Population as a function

FIGURE 18. (a) C—S bond overlap population as a function of molecular geometry (b) the same for the S—O BOP. (c) Total charge on sulphur, and (d), p-part of the charge. The black dots are the values for the S02 molecule itself. 

Cold plasma with reduced temperature is another way to cope with the most annoying problems from interferences, even in the case of low-resolution instruments [394], The effect consists of weaker ionisation conditions coming close to chemical ionisation [395]. In particular, argides are reduced by orders of magnitude in comparison to conventional ICP operation. However, at lower plasma temperatures, evaporation of analyte material is considerably reduced. Reducing the plasma temperature also has a dramatic effect on the ionisation (and therefore sensitivity) of many elements. Table 8.65 shows the ion population as a function of plasma temperature and ionisation potential. As a result, the cold plasma technique is only advantageous for a rather small number of elements and applications. 

Table 8.65 Ion population (%) as a function of plasma temperature and ionisation potential...

The limits of the allowable values around the hypothesized values close in on it as n increases. This behavior is shown in Figure 20-1. If, in fact, we were to plot the mean of the population as a function of n, it would be a horizontal line, just as shown. The mean of the actual data would vary around this horizontal line (assuming the null hypothesis was correct), at smaller and smaller distances, as n increased. 

Figure 8. Li + H2 Ground-state population as a function of time for a representative initial basis function (solid line) and the average over 25 (different) initial basis functions sampled (using a quasi-classical Monte Carlo procedure) from the Lit2/j) + H2(v — 0, j — 0) initial state at an impact parameter of 2 bohr. Individual nonadiabatic events for each basis function are completed in less than a femtosecond (solid line) and due to the sloped nature of the conical intersection (see Fig. 7), there is considerable up-funneling (i.e., back-transfer) of population from the ground to the excited electronic state. (Figure adapted from Ref. 140.)...

Fig. 7.2. Calculated [40] relative ion population as a function of ion charge state in solid Ti heated at temperatures ranging from 10 to lOOeV. Also shown in the same plot is the separation energy of the 2p-ls transitions as a function of the ion charge. Higher ionization stages from B-like Ti to O-like Ti are expected to emit in the range between 4,550 and 4,750 eV...

In order to study the origin of the deviations observed, we first consider the statistical convergence of the QCL data. As a representative example. Fig. 14 shows the absolute error of the adiabatic population as a function of the number of iterations N—that is, the number of initially starting random walkers. The data clearly reveal the well-known 1/Vn convergence expected for Monte Carlo sampling. We also note the occurrence of the sign problem mentioned above. It manifests itself in the fact that the number of iterations increases almost exponentially with propagation time While at time t = 10 fs only 200 iterations are sufficient to obtain an accuracy of 2%, one needs N = 10 000 at t = 50 fs. 

If the variation of the population as a function of delay time features damped oscillations with Rabi frequency, it is expected to see the Rabi splitting. Can this be observed ... 

Fig. 11.14 Field ionization signal when the Xe 27f state is populated as a function of ionizing field strength (a) without NH3, (b) with 10 5 Torr NH3. The resonant rotational NH3 transitions are indicated beneath each field ionization feature (from ref. 63).

Figure la. Fractional populations as a function of rotational quantum number F2(3) is pumped. A2X state (O),Ft levels, (9),F, levels. 

Fig. 8.10 Control over dimethylallene enantiomer populations as a function of detuning A i1 for various laser powers. First column corresponds to probabilities of L (dot-dash curves) and" D (solid curves) after a single laser pulse, assuming that the initial state is all L. Second column is similar, but for an initial state, which is all D. Rightmost column corresponds toy probabilities of L and D after repeated excitation-relaxation cycles, as described in the text (This is a corrected version of Fig. 2, Ref. [260].) i g...

As mentioned above, by keeping the population of the intermediate resonance low (as is the case in Fig. 11,10), the spontaneous emission losses are effectively i eliminated. Figure 11.11 shows the intermediate level population as a function of four different pulse intensities. The reaction probability for all plotted intensities isj near unity. However, it is evident that the intermediate state population throughout the process decreases with increasing pulse intensity. Thus, to avoid spontaneails j emission losses, high pulse intensities should be used. i ... 

Changes in four A-Ox bond overlap populations as a function... 

Change in Ti-Oz+ bond overlap population as a function of ferroelectric displacement of Ti and O along the z-axis... 

Mo—S Overlap Populations as a Function of the Sulfur-Fold Angle"... 

Fig. 5.3. Population as a function of temperature, p(T), corresponding to the conformations in which ligand is proximal to the heme iron. The proximal state population increases monotonically with temperature, indicating that the proximal state is stabilized by conformational entropy at temperatures greater than at least 268 K. This is borne out by the expression for the conformational entropy difference between the proximal and the distal states S = k ln[p/(l — p) + kT/ p( 1 — p)] dp/dT, where the second term is positive and the first term is positive for T > 268 K (p(T) >1/2)...

The progress of the GA structure solution calculation is assessed from the Evolutionary Progress Plot (EPP), which shows the best (Rmin) and average (Rave) values of Rwp for the population as a function of generation number. The EPPs for the a and / phases are shown in Fig. 4, from which it is clear that the GA structure solution calculation converges rapidly in both cases. 

The Mossbauer spectra of iron in numerous minerals have been studied, but a few examples will serve to illustrate this technique. In the rockforming silicate minerals, Mdssbauer spectroscopy has been used to study the oxidation state, spin state and coordination of iron, and its distribution between different sites in a structure. Thus, Fig. 2.46 (after Williams et al., 1971) shows the spectrum of an augite [essentially (Ca,Mg,Fe)2Si20J, the structure of which contains two kinds of sixfold-coordinate sites that may be occupied by iron (the Ml and M2 sites). The Mdssbauer spectrum can be fitted to three quadrupole doublets peaks 1 and 1 have parameter characteristic of Fe (in both Ml and M2 sites), peaks A and A have parameters characteristic of Fe in Ml, and peaks C and C of Fe + in the M2 sites. These assignments, based chiefly on comparisons with endmember compositions and related species, also enable estimates of site populations to be made on the basis of the areas under the peaks. Studies of the variation in site populations as a function of composition and thermal treatment have led to important advances in understanding intercrystalline order-disorder equilibria, as pioneered in the work of Virgo and Hafner (1970). 

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