Deviation Of Electron Density Research Articles

Electron Density in Long Carbon–Carbon Bonds

THE crystal structures of ammonium oxamate and lithium oxalate have been studied by X-ray diffraction methods. Three-dimensional intensity data were collected with a xenon-filled proportional counter using copper K α-radiation. Refinement of the three positional and six anisotropic vibrational parameters for each atom, including hydrogen, was carried out by the method of least squares; convergence occurred at R = 0.044 for ammonium oxamate and R = 0.060 for lithium oxalate. At this stage, three-dimensional FO–FC Fourier syntheses were computed. These are shown in the form of superimposed sections in Figs. 1a and b. Contours are drawn at intervals of 3σ, where σ is the root mean square deviation of electron density averaged over the whole unit cell.

Relation of turbulence theory to ionospheric scatter propagation experiments

Summary— After a brief historical introduction the author considers the statistical behavior of ionospheric scatter signals. The random fading of the signals is taken to be suggestive of a scatter process, and predictions as to amplitude distribution (Rayleigh) and as to space or time correlations, made on this basis, are found to be in fair agreement with empirical results. It is noted that no attempts have as yet been made to predict the correlation coefficients. The scattering of electromagnetic waves by turbulent irregularities is discussed next. The Born approximation (single scattering) is employed. This together with the far-field approximation leads to an expression for the received power in terms of the spectrum of mean square deviations in electron density. Neglecting polarization effects and assuming isotropy and homogeneity of electron density deviations within the common volume, the received power is given by where PR and PT are the received and transmitted powers, respectively, ro is the classical radius of the electron, AR and GR are the effective area and gain of the receiving antenna, b is the vertical depth of the scattering layer, R2 is the distance from the scattering volume to the receiver, θ is the angle through which the energy is scattered, λ is the radio wavelength, and Γ (k) is the spectral representation as a function of wave-number magnitude only of the contributions to the mean square deviations in electron density. It is noted that this expression is the only linkage, so far, between turbulence theory and the results of radio experiments. Caution is advised in applying it because of the unsubstantiated assumptions employed in its derivation.