Sum Of Spin Research Articles

A systematic study on interplay between intermolecular hydrogen bonding and aromaticity

In this study, the interplay between aromaticity and intermolecular hydrogen bonding was investigated in some heterocyclic compounds using quantum mechanical calculations. The NH … O intermolecular hydrogen bonds between formamide and NH and CO functional groups of the selected compounds enhance the delocalisation of the six-membered ring electron cloud, resulting in an increase in the aromaticity of the ring. The contribution of various factors to the binding energy, including the stabilisation energy of the interplay between aromaticity and H-bonding, was estimated using two model systems. The relative binding energies and the estimated stabilisation energies of the aforementioned interplay can be explained by the weights of resonance structures calculated using the natural resonance theory (NRT) analysis with the natural bond orbitals (NBO) method. These weights reflect the tendency of ring nitrogen lone pairs to contribute to the π electron cloud of the ring. The results of the topological analysis of electron charge densities using the atoms in molecules (AIM) method were used to estimate the aromaticity of the ring. Aromaticity indices, particularly nucleus-independent chemical shifts (NICS) calculated one angstrom above the ring plane, are in good linear correlation with the estimated stabilisation energies and electron density at the H-bond critical points. The sum of the total nuclear spin–spin coupling 1J of adjacent atoms of the ring (Σ1J), and the J values of H-bond donor and H-bond acceptor atoms, 1HJNO, which are in good agreement with the energy data and aromaticity indices, can be used as measures of the interplay between aromaticity and H-bonding. The interplay between H-bonding and the aromaticity of the ring is clearly evident from the changes in the pattern of the molecular electrostatic potential (MEP) contour maps at 1.7 Å above the plane of the molecule upon H-bond complexation.

Performance of an atomic mean-field spin–orbit approach within exact two-component theory for perturbative treatment of spin–orbit coupling

ABSTRACT Development of an atomic mean-field (AMF) spin–orbit approach within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e) together with pilot applications are reported. The effective one-electron spin–orbit integral matrix in the four-component representation is assembled as a direct sum of one-centre spin–orbit integral matrices with the mean-field two-electron contributions evaluated using atomic SFX2C-1e Hartree–Fock density matrices. It is then transformed into two-component representation using analytic SFX2C-1e energy derivative formulation. The resulting two-component spin–orbit integral matrix is by design suitable for use in perturbative calculations of spin–orbit coupling, treating SFX2C-1e wavefunctions as unperturbed states. The accuracy of the present AMF approach has been demonstrated using benchmark calculations of spin–orbit splittings for representative diatomic radicals at the equation-of-motion coupled-cluster singles and doubles level. To demonstrate the applicability and accuracy of the present perturbative spin–orbit scheme in calculations of challenging heavy-element containing systems, a thorough computational investigation of six low-lying electronic states of ThO + is reported.

Experimental demonstration of generating arbitrary total angular momentum states

We experimentally demonstrated an approach to generate arbitrary total angular momentum (TAM) states by using two liquid crystal devices. Photons’ TAM, the sum of spin and orbital angular momenta (SAM and OAM) under paraxial approximation, has found many applications in optics and attracted increasing attention in recent years. Our approach is based on the orthogonality of two eigen SAM components, that arbitrary TAM states will be produced through encoding different holograms in one system. The comparison with theoretical predications yields an excellent agreement, including both the separable state and the non-separable state. The proposed scheme takes a step forward for generating complex structured fields and broadens its application to various fields like laser processing and large capacity data transmission.

