Spin-orbit Correlations Research Articles

The electronic spectrum of CUONg4 (Ng = Ne, Ar, Kr, Xe): New insights in the interaction of the CUO molecule with noble gas matrices

The electronic spectrum of the CUO molecule was investigated with the IHFSCC-SD (intermediate Hamiltonian Fock-space coupled cluster with singles and doubles) method and with TD-DFT (time-dependent density functional theory) employing the PBE and PBE0 exchange-correlation functionals. The importance of both spin-orbit coupling and correlation effects on the low-lying excited-states of this molecule are analyzed and discussed. Noble gas matrix effects on the energy ordering and vibrational frequencies of the lowest electronic states of the CUO molecule were investigated with density functional theory (DFT) and TD-DFT in a supermolecular as well as a frozen density embedding (FDE) subsystem approach. This data is used to test the suitability of the FDE approach to model the influence of different matrices on the vertical electronic transitions of this molecule. The most suitable potential was chosen to perform relativistic wave function theory in density functional theory calculations to study the vertical electronic spectra of the CUO and CUONg(4) with the IHFSCC-SD method.

Beam-Target Double-Spin AsymmetryALTin Charged Pion Production from Deep Inelastic Scattering on a Transversely PolarizedHe3Target at1.4<Q2<2.7 GeV2

We report the first measurement of the double-spin asymmetry A{LT} for charged pion electroproduction in semi-inclusive deep-inelastic electron scattering on a transversely polarized {3}He target. The kinematics focused on the valence quark region, 0.16<x<0.35 with 1.4<Q{2}<2.7 GeV{2}. The corresponding neutron A{LT} asymmetries were extracted from the measured {3}He asymmetries and proton over {3}He cross section ratios using the effective polarization approximation. These new data probe the transverse momentum dependent parton distribution function g{1T}{q} and therefore provide access to quark spin-orbit correlations. Our results indicate a positive azimuthal asymmetry for π{-} production on {3}He and the neutron, while our π{+} asymmetries are consistent with zero.

Strong configuration interaction in the double ionization spectra of noble gases studied by the relativistic propagator method

In this work, the four-component two-particle propagator technique is employed for the calculation of double ionization spectra of the noble gas atoms Ne through Rn. For a correct assignment of the individual final states, inclusion of spin-orbit coupling and electron correlation is mandatory and is accounted for in the framework of the relativistic propagator. It was observed that the $n{s}^{2}n{p}^{4}$(${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2,1,0}$, ${}^{1}\phantom{\rule{-0.16em}{0ex}}{D}_{2}$, ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}$) manifolds of all investigated noble gas dications exhibit a clear main-state character with only small admixture from other configurations. This also refers to the $2{s}^{1}2\phantom{\rule{-0.16em}{0ex}}{p}^{5}$(${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2,1,0}^{o}$, ${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{o}$) states of Ne${}^{2+}$. In the argon, krypton, and xenon dications, the $n{s}^{1}n{p}^{5}$(${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2,1,0}^{o}$) states, and especially the $n{s}^{1}\phantom{\rule{-0.16em}{0ex}}n{p}^{5}$(${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{o}$) ones, lose intensity due to pronounced configuration interaction. These states experience strong mixings with ground-state shake-up satellites, which occupy the same energy region. The composition of the $5{s}^{1}5{p}^{5}$(${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{o}$) singlet state of Xe${}^{2+}$ is studied in detail by analyzing the corresponding eigenvector. As long as a $LS$ coupling picture can be approximately maintained, the amount of singlet-triplet splitting decreases in the sequence from neon to xenon. In the $6{s}^{1}6{p}^{5}$ manifold of Rn${}^{2+}$, a complete disappearance of well-defined main states takes place leading to a dense and complicated spectrum governed by very strong multiconfiguration effects. Relativistic corrections to the Coulomb interaction are accounted for by inclusion of the Gaunt (magnetic) term.

Semi-inclusive DIS Experiments Using Transversely Polarized Targets in Hall-A: Current Results and Future Plans

Measurement of single (SSA) and double spin asymmetries (DSA) in semi- inclusive DIS reactions using polarized targets provide a powerful method to probe trans- verse momentum dependent parton distribution functions (TMDs). In particular, the ex- perimentally measured SSA on nucleon targets can help in extracting the transversity and Sivers distribution functions of u and d-quarks. Similarly, the measured DSA are sensitive to the quark spin-orbital correlations, and provide an access to the TMD parton distribu- tion function (g1T ). A recent experiment conducted in Hall-A Jefferson Lab using trans- versely polarized 3 He provide first such measurements on effective neutron target. The measurement was performed using 5.9 GeV beam from CEBAF and measured the target SSA/DSA in the SIDIS reaction 3 He (e, e 0 � � )X. The kinematical range, x = 0.19�0.34, at Q 2 = 1.77�2.73 (GeV/c) 2 , was focused on the valence quark region. The results from this measurement along with our plans for future high precision measurements in Hall-A are presented.

