically to an excess of d̄ over ū and introduces a sizeable contribution of orbital angular momentum to the spin of the proton. Whereas the flavor asymmetry and the orbital angular momentum are dominated by pion loops, the contribution of the sea quark spins to the proton spin arises almost entirely from (excited) vector meson loops.

The spin structure of the proton from lattice QCD

This proceeding discusses recent achievements in lattice QCD calculations of the longitudinal and transverse spin structure of the nucleon. Starting from the latest lattice results on moments of generalized parton distributions, we focus on the decomposition of the proton spin 1/2 in terms of quark (and gluon) spin and orbital angular momentum contributions. Recent results on the transverse nucleon spin structure obtained from lattice studies of transverse momentum distributions will be discussed and illustrated in the form of spin densities of quarks in the proton. We compare the results with expectations from phenomenological and model studies, and point out the most important systematic uncertainties and remaining challenges in the lattice approach.

Seven-coordinate Mn(II) and Co(II) complexes of the pentadentate ligand 2,6-diacetyl-4-carboxymethyl-pyridine bis(benzoylhydrazone): Synthesis, crystal structure and magnetic properties

The metal complexation properties of a functionalized N3O2 donor ligand H2L2, where H2L2 stands for 2,6-diacetyl-4-carboxymethyl-pyridine bis(benzoylhydrazone), are investigated by structural and spectroscopic (IR, ESI-MS and EPR) characterization of its Mn(II) and Co(II) complexes. The ligand H2L2 is observed to react essentially in the same fashion as its unmodified parent H2L1 producing mixed-ligand [M(H2L2)(Cl2)] complexes (M=MnII (1), CoII (3)) upon treatment with MCl2. Complexes [M(HL2)(H2O)(EtOH)]BPh4 (M=Mn 2, M=Co 4), incorporating the supporting ligand in the partially deprotonated form (HL2)−, are formed by salt elimination of the [M(H2L2)(Cl2)] compounds with NaBPh4. Compounds 2 and 4 are isostructural featuring distorted pentagonal–bipyramidal coordinated MnII and CoII ions, with the H2O and EtOH ligands bound in axial positions. Intermolecular hydrogen bonding interactions of the type M–OH2⋯O–M involving the H2O ligands and the carbonyl functions of the supporting ligand assembles the complexes into dimers. Temperature-dependent magnetic susceptibility measurements (2–300K) show a substantially paramagnetic Curie behavior for the Mn2+ compound (2) influenced by zero-field splitting and significant orbital angular momentum contribution for 4 (high-spin CoII). The exchange coupling across the MnII–OH2⋯O–MnII bridges in 2 was found to be less than 0.1cm−1, suggesting that no significant intradimer exchange coupling occurs via this path.

Lattice QCD Calculations of Hadron Structure: Status and Perspectives

The last years have seen significant advances in hadron structure calculations in lattice QCD. While extrapolations to the physical point and direct comparisons with experiment are still very challenging, lattice calculations provide already very valuable insights into a number of fundamental physics questions related to, e.g., the distribution of charge and momentum inside hadrons and the nucleon spin structure. To illustrate the recent achievements, we present and discuss latest lattice results for a small number of observables related to nucleon form factors and generalized parton distributions. We also present a study of the decomposition of the nucleon spin 1/2 in terms of quark spin and orbital angular momentum contributions. We briefly discuss results and limitations of the relevant chiral fits and extrapolations.

Structure of the nucleon in the unquenched quark model

We discuss the flavor asymmetry of the nucleon sea and the spin content of the proton in an unquenched quark model. It is shown that the inclusion of hadron loops leads automatically to an excess of d̄ over baru and introduces a sizeable contribution of orbital angular momentum to the spin of the proton and the Λ hyperon. Special attention is paid to the symmetries of the unquenched quark model.

Double-helicity dependence of jet properties from dihadrons in longitudinally polarizedp+pcollisions ats=200 GeV

It has been postulated that partonic orbital angular momentum can lead to a significant double-helicity dependence in the net transverse momentum of Drell-Yan dileptons produced in longitudinally polarized p+p collisions. Analogous effects are also expected for dijet production. If confirmed by experiment, this hypothesis, which is based on semiclassical arguments, could lead to a new approach for studying the contributions of orbital angular momentum to the proton spin. We report the first measurement of the double-helicity dependence of the dijet transverse momentum in longitudinally polarized p+p collisions at s=200 GeV from data taken by the PHENIX experiment in 2005 and 2006. The analysis deduces the transverse momentum of the dijet from the widths of the near- and far-side peaks in the azimuthal correlation of the dihadrons. When averaged over the transverse momentum of the triggered particle, the difference of the root mean square of the dijet transverse momentum between like- and unlike-helicity collisions is found to be −37±88stat±14syst MeV/c.Received 6 October 2009DOI:https://doi.org/10.1103/PhysRevD.81.012002©2010 American Physical Society

HIGH PROBABILITY OF LARGE ORBITAL ANGULAR MOMENTUM CONTRIBUTION TO THE MAGNETIC MOMENT OF COBALT(II) ION IN NEWLY REPORTED MACROCYCLIC COMPLEX CONTAINING AMIDE, IMINE AND SECONDARY AMINE FUNCTIONS

Article HIGH PROBABILITY OF LARGE ORBITAL ANGULAR MOMENTUM CONTRIBUTION TO THE MAGNETIC MOMENT OF COBALT(II) ION IN NEWLY REPORTED MACROCYCLIC COMPLEX CONTAINING AMIDE, IMINE AND SECONDARY AMINE FUNCTIONS was published on July 1, 2008 in the journal Reviews in Inorganic Chemistry (volume 28, issue 3).

