Valence Approximation Research Articles

Light-front transverse momentum distributions for J=1/2 hadronic systems in valence approximation

The semi-inclusive correlator for a ${\cal J}$=1/2 bound-system, composed by A spin-1/2 fermions, is linearly expressed in terms of the light-front Poincar\'e covariant spin-dependent spectral function, in valence approximation. The light-front spin-dependent spectral function is fully determined by six scalar functions that allow for a complete description of the six T-even transverse-momentum distributions, suitable for a detailed investigation of the dynamics inside the bound system. The application of the developed formalism to a case with a sophisticated dynamical content, like $^3$He, reaches two goals: (i) to illustrate a prototype of an investigation path for gathering a rich wealth of information on the dynamics and also finding valuable constraints to be exploited from the phenomenological standpoint; (ii) to support for the three-nucleon system a dedicated experimental effort for obtaining a detailed 3D picture in momentum space. In particular, the orbital-angular momentum decomposition of the bound state can be studied through the assessment of relations among the transverse-momentum distributions, as well as the relevance of the relativistic effect generated by the implementation of macrocausality. A fresh evaluation of the longitudinal and transverse polarizations of the neutron and proton is also provided, confirming essentially the values used in the standard procedure for extracting the neutron structure functions from both deep-inelastic scattering and semi-inclusive reactions, in the same kinematical regime.

High-pressure and high-temperature transformation of Pb(II)-natrolite to Pb(II)-lawsonite.

We report on high-pressure and high-temperature chemical transformations of Pb(2+)-exchanged natrolite (Pb-NAT, Pb8Al16Si24O80·16H2O) using a combination of in situ synchrotron X-ray powder diffraction and ex situ HAADF-STEM real space imaging. Three high-pressure polymorphs of natrolites (Pb-NAT-I, II, III) are observed via step-wise pressure-induced hydrations (PIH) up to 4.5 GPa, during which the number of H2O molecules located inside the natrolite channel increases from 16 to 40 H2O per unit-cell. At 4.5 GPa after heating the high-pressure Pb-NAT-III phase at 200 °C a reconstructive phase transits into a lawsonite phase (Pb-LAW, Pb4Al8Si8O28(OH)8·4H2O) with an orthorhombic space group Pbnm and a = 5.8216(9), b = 9.114(1) and c = 13.320(1) Å is observed. The structure of the recovered Pb-LAW phase was characterized using Rietveld refinement of the in situ synchrotron X-ray powder diffraction data and HAADF-STEM real space imaging. In the recovered Pb-LAW phase the Pb(2+) content is close to 42 wt% and as bond valence approximations reveal the Pb(2+) cations are more tightly coordinated to the framework oxygen atoms than originally in the natrolite phase.

Transverse momentum distributions and nuclear effects

A distorted spin-dependent spectral function for 3He is considered to take care of the final state interaction in the extraction of the quark transverse-momentum distributions in the neutron from semi-inclusive deep inelastic electron scattering off polarized 3He at finite momentum transfers. The generalization of the analysis in a Poincaré covariant framework within the light-front dynamics is outlined. The definition of the light-front spin-dependent spectral function for a J=1/2 system, as the nucleon, allows us to show that within the light-front dynamics and in the valence approximation only three of the six leading twist T-even transverse-momentum distributions are independent.

A Light-Front Approach to the 3He Spectral Function

The analysis of semi-inclusive deep inelastic electron scattering off polarized 3He at finite momentum transfers, aimed at the extraction of the quark transverse-momentum distributions in the neutron, requires the use of a distorted spin-dependent spectral function for 3He, which takes care of the final state interaction effects. This quantity is introduced in the non-relativistic case, and its generalization in a Poincaré covariant framework, in plane wave impulse approximation for the moment being, is outlined. Studying the light-front spin-dependent spectral function for a J = 1/2 system, such as the nucleon, it is found that, within the light-front dynamics with a fixed number of constituents and in the valence approximation, only three of the six leading twist T-even transverse-momentum distributions are independent.