Hořava-Lifshitz gravity and effective theory of the fractional quantum Hall effect

We show that Horava-Lifshitz gravity theory can be employed as a covariant framework to build an effective field theory for the fractional quantum Hall effect that respects all the spacetime symmetries such as non-relativistic diffeomorphism invariance and anisotropic Weyl invariance as well as the gauge symmetry. The key to this formalism is a set of correspondence relations that maps all the field degrees of freedom in the Horava-Lifshitz gravity theory to external background (source) fields among others in the effective action of the quantum Hall effect, according to their symmetry transformation properties. We originally derive the map as a holographic dictionary, but its form is independent of the existence of holographic duality. This paves the way for the application of Horava-Lifshitz holography on fractional quantum Hall effect. Using the simplest holographic Chern-Simons model, we compute the low energy effective action at leading orders and show that it captures universal electromagnetic and geometric properties of quantum Hall states, including the Wen-Zee shift, Hall viscosity, angular momentum density and their relations. We identify the shift function in Horava-Lifshitz gravity theory as minus of guiding center velocity and conjugate to guiding center momentum. This enables us to distinguish guiding center angular momentum density from the internal one, which is the sum of Landau orbit spin and intrinsic (topological) spin of the composite particles. Our effective action shows that Hall viscosity is minus half of the internal angular momentum density and proportional to Wen-Zee shift, and Hall bulk viscosity is half of the guiding center angular momentum density.

Dynamical polarization of nuclear spins by acceptor-bound holes in a zinc-blende semiconductor

The ground state of an acceptor-bound hole in a zinc-blende semiconductor is formed by four eigenstates of the total angular momentum, which is a vector sum of spin and orbital moment of the hole. As a result, the hyperfine interaction of the hole with lattice nuclei becomes anisotropic and coordinate dependent. We develop a theory of dynamic polarization of nuclear spins by the acceptor-bound hole, giving full account for its complex spin structure. The rate of hole-nuclear flip-flop transitions is shown to depend on the angle between the total angular momentum of the hole and the position vector of the nucleus with respect to the acceptor center. The resulting spatially inhomogeneous spin polarization of nuclei gives rise to nonequidistant spin splitting of the hole, which can be detected by methods of optical or microwave spectroscopy.

Higher Order Pancharatnam-Berry Phase and the Angular Momentum of Light

The first experimental demonstration of a new Pancharatnam-Berry phase for light beams with spatially inhomogeneous, or vector, states of polarization referred to as the higher-order Pancharatnam-Berry phase is presented. This new geometric phase is proportional to light's total angular momentum, a sum of spin and higher dimensional orbital angular momentum, sharply contrasting the well-known Pancharatnam-Berry phase associated with the plane wave state of polarization of a spatially homogeneous light beam. The higher-order Pancharatnam-Berry phase is directly related to the rotational symmetry of a vortex-bearing electromagnetic field, associated with the rotational frequency shift of a light beam, and has implications in quantum information science as well as other physical systems such as electron vortex beams.

Contribution of polaron hopping to the electron paramagnetic resonance linewidth in La1−xCaxMnO3 and related materials

We analyze the contribution of polaron hopping to the electron paramagnetic resonance linewidth in La1−xCaxMnO3 and related materials. The material is assumed to be in the paramagnetic phase and the conductivity is associated with the activated polaron hopping. It is also assumed that the adiabatic, small polaron picture is appropriate so that the conductivity varies as exp[−Ea/T]/T, where Ea denotes the polaron activation energy. The polaron contribution to the linewidth is given by the expression C[χ0(T)/χ(T)]exp[−Ea/T] where χ0(T) is the Curie susceptibility (∼1/T), χ(T) is the measured susceptibility and C is a material-dependent parameter. Various experimental studies reporting polaron contributions to the linewidth are discussed. It is pointed out that fitting the linewidth to the functional form ΔH0+(A/T)exp[−Ea/T] is not physically justified. In the high temperature–mean field regime, the exchange narrowed width, (1−Θ/T)k(∞), where Θ is the paramagnetic Curie temperature, replicates the exponential functional form with reasonable values for the activation energy. From previous measurements of the conductivity that showed activated polaron hopping as the leading transport mechanism, we concluded that the linewidth in La0.7Ca0.3MnO3 is a sum of exchange narrowing and one-phonon spin–lattice terms with no evidence of a contribution from polaron hopping or band transport as had been previously proposed. A similar conclusion is reached for La0.8Ca0.2MnO3, nanometer-sized La0.9Ca0.1MnO3, and La0.9Te0.1MnO3.

