Halfwidth parameter

The pressure and temperature dependence of the halfwidth parameter 7. is given by... 

The most recent calculations, however, of the photoemission final state multiplet intensity for the 5 f initial state show also an intensity distribution different from the measured one. This may be partially corrected by accounting for the spectrometer transmission and the varying energy resolution of 0.12, 0.17, 0.17 and 1,3 eV for 21.2, 40.8, 48.4, and 1253.6 eV excitation. However, the UPS spectra are additionally distorted by a much stronger contribution of secondary electrons and the 5 f emission is superimposed upon the (6d7s) conduction electron density of states, background intensity of which was not considered in the calculated spectrum In the calculations, furthermore, in order to account for the excitation of electron-hole pairs, and in order to simulate instrumental resolution, the multiplet lines were broadened by a convolution with Doniach-Sunjic line shapes (for the first effect) and Gaussian profiles (for the second effect). The same parameters as in the case of the calculations for lanthanide metals were used for the asymmetry and the halfwidths ... 

Thus even approximate analytical solutions are often more instructive than the more accurate numerical solutions. However considerable caution must be used in this approach, since some of the approximations, employed to make the equations tractable, can lead to erroneous answers. A number of approximate solution for the hot spot system (Eq 1) are reviewed by Merzhanov and their shortcomings are pointed out (Ref 14). More recently, Friedman (Ref 15) has developed approximate analytical solutions for a planar (semi-infinite slab) hot spot. These were discussed in Sec 4 of Heat Effects on p H39-R of this Vol. To compare Friedman s approximate solutions with the exact numerical solution of Merzhanov we computed r, the hot spot halfwidth, of a planar hot spot by both methods using the same thermal kinetic parameters in both calculations. Over a wide range of input variables, the numerical solution gives values of r which are 33 to 43% greater than the r s of the approximate solution. Thus it appears that the approximate solution, from which the effect of the process variables are much easier to discern than from the numerical solution, gives answers that differ from the exact numerical solution by a nearly constant factor... 

As described in the section on nonlinear absorption, the transmission of a pulse which is short compared to the various molecular relaxation times is determined by its energy content. A measurement of the energy transmission ratio will then give the peak intensity of the pulse when its pulse shape is known 44>. In fact, the temporal and spatial pulse shape is of relatively little importance. Fig. 11 gives the energy transmission as a function of the peak intensity I [W/cm2] for the saturable dye Kodak 9860 with the pulse halfwidth as a parameter. It is seen that this method is useful in the intensity region between 10 and 1010 MW/cm2 for pulses with halfwidths greater than 5 to 10 psec. Since one can easily manipulate the cross-section and hence the intensity of a laser beam with a telescope, this method is almost universally applicable. 

The collision halfwidth for a given transition is a function of temperature and the broadening species. In the present diode laser experiments, the temperature (and hence AVp) is known so that it is straightforward to infer values for the parameters a and AVq, and hence 2y, from the observed absorption linewidths. 

Figure 11.2. Dispersion mode (first-derivative) Lorentzian signal. The position of a dispersion mode signal is where the line crosses its baseline the halfwidth is the horizontal distance between the maximum and the minimum of the signal curve. Compare this signal with the absorption mode Lorentzian signal in Figure 3.18 both were plotted using the same parameter values (see review problem 11.5).

This potential amount of information can only be supplied if each channel produces information which is independent of that supplied by other channels (Fig. 3.3-13a Schrader et al., 1981). However, spectra consist of bands in which neighboring data points are strongly correlated. Spectral lines may be described by Gaussian or Lorentzian functions, in which parameters define the position, intensity and halfwidth. The information content of a spectrum therefore consists of these significant parameters of all lines or unresolved bands (Fig. 3.3-13b). This makes it possible to store spectra in a reduced form. 

In Fig. 49 the band center frequency is plotted against the potential for the 1220-1280 cm mode at both pH values. Potentials in this plot are referred to the normal hydrogen electrode. The wavenumbers for the band centers coincide at both pHs, giving a common slope of 112cm V. Other parameters, such as the halfwidths measured at the potential of maximum adsorption, are also similar (36.5 and 37.5 cm at pH 2.8 and 0.23, respectively). These properties, which are a... 

The parameter d represents the initial level of M(t), and c represent the halfwidth between initial and equilibrium levels of M(t). The product ac is the slope... 

In the Dubinin-Stoeckli (DS) method, a Gaussian pore size distribution is assumed for 7(B) in Eq. (39), based on the premise that for heterogeneous carbons, the original DR equation holds only for those carbons that have a narrow distribution of micropore sizes. This assumption enables Eq. (39) to be integrated into an analytical form involving the error function [119] that relates the structure parameter B to the relative pressure A = -RT ln(P/Po)-The structure parameter B is proportional to the square of the pore halfwidth, for carbon adsorbents that have slit-shaped micropores. 

The parameters /min and /max are the lower and upper limits, respectively, for the inicropore size range. The lower limit / min is for a pore that has the same adsorption potential energy as that of a single lattice layer or for a pore that has zero potential energy. The volume of pores having sizes between these two values of / min is very small, and hence either value of / mm will suffice. The upper limit /-max is cut off at 3.5a for convenience, since the adsorption potential energy in pores with halfwidths larger than this value is effectively zero,... 

It is well known that the polydispersity of crystallites can be characterized by the halfwidth of the melting peaks provided by the DSC method. The changes of this parameter for the two components are illustrated in Fig. 34. 

Fig. 13. The structural parameters of water with density and temperature, (a) The number of water molecules at the nearest neighbors n, (b) interatomic distance r, (c) halfwidth at half-height a of the peaks 1 (O) and II (A) and their sum ( ) [54].

The halfwidth = ho) of the saturation-broadened line increases with the saturation parameter So at the line center coo If the induced transition rate at coo equals the total relaxation rate R, the saturation parameter 5o = [B 2p coo)VR becomes 5o = 1, which increases the linewidth by a factor /2, compared to the unsaturated linewidth Scuq for weak radiation fields (p 0). 

Finally, the apparatus function (see Section 6.3) should be known because it yields the apparatus-caused smearing of the thermal effect and the time constant. The apparatus function is obtained by generating a heat pulse in the sample and dividing the obtained heat flow rate function by the peak area (normalization) (see Section 6.3.4 and Figure 9.4). Such parameters as the sample mass, the magnitude of the heat pulse, and occasionally the heating rate are to be varied. If all the normalized curves obtained in this manner are identical, there is one single apparatus function, and the measured heat flow rate function of the calorimeter can be desmeared (see Section 6.3). The halfwidth of the apparatus function yields approximately the time constant of the calorimeter. 

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