Some Magnetic Properties of YTiFe$_{11-{\rm x}}$Si$_{\rm x}$C Carbides

The effect of carbonation on the structure and the magnetic properties of polycrystalline YTiFe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11-x</sub> Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> (0 les x les 2) have been investigated by means of x-ray diffraction (XRD) at room temperature and magnetic measurements at low temperature. The alloys were prepared by typical induction melting and the carbonation was performed by solid-solid reaction. The cell volume of ThMn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> structure and the Curie temperature increase after carbonation, but decrease with Si content. The saturation magnetization and the magnetic moment were determined from parallel magnetic isotherms using the common law of approach to saturation. The experimental average magnetic moment per atom decreases with Si content. The comparison of experimental 3d-magnetic moment with the calculated values from the magnetic valence approximation (MVA) shows a strong ferromagnetism, induced by carbonation. The XRD patterns of magnetically oriented powder show an uniaxial anisotropy for YFe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11-x</sub> Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> TiC. The second and fourth order magnetocrystalline constants, K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> have been determined using an analytical interpretation, based on the statistical model, of perpendicular magnetization isotherms of the magnetically aligned powder samples. The magnetocrystalline constants and anisotropy field have been determined versus temperature and composition.

A novel covalent crystal formed by carbon (6, 0) nanotubes: Structure and electronic properties

The structure of a carbon crystal formed by (6, 0) nanotubes is simulated. The electronic spectrum of the crystal is calculated by the crystalline-orbital method in the valence approximation. The band gap of the studied crystal is found to be equal to 1.3 eV.

Modeling of the molecular and electronic structures of multiple-decker sandwich macromolecules with η5-π bonds on the basis of biscyclopentadienyl derivatives 60H10 of a C60 fullerene

The molecular and electronic structures of the (CpFe)2C60H10 complex of the D5d symmetry, where Cp is the \(^ \cdot C_5 H_5 \) cyclopentadienyl radical, are simulated using the ab initio Hartree-Fock-Roothaan method in the 3–21G basis set. In this complex, hydrogen atoms are attached to carbon atoms of the C60 fullerene which occupy α-positions with respect to two oppositely lying five-membered rings. Each FeCp semisandwich moiety is linked to atoms of one of these five-membered rings by the η5-π-type bond. It is found that the energy of the η5-π Fe-C60H10 bonds in the (CpFe)2C60H10 complex is comparable to that of the η5-π Fe-Cp bond in the FeCp2 ferrocene molecule. The optimum geometry calculated for the (CpFe)2C60H10 complex is used for modeling of the structure of the quasi-linear macromolecule [-FeC60H10-]n, Open image in new window (I). The band structure of the energy spectrum of macromolecule I is calculated in the valence approximation of the extended Huckel method within the crystalline-orbital approach. The band gap in the spectrum of macromolecule I is ∼2.27 eV. The band structure of the spectrum of this macromolecule is compared with the spectra of the hypothetical molecules [-FeCp-]n and [-FeC20-]n.

The Effect of cis-trans Isomerism on the Electronic-vibrational Structure of the Ground and Excited States and Reactivity of 2-(2-Furyl)- and 2-(2-Thienyl)oxazole

The fluorescent properties, structure, and electronic structure of the ground and excited singlet and triplet electronic states of the cis and trans forms of 4,5-dihydro-2-(2-furyl)oxazole, 4,4-dihydro-2-(2-thienyl)oxazole, 2-(2-furyl)oxazole (FO), and 2-(2-thienyl)oxazole (TO) have been studied. The orbital nature of the lower excited singlet and triplet states has been studied by the semiempirical INDO/S (valence approximation) and PPP/S (π approximation) methods. It was shown that for FO and TO molecules the lower triplet state is of the ππ* type, for which delocalization of the electronic excitation on atoms is characteristic. In the singlet excitation state inversion was observed of the energy levels of the delocalized ππ* states and nπ* states localized over several bonds (for the free TO and FO molecules the lower excited singlet states S1* were assigned to ππ* and nπ* types respectively). Owing to the low position of the Tππ* and Tnπ* levels relative to the singlet level of ππ* type, the rate constant for intercombination conversion is greater than the rate constant for radiative decay. Consequently an efficient population of the triplet states of the molecules occurs under conditions of electronic-vibrational excitation. The direction of reactions during synthesis was compared with the localization indices in the ground state for electrophilic, nucleophilic, and radical substitution, and also with the excitation localization numbers Lμ for a wide selection of electronically excited states. It was concluded that the change in the structure of the azole molecule on replacing an O atom by an S atom, or on changing from a partially hydrogenated to a heteroaromatic system, was the main reason for the change of all the spectral parameters characterizing the electronic-vibrational or the spin-orbital interaction of the most reactive groups of atoms in the molecular structure.