Active control of coupled flexural-torsional vibration in a flexible rotor–bearing system using electromagnetic actuator

Rotor–shaft systems are subject to non-uniform spin speed during start-up, coast-down or any non-stationary situation changing the spin speed suddenly, e.g., load fluctuation or sudden mass-loss like loss of a blade or a part thereof. For a flexurally and torsionally compliant rotor-shaft, the dynamics under non-uniform spin-speed shows inertial coupling among transverse and torsional coordinates through mass-unbalance and gyroscopic effect. This results into coupled transverse-torsional vibration, where torsional response consists of significant harmonic components at bisynchronous spin frequency, torsional natural frequency of the shaft, and at combination frequencies corresponding to sum and difference of spin and transverse natural frequencies and twice the transverse natural frequency of the rotor-shaft. As a result of the coupling, transverse rotor motion also influences the torsional motion. The Method of Multiple Scales (MMS) is used in this work to carry out an analysis of a simplified system to get an idea about the dominant frequencies of excitation. Results of numerical simulation are presented next to show the effectiveness and influence of actively controlling the transverse rotor motion on its torsional motion, at the dominant frequencies, with the help of non-contact electromagnetic force from an actuator. Transverse vibration control is also observed to control the torsional oscillations due to coupled nature of the problem. The Stability Limit Speed (SLS) of the system is also increased as a result of application of the active control action. Constant axial torque is observed to diminish the influence of coupling, and protect the system against torsional instability, but control action is a must to stabilize the transverse vibration of the system above SLS.

Higher Spin Superalgebras in any Dimension and their Representations

Fock module realization for the unitary singleton representations of the d?1 dimensional conformal algebra o(d?1,2), which correspond to the spaces of single-particle states of massless scalar and spinor in d?1 dimensions, is given. The pattern of the tensor product of a pair of singletons is analyzed in any dimension. It is shown that for 3$>d>3 the tensor product of two boson singletons decomposes into a sum of all integer spin totally symmetric massless representations in AdSd, the tensor product of boson and fermion singletons gives a sum of all half-integer spin symmetric massless representations in AdSd, and the tensor product of two fermion singletons in 4$>d>4 gives rise to massless fields of mixed symmetry types in AdSd depicted by Young tableaux with one row and one column together with certain totally antisymmetric massive fields. In the special case of o(2,2), tensor products of 2d massless scalar and/or spinor modules contain infinite sets of 2d massless conformal fields of different spins. The obtained results extend the 4d result of Flato and Fronsdal [1] to any dimension and provide a nontrivial consistency check for the recently proposed higher spin model in AdSd [2]. We define a class of higher spin superalgebras which act on the supersingleton and higher spin states in any dimension. For the cases of AdS3, AdS4, and AdS5 the isomorphisms with the higher spin superalgebras defined earlier in terms of spinor generating elements are established.

Spin relaxation in isolated molecules and clusters: the interpretation of Stern-Gerlach experiments.

Intramolecular spin relaxation may occur in isolated molecules or clusters provided that the density of rovibrational eigenstates is sufficiently high to serve as an energy bath and angular momentum is conserved. In the coupled, zero-field limit, total angular momentum (J) is the sum of spin (S) and rotational (N) momenta such that J and M(J) are good angular momentum quantum numbers. In the coupled limit, transitions between Zeeman levels (Delta M(J)++0) cannot occur in the absence of an external torque. However, in the high-field limit, J and M(J) are no longer good quantum numbers, as N and S are decoupled and only their projections on the z axis defined by the external field are invariant. In this case M(N) and M(S) remain as good quantum numbers so that angular momentum conserving transitions can occur subject to the selection rule Delta M(N)=-Delta M(S). Determination of the magnetic moments of isolated molecules and clusters via a thermodynamics-based analysis requires that their magnetizations are measured at sufficiently large fields that spin-rotation effects become negligible and the Zeeman level structure approaches the free-spin case.

