Angular correlation curve

Fig. 7.21. Angular correlation curves for mixtures of O2 and CI2 gases with an overall pressure of 120 atmospheres, (a) Pure O2, (b) O2 with 0.02 atmospheres of Cl2, (c) O2 with 0.05 atmospheres of CI2, (d) 02 with 0.2 atmospheres of CI2 and (e) O2 with 1 atmosphere of CI2. Goldanskii and Mokrushin (1968) attributed the components labelled Wi, W2 and W3 to the annihilation of thermalized para-positronium atoms (Wi, the narrow component), the annihilation of free positrons in O2 (W2) and the annihilation of positrons in the PsCl compound (W3). The intensity of the last, i.e. W3, grows progressively with the addition of CI2 to the O2 buffer.

One detector is held stationary and the other is rotated about the sample axis the coincidence count rate is recorded by the scaler at each angle chosen. A typical time required to obtain an angular correlation curve with good statistics and with an angular resolution of 10 mr is lOOh. 

The data analysis chosen by these authors departs from that used by Mogensen and others [17, 18], who fit each ID angular correlation curve to a set of Gaussian functions. The minimum number of Gaussians is used to achieve a good fit, and the width of each is optimized. The momentum components of each 7-ray spectrum are then interpreted in terms of annihilation of core vs. valence electrons without appeal to a preconceived chemical model. The experiment-theory connection can be made if one has an adequate wave function in hand, for then the Doppler profiles or angular correlation curves can be calculated and compared to those measured. 

Figure 27.5 Typical angular correlation curves in metals (Al and Cu).

Figure 2 The decay of Cd-a commonly used PAC isotope (a) Cd decays by the successive emission of two y rays, and in PAC spectroscopy the hyperfine splitting of the intermediate nuclear level (7 = 5/2) is measured. The hyperfine splitting is shown magnified by about a factor of 10 in the circle to the left for the case of an axially symmetric EFG from the surrounding charge distribution (rj = 0, see the text), (b) The angular correlation between y and Y2 is shown the distance from the center to the curve is proportional to the probability of detecting Y2 at a given angle, 0, with respect to yi...

The next type of motion in the above theory corresponds to the overall reptational (sliding) motion of the polymer chain within its tube-like constraint. This motion affects the orientation of bonds, not only because the constraining tube is itself curved, but also because in places it may be sufficiently large to accommodate tight loops of chain. As a particular bond is pulled past the extremity of a loop, it may reverse its direction completely. The loss of angular correlation B t) which results is not exponential, and is therefore not strictly describable by a correlation time. Instead,... 

For the continuous curve the angular correlation is related to the relative orientation between the unit vector tangent tt> die curve... 

Figure 9 Top Perturbed angular correlation of y-rays (PAC) spectrum of Cd-labeled Cd7MT from rabbit liver in 65% sucrose solution atO°C, pH 8.0. W(180°)AV (90°) is plotted versus delay time. The fully drawn curve represents least-squares fit to the spectrum. The bars indicate 1 standard deviation. The viscosity of the sucrose solution immobilized the protein within the time scale of the experiment. Bottom Resolution of the least-square fit of the spectrum into a low frequency, coi = 116 MHz (dashed line) and a high frequency component CO2 = 579 MHz (stippled line). Adapted from [81] with permission from the American Chemical Society, copyright 1982.

Fig. 1.11. The normalized angular momentum correlation function Kj(t)/Kj(0) at k — 0.25 in differential (curve a), integral (curve b) and impact (curve c) theories.

The 2 angular-distribution parameters show somewhat more molecule-to-molecule variation, but are essentially still quite similar to one another. They also display low energy structures that readily correlate with the noted features in the cross-section curves, and the variations are mainly confined to changes in the relative intensity of these. Much bigger differences are, however, found in the calculated chiral parameters, though here as well there is a common... 

Figure 5. Dry film thickness versus angular speed correlation [Equation 5] at fixed values of solvent evaporation parameters. Different curves result from different values of and this shows the non-uniqueness of thickness versus speed correlations.

It is instructive to compare the SCF three-body interaction, represented by the solid curve in Fig. 5.21, with the induction energy, with which there is a tendency to approximate it in the literature. In this context, it should be noted that the induction curve is far too attractive, by a factor of more than 2 in the vicinity of 20°. Other characteristics of its shape differ from the full SCF curve or deformation energy in Fig. 5.21 as well. The three-body forces at the correlated MP2 level are very small in magnitude, and insensitive to angular characteristics of the trimer. Most of these conclusions have been verified by later calculations and by symmetry-adapted perturbation theory calculations, although there were a number of discepancies as welF. The issue is not entirely closed. 

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