Hadron properties and Dyson–Schwinger equations

An overview of the theory and phenomenology of hadrons and QCD is provided from a Dyson–Schwinger equation viewpoint. Following a discussion of the definition and realization of light-quark confinement, the nonperturbative nature of the running mass in QCD and inferences from the gap equation relating to the radius of convergence for expansions of observables in the current-quark mass are described. Some exact results for pseudoscalar mesons are also highlighted, with details relating to the U A ( 1 ) problem, and calculated masses of the lightest J = 0 , 1 states are discussed. Studies of nucleon properties are recapitulated upon and illustrated: through a comparison of the ln -weighted ratios of Pauli and Dirac form factors for the neutron and proton; and a perspective on the contribution of quark orbital angular momentum to the spin of a nucleon at rest. Comments on prospects for the future of the study of quarks in hadrons and nuclei round out the contribution.

Supramolecular motifs and solvatomorphism within the compounds [M(bpy)3]2[NbO(C2O4)3]Cl·nH2O (M = Fe2+, Co2+, Ni2+, Cu2+and Zn2+; n = 11, 12). Syntheses, structures and magnetic properties

Solvatomorphism has been found between two series of complexes of the composition [M(bpy)3]2[NbO(C2O4)3]Cl.nH2O [M = Fe2+ (1, 2), Co2+ (3, 4), Ni2+ (5, 6), Cu2+ (7) and Zn2+ (8, 9); bpy = 2,2'-bipyridine)], crystallizing in the monoclinic space group P2 1/c [3, 5, 8 (n = 11)] or in the orthorhombic space group P21 21 21 [2, 4, 6, 7 (n = 12)]. All the structures contain two symmetry independent [M(bpy)3]2+ cations, one [NbO(C2O4)3]3- anion, one Cl(-) anion, and crystal water molecules. The cations possess a trigonally distorted octahedral geometry, with an additional tetragonal distortion in 7. Analysis of crystal packing reveals a specific type of supramolecular contact comprising four bipyridine ligands from two neighbouring [M(bpy)3]2+ cations--quadruple aryl embrace (QAE) contact. The contact is realized by the alignment of two molecular two-fold rotation axes, preserving the parallel orientation of the molecular three-fold rotation axes. The resulting two-dimensional honeycomb lattices of [M(bpy)3]2+ cations are placed between the hydrogen bonding layers made of [NbO(C2O4)3]3- and Cl(-) anions and the majority of the crystal water molecules. The temperature-dependent magnetic susceptibility measurements (1.8-300 K) show a significant orbital angular momentum contribution for 3 and 4 (high-spin Co2+), the influence of zero-field splitting for 5 and 6(Ni2+) and a substantially paramagnetic Curie behaviour for the Cu2+ compound (7).

Evidence for the absence of gluon orbital angular momentum in the nucleon

The Sivers mechanism for the single-spin asymmetry in unpolarized lepton scattering from a transversely polarized nucleon is driven by the orbital angular momentum carried by its quark and gluon constituents, combined with QCD final-state interactions. Both quark and gluon mechanisms can generate such a single-spin asymmetry, though only the quark mechanism can explain the small single-spin asymmetry measured by the COMPASS collaboration on the deuteron, suggesting the gluon mechanism is small relative to the quark mechanism. We detail empirical studies through which the gluon and quark orbital angular momentum contributions, quark-flavor by quark-flavor, can be elucidated.

Light cone sum rules forγ*N→Δtransition form factors

A theoretical framework is suggested for the calculation of gamma* N -> Delta transition form factors using the light-cone sum rule approach. Leading-order sum rules are derived and compared with the existing experimental data. We find that the transition form factors in a several GeV region are dominated by the ``soft'' contributions that can be thought of as overlap integrals of the valence components of the hadron wave functions. The ``minus'' components of the quark fields contribute significantly to the result, which can be reinterpreted as large contributions of the quark orbital angular momentum

Helicity dependent and independent generalized parton distributions of the nucleon in lattice QCD

A complete description of the nucleon structure in terms of generalized parton distributions (GPDs) at twist 2 level requires the measurement/computation of the eight functions H, E, \tilde H, \tilde E, H_T, E_T, \tilde H_T and \tilde E_T, all depending on the three variables x, \xi and t. In this talk, we present and discuss our first steps in the framework of lattice QCD towards this enormous task. Dynamical lattice QCD results for the lowest three Mellin moments of the helicity dependent and independent GPDs are shown in terms of their corresponding generalized form factors. Implications for the transverse coordinate space structure of the nucleon as well as the orbital angular momentum (OAM) contribution of quarks to the nucleon spin are discussed in some detail.

Generalized parton distributions from lattice QCD.

We perform a quenched lattice calculation of the first moment of twist-two generalized parton distribution functions of the proton, and assess the total quark (spin and orbital angular momentum) contribution to the spin of the proton.