How Much of the Nucleon Spin is Carried by Glue?

We estimate in the QCD sum rule approach the amount of the nucleon spin carried by the gluon angular momentum: the sum of the gluon spin and orbital angular momenta. The result indicates that gluons contribute at least one half of the nucleon spin at scale of 1 GeV^2.

Hyperons in the bound-state approach to the Nambu-Jona-Lasinio chiral soliton

For the Nambu-Jona-Lasinio (NJL) model in the proper-time regularization scheme the chiral soliton is investigated for the case of three flavors within the framework of the bound-state approach to strangeness. For this purpose meson fluctuations off the non-strange soliton are considered. For the kaon P-wave channel the emerging Bethe-Salpeter equation is solved yielding the bound-state energy and wave function. This kaon bound state also induces a strange valencequark wave function. Collective coordinates are introduced for the SU(2) isorotations and the coupling of the bound state to these rotations is determined. The total spin is decomposed into parts carried by the soliton and the bound state. The absolute value of the former is identical to the total isospin while the latter is demonstrated to be identical to the expectation value of the grand spin, the sum of spin and isospin. The functional trace involves quark states with various grand spins which get polarized by the kaon bound state. This polarization results in a normalization of the coupling between the collective rotation and the bound state different from the Skyrme model. Nevertheless after quantization the expression for the baryon masses can be cast into the form found by Callan and Klebanov for the Skyrme model. Numerical results for the baryon spectrum are compared to those obtained in the same model using the collective approach of Yabu and Ando. It is found that for 1 2 + baryons the bound-state treatment reproduces the experimental data better than the collective approach while there are only small differences between the two approaches for the 3 2 + baryons. Both treatments underestimate the mass splittings for baryons with different strangeness. This short-coming is conjectured to be inherited from the meson sector of the NJL model where too small a ratio of the kaon and pion decay constants is predicted.

Polarization of partons in the proton.

The spin-dependent distribution functions of quarks and gluons in a proton are studied so as to explain the European Muon Collaboration {ital g}{sub 1}{sup {ital p}}({ital x}) data by introducing a new model, in which characteristics of both the static quark and the quark-parton model are taken into account. The {ital x} dependence of {ital g}{sub 1}{sup {ital p}}({ital x}) is reproduced well. It is shown that polarized gluons through the anomaly play a significant role and the resultant sum of quark spin is 0.375. Furthermore, {ital g}{sub 1}{sup {ital n}}({ital x}) as well as {ital g}{sub 1}{sup {ital p}}({ital x}) is predicted for future experiments.

Spin and orbital magnetisation densities determined by Compton scattering of photons

Compton scattering of a circularly polarised photon beam is shown to provide direct information on orbital and spin magnetisation densities. Experiments are reported which demonstrate the feasibility of the method by correctly predicting the ratio of spin to orbital magnetisation components in iron and cobalt. A partially polarised beam of 45 keV photons from the Daresbury Synchrotron Radiation Source produces charge-magnetic interference scattering which is measured by a field-difference method. Theory shows that the interference cross section contains the Compton profile of polarised electrons modulated by a structure factor which is a weighted sum of spin and orbital magnetisations. In particular, the scattering geometry for which the structure factor vanishes yields a unique value for the ratio of the magnetisation densities. Compton scattering, being an incoherent process, provides data on total unit-cell magnetisations which can be directly compared with bulk data. In this respect, Compton scattering complements magnetic neutron and photon Bragg diffraction.

Thermostatic properties of polarized nuclear matter.

