Coincidence width

Figure Bl.10.8. Time spectrum ftom a double coincidence experiment. Tln-ough the use of a delay in the lines of one of the detectors, signals that occur at the same instant in botii detectors are shifted to tlie middle of the time spectrum. Note the unifonn background upon which the true comcidence signal is superimposed. In order to decrease the statistical uncertainty in the detemiination of the true coincidence rate, the background is sampled over a time Aig that is much larger than the width of the true coincidence signal. Ax.

It should be remembered, however, that a linear relationship between T and n is only valid within the limits of binary impact theory. Its restrictions have already been discussed in connection with Fig. 1.23, where the straight line drawn through zero corresponds to relation (3.46). The latter is acceptable within the whole region of the gas phase up to nearly the critical point. Therefore we used Eq. (3.46) to plot experimental data in Fig. 3.8. The coincidence of maxima in theoretical and experimental dependence Aa)i/2(r) is rather good, as it is achieved by choice of cross-section (3.44), which is the only fitting parameter of the theory. Moreover, within the whole range of the gas phase the experimental widths do not fall outside the narrow corridor of possible values established by the theory. The upper curve corresponds to strong collisions and the lower to the weak collision limit. As follows from (3.23), they differ by a factor... 

The values of the half-widths of the components of the rotational absorption spectrum of HC1, dissolved in various noble gases, are borrowed from [291]. In order to make this example obvious, a continuous curve is drawn through the calculated points. Comparison between experimental data and calculated results demonstrates, in line with the qualitative agreement, a good numerical coincidence of the observed. /-dependence of the half-widths of the rotational lines with the theoretical one in the case of HC1 dissolved in Kr and Xe. This allows one to estimate the model parameters for these systems dispersion of the potential... 

Here U is the orientation of vector u before the collision. This only has physical sense for angle S = arccos ( ), which is an even argument of the function ip. This means that, as a result the collision vector u may be oriented inside a cone, whose axis coincides with the position of A characteristic value of conical angle S depends on the width of function ip. 

Thus, the region 2100-1830 cm 1 can be covered. This allows us to monitor CO(v,J) by resonance absorption and various M(CO)n [n = 3-6] as a result of near coincidences between the CO laser lines and the carbonyl stretching vibrations of these species. The temporal response of the detection system is ca. 100 ns and is limited by the risetime of the InSb detector. Detection limits are approximately 10 5 torr for CO and M(CO)n. The principal limitation of our instrumentation is associated with the use of a molecular, gas discharge laser as an infrared source. The CO laser is line tuneable laser lines have widths of ca. lO cm 1 and are spaced 3-4 cm 1 apart. Thus, spectra can only be recorded point-by-point, with an effective resolution of ca. 4 cm 1. As a result, band maxima (e.g. in the carbonyl stretching... 

Fig. 5.3. Energy band-structure diagram (in eV) of Ni/ZnO support and pre-(post-)chemisorbed hydrogen adatom level at e0(e ). VB (shaded) and CB of ZnO are of width 6. Fermi level (e/), which coincides with lower edge of CB, is taken as zero of energy. 6-layer Ni film has 6 localized levels lying between band edges (dashed lines), which just overlap ZnO energy gap. Reprinted from Davison et al (1988) with permission from Elsevier.

Similar information as in Fig. 3.4 is given in Fig. 3.17 which plots surface charge (due to protonation or deprotonation vs -ApH (= pH - pHpzc) for three oxides. Within a certain band width these curves coincide. 

Temperature congruence for the double layer on rutile in the presence of the indicated concentrations of KN03. Between 5 and 50° C all data coincide within the band width. 

Present M sbauer Studies of Natural Pyroxenes and Olivines. Table IX gives the major element chemical compositions of the silicate minerals examined in this study. Table X compares the Mossbauer parameters of these minerals, while Figures 9-13 show representative Mossbauer spectra. Fayalite (Figure 9) is the only olivine in this group. The two lines are, however, somewhat broadened (0.35 and 0.39 mm./ sec.) compared with the width of natural iron foil lines observed with our source (0.24 mm./sec.) and suggest the near coincidence of two quadrupole-split doublets resulting from Mi and M2 sites. Analysis of this "two-line spectrum into a four-line spectrum in the manner described by Evans et al (11) could possibly yield parameters for the two iron sites, but this was not undertaken since both lines appear symmetric. The "two-line quadrupole splitting of 2.78 mm./sec. is somewhat smaller... 

Fig, 26. Experimental dispersion curve of the Kr monolayer and measured line width broadening As of the Kr creation phonon peaks. The solid line in the dispersion plot is the clean Pt(lll) Rayleigh phonon dispersion curve and the dashed line the longitudinal phonon bulk band edge of the Pt(l 11) substrate, both in the r Mn azimuth which is coincident with the r Kk, azimuth. 

The width of the image can be deduced using this simple idea of contrast being formed when the misorientation around the defect exceeds the perfect crystal reflecting range. We consider the case of a screw dislocation nmning normal to the Bragg planes, where the line direction / coincides with the diffraction vector g. The effective misorientation at distance r from the core is =bH r (8.41)... 

Figure 5.13 shows the correlation function for sensors that are separated by a fixed distance equal to L. The inner sensor moves throughout the field and its position is denoted by y, as shown in the sketch. The sensor location is normalized by the standard deviation of the time-averaged profiles (see Fig. 5.7). With this scaling, the profiles at the four downstream locations are coincident, which suggests that the integral length scale is the correct scaling length for the sensor separation and that the sensor location is properly scaled by the width of the time-averaged plume.

If e t) corresponds to sufficiently slow rates of interruption/modulation v, the spectrum of Ffco) is much narrower than the interval of change of G( ) around , the resonance frequency of the system. Then Ffco) can be replaced by 8 co), so that the spectral width of G plays no role in determining R, and we may as well replace G(a> mf) by a spectrally finite, flat white-noise) reservoir, that is, take the Markovian limit. The result is that Eq. (4.49) coincides with the GR rate, Eq. (4.35) (Figure 4.4a) ... 

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