Gluon-field contribution in QCD sum rules for the magnetic moments of the nucleons

The Wilson coefficient corresponding to the gluon-field strength GμνGμν is evaluated for the nucleon current correlation function in the presence of a static external electromagnetic field, using a regulator mass Λ to separate the high-momentum part of the Feynman diagrams. The magnetic-moment sum rules are analyzed by two different methods and the sensitivity of the results to variations in Λ are discussed.

Charge distribution in and dipole moments of some aliphatic alcohols

Using the treatment of Smith, et al.,1 charge distributions in several aliphatic alcohols and consequently their dipole moments have been evaluated. The dipole moments of trichloroethanol (2.04 D) and 1,3-dichloropropan-2-ol (2.11 D) have been measured in benzene solution at 35°. The results of evaluation and measurements are interpreted in terms of the occurrence of intramolecular interaction between the hydroxyl hydrogen and an acceptor atom X (halogen or oxygen) at the β-carbon atom.

Charge distribution in and electric moments of some aliphatic acids

Using the treatment of Smith et al., charge distribution in and consequently the dipole moments of several aliphatic acids have been evaluated. The electric moments of chloro (2·86 D), bromo (2·90 D), iodo (2·06 D) and trichloro (3·00 D) acetic acids have been measured in dioxan solution at 35°. The experimental values are compared with those calculated theoretically and discussed in terms of the various possible structures.

The dipole moments and molecular structure of substituted acetamides

Thioacetamide has a dipole moment substantially higher than the vector sum of the normal characteristic moments of its constituent bonds. However, the effect can reasonably be accounted for on the scheme of alterations in charge distribution and hence of bond moments proposed by Smith, Ree, Magee and Eyring. The same is probably true for chloroacetamide even though the problem of rotation about the C-C single bond renders the conclusion less certain. For cyanoacetamide, the observed moment cannot be accounted for satisfactorily on this basis.

Charge distribution, dipole moments and molecular structure of some organogermanium compounds

Formal charge distributions in, and the electric dipole moments of, a few simple organogermanium compounds have been evaluated by the method of R. P. Smith et al. [J. Amer. Chem. Soc., 73(1951) 2263]. The difference between the experimental and calculated moments in the case of alkylhalogermanes is explained in terms of the pπ—dπ back bonding effect outweighing the electron releasing effect. In unsaturated compounds, the differences are attributed to possible mesmeric effects involving the expansion of the germanium valence shell.

Dipole moments and structure of organophosphine and organoarsine compounds

The formal charge distributions in and the dipole moments of some organophosphines and arsines have been calculated, and the dipole moments of (p-chlorophenyl)dichlorophosphine (2.28 D) and (p-bromophenyl)dichlorophosphine (2.04 D) have been determined in benzene at 35° C. The differences between the observed and the calculated moments are explained in terms of dπ---pπ back-bonding and hyperconjugative effects in alkylhaloarsines. The mesomeric effects operating in the aromatic systems are evaluated by comparing the moments with those for the corresponding aliphatic systems. In unsaturated compounds the differences are attributed to mesomeric effects involving the expansion of arsenic valence shell.

Charge distribution, dipole moments and infrared spectra of some thiol and thio acids

The dipole moments of thioglycollic (2.28 D), β-mereaptopropionic (2.25 D), thiomalic (2.47 D), malic (3.12 D), and dithiodiacetic (3.17 D) acids have been measured in dioxan at 35° C. Using the scheme of Smith, Ree, Magee and Eyring, the formal charge distribution in and hence the electric moments of these acids have been evaluated, compared with the theoretical moments, and discussed in terms of their various possible structures. Infrared spectra of these acids (liquid and nujol mull) indicate association through hydrogen bonding. These bonds are broken in solution. © 1969.

Charge distribution, dipole moments and infrared spectra of some thiol and thio acids

The dipole moments of thioglycollic (2.28 D), β-mereaptopropionic (2.25 D), thiomalic (2.47 D), malic (3.12 D), and dithiodiacetic (3.17 D) acids have been measured in dioxan at 35° C. Using the scheme of Smith, Ree, Magee and Eyring, the formal charge distribution in and hence the electric moments of these acids have been evaluated, compared with the theoretical moments, and discussed in terms of their various possible structures. Infrared spectra of these acids (liquid and nujol mull) indicate association through hydrogen bonding. These bonds are broken in solution.