The thermostatic properties of polarized nuclear matter are calculated using an extended form of the Seyler-Blanchard potential. Different special cases of polarized nuclear matter are considered according to the values of X, Y, and Z, the neutron excess parameter, and the sum and difference of neutron and proton spin up excess parameters, respectively. The reliability of the ${T}^{2}$ approximation is also discussed. A reasonable agreement with previous results is obtained.

Variational calculations of models of nuclear and neutron matter

We report results of variational calculations of models of nuclear matter in which the nuclear interaction is approximated by a sum of central, spin, isospin and tensor forces. The models are based on realistic potentials such as those of Reid, Bethe-Johnson, Hamada-Johnston, and Gammel-Thaler. The correlation operator in the variational wave function contains central, spin, isospin and tensor terms. We briefly review the Fermi-hypernetted-chain, and single-operator-chain (SOC) methods used to calculate the energy expectation value. The energies obtained for these simple models by various variational and reaction matrix calculations seem to be in reasonable agreement. Results with the SOC approximation for the ν 3 model of neutron matter, in which the interaction has only central and spin components, are also reported. These are in good agreement with the energies obtained by summing multiple operator chains.

Bound states with a gauge monopole

Relativistically exact bound states of a Dirac spinor and of a scalar with an SU(2) gauge monopole are determined asymptotically for arbitrary (integer or half-integer) isospin. Independently, zero-energy bound states of the Dirac spinor are proved to exist for each value of total angular momentum $J$ less than the isospin $T$. The spin of the system is shown to be the sum of the original spin and isospin of the bound particle.

Spin-dependentN−Ntmatrix for intermediate energy nucleon-nucleus reactions

A nucleon-nucleon transition matrix fitted to the 50--400 MeV differential cross section and polarization data is presented. The transition operator obtained is a sum of spin- and isospin-dependent central, two-particle spin-orbit, and tensor complex local interactions with Yukawa radial shapes. The application of the transition operator is illustrated and discussed for medium energy nucleon-nucleus inelastic scattering. A comparison is made of the inelastic scattering results with results obtained for electron, pion, and kaon probes. The importance of exchange even at medium energies is stressed. The derived N-N transition operator can be employed in microscopic polarization predictions and is appropriate for explicitly calculating exchange effects.

A variational theory of nuclear matter

The pair-correlation operator f ij in the variational wave function of nuclear matter is generated from a two-body Schrc̈dinger equation with boundary conditions which require the correlated wave function to heal at a distance d. The two-body cluster energy is calculated exactly, while the f ij is approximated by a sum of central, spin, isospin and tensor correlation operators to evaluate the many-body cluster contributions (MBCC). The distribution functions that represent the MBCC are expanded in powers of the non-central correlations. The zeroth order term in this expansion represents a sum of all MBCC with central correlations, and is evaluated by the Fermi hypernetted chain equations. The first order terms are identically zero, while all the second order terms are calculated. When the range of correlations d is about 2 r 0 the expansion appears to converge, and is used to obtain upper bounds to the nuclear matter energy with various potentials. The upper bounds are much lower than energies suggested by earlier calculations; for example the Reid soft core potential gives E( k F = 1.7 fm −1) < −25 MeV. More stringent upper bounds, hopefully close to the true energy, may be obtained by minimizing E( d). The minimum is expected at d ≈ 3 r 0; however at such large vales of d the three-body tensor rings in the second order terms give large negative contribution. General rules for calculating higher order terms in the expansion are given and the method seems simple enough to study the third and higher order terms.

Collision dynamics of three interacting atoms: foundation of the spectator-stripping model

The atom - diatom reaction A + BC → AB + C is described within the Faddeev formalism using sum of spin- dependent pair potentials. This provides a rigorous basis for the spectator-stripping model in the limit of high collision energies. Reaction cross sections for specific vibration - rotation states of AB are calculated for T + H 2 in the 10 eV region of collision energies.