Studies of spin-orbit correlations at JLAB

Studies of single spin asymmetries for pion electroproduction in semi-inclusive deep-inelastic scattering are presented using the polarized ∼6 GeV electrons from at the Thomas Jefferson National Accelerator Facility (JLab) and the Continuous Electron Beam Accelerator Facility (CEBAF) Large Acceptance Spectrometer (CLAS) with the Inner Calorimeter. The cross section versus the azimuthal angle ϕh of the produced neutral pion has a substantial sin ϕh amplitude. The dependence of this amplitude on Bjorken xB and on the pion transverse momentum is extracted and compared with published data.

Transverse-momentum-dependent parton distribution/fragmentation functions at an electron-ion collider

We present a summary of a recent workshop held at Duke University on Partonic Transverse Momentum in Hadrons: Quark Spin-Orbit Correlations and Quark-Gluon Interactions. The transverse momentum dependent parton distribution functions (TMDs), parton-to-hadron fragmentation functions, and multi-parton correlation functions, were discussed extensively at the Duke workshop. In this paper, we summarize first the theoretical issues concerning the study of partonic structure of hadrons at a future electron-ion collider (EIC) with emphasis on the TMDs. We then present simulation results on experimental studies of TMDs through measurements of single spin asymmetries (SSA) from semi-inclusive deep-inelastic scattering (SIDIS) processes with an EIC, and discuss the requirement of the detector for SIDIS measurements. The dynamics of parton correlations in the nucleon is further explored via a study of SSA in D (`D) production at large transverse momenta with the aim of accessing the unexplored tri-gluon correlation functions. The workshop participants identified the SSA measurements in SIDIS as a golden program to study TMDs in both the sea and valence quark regions and to study the role of gluons, with the Sivers asymmetry measurements as examples. Such measurements will lead to major advancement in our understanding of TMDs in the valence quark region, and more importantly also allow for the investigation of TMDs in the sea quark region along with a study of their evolution.

Measurement of Single- and Double-Spin Asymmetries in Deep Inelastic Pion Electroproduction with a Longitudinally Polarized Target

We report the first measurement of the transverse momentum dependence of double-spin asymmetries in semi-inclusive production of pions in deep-inelastic scattering off the longitudinally polarized proton. Data have been obtained using a polarized electron beam of 5.7 GeV with the CLAS detector at the Jefferson Lab (JLab). Modulations of single spin asymmetries over the azimuthal angle between lepton scattering and hadron production planes ϕ have been measured over a wide kinematic range in Bjorken x and virtual photon squared four-momentum Q2. A significant nonzero sin2ϕ single spin asymmetry was observed for the first time indicating strong spin-orbit correlations for transversely polarized quarks in the longitudinally polarized proton.

Single-photon spin-orbit entanglement violating a Bell-like inequality

Single photons emerging from q-plates (or Pancharatnam-Berry phase optical element) exhibit entanglement in the degrees of freedom of spin and orbital angular momentum. We put forward an experimental scheme for probing the spin-orbit correlations of single photons. It is found that the Clauser-Horne-Shimony-Holt (CHSH) parameter S for the single-photon spin-orbit entangled state could be up to 2.828, evidently violating the Bell-like inequality and thus invalidating the noncontextual hidden variable (NCHV) theories.

Theoretical characterisation of the SSO, cyclic SOS and SOS isomers

The SSO, cyclic SOS and open SOS isomers have been investigated, employing the CCSD(T) methodology and the cc-pV(X + d)Z X = 3, 4, 5, 6 basis sets. The anharmonic force fields have been calculated to predict the fundamental vibrational frequencies, rotational constants, vibration-rotation corrections, anharmonic corrections to zero-point energies, and structural parameters. At the CCSD(T)/CBS limit and including corrections for scalar relativistic effects, complete quadruple excitations, spin-orbit and core-valence correlation effects, the estimated enthalpies of formation are −13.9 ± 1, 32.1 ± 1, and −51.2 ± 1 kcal/mol, for SSO, cyclic-SOS and open-SOS, respectively. Finally, it was found that the asymmetric SO stretch of the open and cyclic SOS isomers are located in a nearly identical position and it is likely that SOS also maybe present in the surface of Io.