Dipole moments and structure of some organoselenium compounds

The dipole moments of di-p-tolyl selenide (1.74 D), di-p-tolyl selenide (1.00 D), di-m-tolyl selenide (1.66 D), di-p-anisyl selenide (2.35 D) and di-p-tolyl selenium dichloride (3.69 D) have been determined in benzene at 35°. The results are analysed in terms of mesomeric effects and internal rotation in these systems. The dipole moments of a few aliphatic selenides have been theoretically evaluated.

Electric dipole moments and molecular structure of aliphatic nitro compounds and oximes

Using the treatment of Smith et al. charge distributions in and consequently the dipole moments of some aliphatic nitro compounds and oximes have been evaluated. The mesomeric moment derived as a difference between the calculated and the observed values gives a clear picture as to how the positive (+M) and the negative (-M) mesomeric effects operate in such systems.

Lattice vibrations and specific heat of zinc blende

The dispersion relations, frequency distribution function and specific heat of zinc blende have been calculated using Houston's method on (1) A short range force (S. R.) model of the type employed in diamond by Smith and (2) A long range model assuming an effective charge Ze on the ions. Since the elastic constant data on ZnS are not in agreement with one another the following values were used in these calculations: {Mathematical expression}. As compared to the results on the S. R. model, the Coulomb force causes 1. A splitting of the optical branches at (000) and a larger dispersion of these branches; 2. A rise in the acoustic frequency branches the effect being predominant in a transverse acoustic branch along [110]; 3. A bridging of the gap of forbidden frequencies in the S. R. model; 4. A reduction of the moments of the frequency distribution function and 5. A flattening of the Θ- T curve. By plotting (Θ/Θ0) vs. T., the experimental data of Martin and Clusius and Harteck are found to be in perfect coincidence with the curve for the short range model. The values of the elastic constants deduced from the ratio Θ0 (Theor)/Θ0 (Expt) agree with those of Prince and Wooster. This is surprising as several lines of evidence indicate that the bond in zinc blende is partly covalent and partly ionic. The conclusion is inescapable that the effective charge in ZnS is a function of the wave vector {Mathematical expression}.

Dipole moments and structure of organophosphine and organoarsine compounds

The formal charge distributions in and the dipole moments of some organophosphines and arsines have been calculated, and the dipole moments of (p-chlorophenyl)dichlorophosphine (2.28 D) and (p-bromophenyl)dichlorophosphine (2.04 D) have been determined in benzene at 35° C. The differences between the observed and the calculated moments are explained in terms of dπ---pπ back-bonding and hyperconjugative effects in alkylhaloarsines. The mesomeric effects operating in the aromatic systems are evaluated by comparing the moments with those for the corresponding aliphatic systems. In unsaturated compounds the differences are attributed to mesomeric effects involving the expansion of arsenic valence shell.

Dipole moments and structure of organophosphine and organoarsine compounds

The formal charge distributions in and the dipole moments of some organophosphines and arsines have been calculated, and the dipole moments of (p-chlorophenyl)dichlorophosphine (2.28 D) and (p-bromophenyl)dichlorophosphine (2.04 D) have been determined in benzene at 35° C. The differences between the observed and the calculated moments are explained in terms of dπ---pπ back-bonding and hyperconjugative effects in alkylhaloarsines. The mesomeric effects operating in the aromatic systems are evaluated by comparing the moments with those for the corresponding aliphatic systems. In unsaturated compounds the differences are attributed to mesomeric effects involving the expansion of arsenic valence shell.

Fast computation of Legendre and Zernike moments

This paper presents recursive algorithms for fast computation of Legendre and Zernike moments of a grey-level image intensity distribution. For a binary image, a contour integration method is developed for the evaluation of Legendre moments using only the boundary information. A method for recursive calculation of Zernike polynomial coefficients is also given. A square-to-circular image transformation scheme is introduced to minimize the computation involved in Zernike moment functions. The recursive formulae can also be used in inverse moment transforms to reconstruct the original image from moments. The mathematical framework of the algorithms is given in detail, and illustrated with binary and grey-level images.

Expansions of tau hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling alpha(s) and other QCD parameters from the hadronic decays of the tau lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher-order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called ``reference model,'' including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.