Alignment parameters

If the principal axis of the sample is moving during the experiment, then every frame has to be aligned individually while proceeding through the sequence of frames. In this case it is helpful if the interactive procedure remembers the last set of alignment parameters and the operator only invokes incremental corrections, whenever they become necessary. 

If Pi is constant, this is the equation of a straight line in the CliqH/Cliqi vs CliqH diagram, which is the foundation of widely used plots like Th/Ta vs Th aimed at identifying partial melting processes. These plots and alignment parameters were used... 

No significant alignment was observed i.e. the LIF-TPD signal-to-noise levels for J<12.5 placed limiting values of <0.1 on the alignment parameter i4 f (J). (i4 can vary from 2 forJ II n, to — 1 for J-Lfl avalueof zero describes an isotropic distribution.)... 

These equations enable us to compute aU the possible photofragmentation cross sections. An example of the use of these equations applied to the photodissociation of HOBr may be found in Ref. 84, and similar applications to electronically nonadiabatic photofragmentation of HF, DF, and HCl can be found in Refs. 76, 97, and 96. Time-dependent methods have been used most recently to compute vector correlations and alignment parameters [98,99]... 

Fig. 9 Critical values as functions of the flow alignment parameter X for various viscosities (a, b) and compressibilities (c, d). In the upper row we plot this dependence for a set of (isotropic) viscosities ranging from v, = 1 (thick solid line,) down to V = 10 3 (thick dashed line,). The lower row illustrates the behavior for varying layer compressibility Bo with Bo 3 f°r the thick solid curve and Bo = 100 for the thick dashed curve. In all plots the thin solid lines give the behavior for some intermediate values. For an interpretation of this behavior see the text...

Out of the five viscosities, only two (V2 and V3) show a significant influence on the critical values. In Fig. 8 we present the dependence of 9C and qc on an assumed isotropic viscosity (upper row) and on these two viscosity coefficients (middle and lower row). Since the flow alignment parameter X has a remarkable influence on these curves we have chosen four different values of X in this figure, namely X = 0.7, X = 1.1, X = 2, and X = 3.5. The curves for X < 1 and X > 3 for an isotropic viscosity tensor are very similar to the corresponding curves where only V2 is varied. In this parameter range the coefficient V2 dominates the behavior. Note that the influence of V3 on the critical values is already much smaller than that of V2. We left out the equivalent graphs for the other viscosity coefficients, because they have almost no effect on the critical values. For further comments on the influence of an anisotropic viscosity tensor see also Sect. 3.4. 

All the parameters we have discussed up to now caused variations in the critical values that did not select specific values of the considered parameter. In this aspect the situation is completely different in the case of the flow alignment parameter X. As shown in Fig. 9 there is a clear change in behavior for X 1 and X 3. The... 

Hence, the emission of Lj-MjMj Auger electrons is isotropic, while that of Auger electrons has an angular distribution coefficient proportional to the alignment parameter. Therefore, a measurement of (Lj-N Mj) is equivalent to a determination of the alignment of the photoionized state, and this quantity can be included in the list of observables in 2p photoionization of magnesium. 

Obviously, different expressions are obtained for the alignment parameters, because these quantities are defined with respect to different quantization axes. However, it is possible to express the alignment properties in a unified manner, e.g., j/2oliin the coordinate frame with the quantization axis along the photon beam direction. Since the alignment tensor s/2k is defined in connection with statistical tensors, equ. (8.115c), one can use the rotation properties in equ. (8.82) to change the reference axis for the representation from the z-axis to the x-axis ... 

This discussion underlines the importance of specifying the chosen reference axis when referring to the alignment parameter. However, in an actual experiment with arbitrary polarization it is the j A-parameter which is unique, as follows from equ. (3.28) ... 

From the / A value, one can then derive and discuss the alignment parameter for a conveniently selected type of polarization, using either equ. (8.127a) or equ. (8.127b). 

FIGURE 26 Nomogram of the dimensionless alignment parameter A > as a function of laser intensity, field strength, and polarizability anisotropy. [Reproduced with permission from Freidrich, B., and Herschbach, D. R. (1995). J. Phys. Chem. 99,15686. Copyright American Chemical Society.]... 

Dubs, R.L., Dixit, S.N. and McKoy, V. (1986). Extraction of alignment parameters from circular dichroic photoelectron angular distribution (CDAD) measurements, J. Chem. Phys., 85, 6267-6269. 

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