Bipartite entanglements in spin–orbital systems

In this Letter we present the bipartite entanglement properties of the spin–orbital systems. After constructing the maximally entangled spin–orbital basis of bipartite, we find that the quantum entanglement length in the noninteracting itinerant electron system with spin and orbit degrees of freedom is considerably larger than that in the system with only spin. In SU ( 2 ) ⊗ SU ( 2 ) spin–orbital interacting system, the bipartite entanglement, expressed in terms of the spin–orbital correlation functions, clearly manifests the close relationship with the quantum phase in strongly correlated systems. The entanglement phase diagram of the finite-size systems is in agreement with the magnetic and orbital phase diagram of the infinite systems. The possible application of the present theory on nucleon systems is suggested.

THE SPIN STRUCTURE OF THE NUCLEON IN LIGHT-CONE QUARK MODELS

The quark spin densities related to generalized parton distributions in impact-parameter space and to transverse-momentum dependent parton distributions are reviewed within a light-cone quark model, with focus on the role of the different spin-spin and spin-orbit correlations of quarks. Results for azimuthal spin asymmetries in semi-inclusive deep inelastic scattering due to T -even transverse-momentum dependent parton distributions are also discussed.

Chiral-odd generalized parton distributions in transverse and longitudinal impact parameter spaces

We investigate the chiral odd generalized parton distributions (GPDs) for non-zero skewnessin transverse and longitudinal position spaces by taking Fourier transform with respect to the transverse and longitudinal momentum transfer respectively. We present overlap formulas for the chiral-odd GPDs in terms of light-front wave functions (LFWFs) of the proton both in the ERBL and DGLAP regions. We calculate them in a field theory inspired model of a relativistic spin 1/2 composite state with the correct correlation between the different LFWFs in Fock space, namely that of the quantum fluctuations of an electron in a generalized form of QED. We show the spin-orbit correlation effect of the two-particle LFWF as well as the correlation between the constituent spin and the transverse spin of the target.

Theoretical study on the spin and orbital orderings in Ruddlesden-Popper compound La3-3xCa1+3xMn3O10(0 ≤ x ≤ 1)

In this paper, the spin and orbital orderings of the n = 3 Ruddlesden-Popper (RP) series of compounds La3-3xCa1+3xMn3O10 have been analyzed theoretically for the whole doping range 0 ≤ x ≤ 1, the calculation is based on the unrestricted Hartree-Fock approximation and the real-space recursion method. In agreement with experimental observations, we find that the ground state of La3-3xCa1+3xMn3O10 is ferromagnetic metal at x=0.3 and is G-type antiferromagnetic insulator at x = 1. The ferromagnetic metallic state is sustained for lower doping range 0 ≤ x 0.96. Our study unveils a strong spin-orbital correlation in the ferromagnetic metallic state for doping range 0 ≤ x < 0.39, an orbital ordering transition takes place at x = 0.06 which changes from the nearest-neighbor antiferro-orbital ordering (0 ≤ x < 0.06) to the layer-type antiferro-orbital ordering (0.06 < x < 0.39).

Theoretical characterization of the HSOH, H2SO and H2OS isomers

The HSOH, H2SO and H2OS isomers have been investigated employing the CCSD(T) methodology and the cc-pV(X + d)Z X = 3,4,5,6 basis sets. The anharmonic force fields have been calculated to predict the fundamental vibrational frequencies, rotational constants, vibration–rotation corrections, anharmonic corrections to zero-point energies, and structural parameters. In addition to this, a spectroscopic characterization of the deuterated isomers D2SO and D2OS was performed. At the CCSD(T)/CBS limit and including corrections for scalar relativistic, spin orbit and core-valence correlation effects, the estimated enthalpies of formation are −28.1 ± 1, −12.3 ± 1, and 10.1 ± 1 kcal/mol for HSOH, H2SO and H2OS, respectively. Finally, we discuss the problems faced during the extrapolation to the CBS limit of the properties investigated.

