Particle width

Eniistiin and Turkevichf prepared SrS04 (p = 3.96 g cm-3) precipitates under conditions that resulted in different particle sizes. Particle sizes were characterized by electron microscopy, and solubilities were determined at 25°C by a radiotracer technique. In the following data the supersaturation ratios are presented for different preparations, each of which is characterized by an average particle width and a minimum particle width ... 

Figure 11 Rate of spreading as a function of particle width for iridium/graphite in at 1238...

It is important to recognise the limitations of formula (6.20), which are as follows (i) the formula applies to a single, isolated resonance (ii) the background continuum must be flat, or vary very little over the width of the resonance (iii) the radiative width must be much smaller than the particle width and (iv) there must be no other channel for particle broadening than the one considered. 

Typically, the vanishing particle width occurs at e = —pTlT1/2 which is related to the width of the broad intruder and the strength of the coupling. This relationship, and the associated effects are discussed in section 8.29. 

More generally, one finds many cases where the particle widths of resonances in a Rydberg series, instead of decreasing in proportion to the spacings between successive members, fluctuate dramatically. An example will be given in section 8.33. 

We also begin in the elastic scattering approximation, which has the advantage of being very simple in this approximation, radiative channels are neglected, and all the observed spectral fluctuations are due to particle widths, i.e. to the decay of the excited state via autoionising channels. Radiative widths are included at a later stage, once the basic effects have been illustrated. 

In principle, the particle width is not the only one which needs to be considered, especially if the autoionisation width is small. Narrow autoionising lines are well suited for study by laser spectroscopy. Since they imply the existence of long lived excited states, they can be investigated directly in atomic beams (see, e.g., [396]). However, the earliest examples appear to have been found by Paschen [397], White [398] and Shenstone [399] - the pioneer to whom we owe the very name autoionisation. In specific cases, where vanishing widths may occur (see section 8.29) or,... 

We use Fano s notation within our K-matrix and, for consistency with the literature [380] emphasise the fact by an additional subscript F let rBF and Ebf be, respectively, the particle width and resonance energy of the giant resonance. 

We follow the treatment of [375, 377]. As in most cases in this chapter so far, the analysis considers only particle widths strictly, it applies only to elastic scattering and may or may not extend to photoionisation, depending on the case considered. It does, however, even in this simple form, exhibit all the main features of the problem. 

With just one particle channel open, one can also show that the q reversals occur at two poles, one of which corresponds to a zero in the particle widths, while the other does not. Thus, one of the poles only is associated with a vanishing width (cf section 8.29 and the spectra in fig. 8.18). 

The cancellation of particle widths of resonances as a result of an intruder state disturbing a sequence of levels is a well-known effect in nuclear physics [425]. In atomic physics, under suitable conditions, the particle width may go to zero [426] A good example is shown in fig. 8.21, where line narrowing in a doubly-excited series of autoionising resonances is observed, as a result of a perturbation by an intruder state. 

The vanishing particle width is perhaps a surprise, since it involves stabilising a level in the continuum by introducing a further perturbation. More... 

Fig. 8.21. The vanishing particle width effect in a doubly-excited series of the Ca spectrum. Note the narrowing of the n — 6 member, although the remainder of the series members are broad. The perturber (hardly visible on account of its breadth and weakness) is indicated by an X in the figure (after U. Griesmann et al. [390]).

Under similar circumstances, particle widths 7 follow the distribution ... 

Taken together, we have observed that most particles stop increasing or decreasing in thickness when they reach a certain height, with an apparent dependence on particle width. This suggests that mechanical factors play a significant role in these exchange reactions, and also most likely in trioctahedral mica to vermiculite transformations. 

Only reactions in which particle widths are known are listed and not all resonances are included. The radiation widths are for thermal neutron capture at an excitation equal to the neutron binding energy. The figures are taken mainly from references [15], [24] and [32]. 

Photograph 6-1 One s method for apparent birefringence of alite in powder mount. Crystal length-to-width ratio = approximately 2 1. Ono measures particle width. Other observers, the present writer included, measure crystal width. (S A6616)... 

The factor of 0.75 in the denominator of Eq. 7 for alite birefringence was statistically derived to account for deviations between true and observed birefrin gences of an alite crystal in which the X vibration direction is not exactly parallel to the microscope stage and the Y and Z directionsarenotpreciselyknown. In order to minimize this deviation, which lessens the birefringence, a crystal thickness-to particle width ra tio of 3/4 is assumed (Ono, letter, 1978). The clinker particle, in this case, was illustrated to contain only part of an alite crystal. 

The aspect ratio (maximum straight-line particle length divided by maximum straight-line particle width) is plotted in (D). 

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