Reply to Boglione and Pennington

In a recent article we presented an argument which, we believe, shows to be incorrect an estimate, by Boglione and Pennington, of corrections to the valence (quenched) approximation predictions for properties of the lightest scalar glueball. Boglione and Pennington's reply to our article, it appears to us, fails to address the specific technical issues we raised.

Comment on “Coupling constant and quark-loop expansion for corrections to the valence approximation”

Lee and Weingarten have recently criticized our calculation of quarkonium and glueball scalars as being "incomplete" and "incorrect". Here we explain the relation of our calculations to full QCD.

Scalar quarkonium masses and mixing with the lightest scalar glueball

We evaluate the continuum limit of the valence (quenched) approximation to the mass of the lightest scalar quarkonium state for a range of different quark masses and to the mixing energy between these states and the lightest scalar glueball. Our results support the interpretation of $f_0(1710)$ as composed mainly of the lightest scalar glueball.

Glueball mass predictions of the valence approximation to lattice QCD

We evaluate the infinite volume, continuum limit of glueball masses in the valence (quenched) approximation to lattice QCD. For the lightest scalar and tensor states we obtain masses of $1648 \pm 58$ MeV and $2267 \pm 104$ MeV, respectively.

ESR spectra and electronic structure of the C120 ·+ radical cation and the paramagnetic C120O2+ dication and C120O2− dianion

Electronic structure of the C120·+ radical cation and the paramagnetic C120O2+ dication and C120O2− dianion in the triplet state was calculated by the MNDO/PM3 method in the valence approximation. The density distributions of the unpaired electrons in these systems were found and the ESR spectra of the above species were interpreted.

Coupling constant and quark-loop expansion for corrections to the valence approximation

For full QCD vacuum expectation values we construct an expansion in quark loop count and in powers of a coupling constant. The leading term in this expansion is the valence (quenched) approximation vacuum expectation value. Higher terms give corrections to the valence approximation. A test of the expansion is presented for moderately heavy quarks on a small lattice. We consider briefly an application of the expansion to quarkonium-glueball mixing.

Continuum limit of scalar masses and mixing energies

We evaluate the continuum limit of the valence approximation to the mass of scalar quarkonium and to the scalar quarkonium-glueball mixing energy for a range of different quark masses. Our results answer several questions raised by the proposed identification of f 0(1710) as composed primarily of the lightest scalar glueball.

Valence quark model from lattice QCD

We study the valence approximation in lattice QCD of hadrons where the cloud quark and antiquark are deleted by truncating the backward time propagation (Z graphs) in the connected insertion. Whereas the sea quarks are eliminated in the disconnected insertions. It is shown in this valence approximation that the ratios of isovector to isoscalar matrix elements (e.g. F A/DA and F S/DS ratios) in the nucleon reproduce the SU(6) quark model predications in a lattice QCD calculation. We also calculate how the hadron masses are affected. It is found that, within statistical errors, the nucleon and the Δ become degenerate in the quark mass range we have studied which ranges from the unambiguously to about 3 times the strange. The π and ρ also become degenerate in this range.

Improved error estimate for the valence approximation

We construct a systematic mean-field-improved coupling constant and quark loop expansion for corrections to the valence (quenched) approximation to vacuum expectation values in the lattice formulation of QCD. Terms in the expansion are evaluated by a combination of weak coupling perturbation theory and a Monte Carlo algorithm.

The scalar quarkonium spectrum and quarkonium-glueball mixing

We evaluate the valence approximation to the mass of scalar quarkonium and to the mixing energy between scalar quarkonium and the lightest scalar glueball for a range of different lattice sizes and quark masses. Our results support the identification of f 0(1710) as the lightest scalar glueball.

Error estimate for the valence approximation and for a systematic expansion of full QCD

We construct a systematic expansion for the lattice formulation of full QCD. The leading term is the valence (quenched) approximation. An error estimate for any truncation of this expansion is then obtained from a second expansion of full QCD, indexed by the number of virtual fermion loops included in each term.

Scalar quarkonium and the scalar glueball

Valence approximation glueball mass and decay calculations support the identification of f J (1710) as the lightest scalar glueball. An alternate glueball candidate is f 0(1500). I present evidence for the identification of f 0(1500) as ss quarkonium.