Latest HERMES results on transverse spin effects in hadron structure and formation⋆

Transverse target single-spin asymmetries in semi-inclusive deep inelastic scattering allow to study the so-called Collins and Sivers mechanisms. The first one connects the poorly known fundamental transversity distribution function, describing the transverse spin-polarization of quarks in a transversely polarized proton, to the Collins fragmentation function, describing spin-orbit correlations in the hadron formation process. The second one is sensitive to the Sivers function, which correlates the intrinsic transverse momentum of quarks with the proton’s spin orientation and is related to the orbital angular momentum of quarks. Preliminary results on azimuthal single target-spin asymmetries in semi-inclusive electro-production of pions and kaons at the HERMES experiment are presented. The full data set collected with a transversely polarized hydrogen target was analyzed providing the HERMES most precise results on the Collins and Sivers azimuthal moments.

Chiral odd generalized parton distributions in impact parameter space

We investigate the chiral odd generalized parton distributions (GPDs) for the quantum fluctuations of an electron in QED. This provides a field theory inspired model of a relativistic spin-(1/2) composite state with the correct correlation between the different light-front wave functions (LFWFs) in Fock space. We express the GPDs in terms of overlaps of LFWFs and obtain their representation in impact parameter space when the momentum transfer is purely transverse. We show the spin-orbit correlation effect of the two-particle LFWF as well as the correlation between the constituent spin and the transverse spin of the target.

Are all Boer–Mulders functions alike?

Chirally odd generalized parton distributions (GPDs) and the Boer–Mulders function provide valuable information about spin–orbit correlations for quarks in nucleons and other hadrons. We compare results for the relevant GPD E¯Tq from a variety of phenomenological models as well as recent lattice results, which all find that E¯Tq>0 for nucleons as well as the pion and for both u and d quark. As a result, the corresponding Boer–Mulders functions are all expected to be negative. We investigate the physical origin of the sign of E¯Tq.

Orbital Order inZnV2O4

In view of recent controversy regarding the orbital order in the frustrated spinel ZnV2O4, we analyze the orbital and magnetic groundstate of this system within an ab initio density functional theory approach. While LDA+U calculations in the presence of a cooperative Jahn-Teller distortion stabilize an A-type staggered orbital order, the consideration of relativistic spin-orbit effects unquenches the orbital moment and leads to a uniform orbital order with a net magnetic moment close to the experimental one. Our results show that ab initio calculations are able to resolve the existing discrepancies in previous theories and that it is the spin-orbit coupling alongwith electronic correlations which play a significant role in determining the orbital structure in these materials.

Towards relativistic ECP / DFT description of chemical bonding in E112 compounds: spin-orbit and correlation effects in E112X versus HgX (X=H, Au)

Abstract The relativistic effective core potential (RECP) approach combined with the spin-orbit DFT electron correlation treatment was applied to the study of the bonding of eka-mercury (E112) and mercury with hydrogen and gold atoms. Highly accurate small-core shape-consistent RECPs derived from Hartree-Fock-Dirac-Breit atomic calculations with Fermi nuclear model were employed. The accuracy of the DFT correlation treatment was checked by comparing the results in the scalar-relativistic (spin-orbit-free) limit with those of high level scalar-relativistic correlation calculations within the same RECP model. E112H was predicted to be slightly more stable than its lighter homologue (HgH). The E112-Au bond energy is expected to be ca. 25–30 % weaker than that of Hg-Au. The role of correlations and magnetic (spin-dependent) interactions in E112-X and Hg-X (X=H, Au) bonding is discussed. The present computational procedure can be readily applied to much larger systems and seems to be a promising tool for simulating E112 adsorption on metal surfaces.

Single-spin observables and orbital structures in hadronic distributions

Within the light-quark sector of the standard model, P-odd observables are generated from point-like electroweak processes while A_t- odd observables (neglecting quark mass parameters) come from dynamic spin-orbit correlations within hadrons or within larger composite systems, such as nuclei. The effects of A_t-odd dynamics can be inserted into transverse-momentum dependent constituent distribution functions and, in this paper, we construct the contribution from an orbital quark to the A_t odd quark parton distribution. Using this distribution, we examine the crucial role of initial- and final-state interactions in the observation of the scattering asymmetries in different hard-scattering processes. This construction provides a geometrical and dynamical interpretation of the Collins conjugation relation between single-spin asymmetries in semi-inclusive deep inelastic scattering and the asymmetries in Drell-Yan production. Finally, our construction allows us to display a significant difference between the calculation of a spin asymmetry generated by a hard scattering mechanism involving color-singlet exchange (such as a photon) and a calculation of an asymmetry with a hard-scattering exchange involving gluons. This leads to an appreciation of the process dependence inherent in measurements of single-spin observables.