Line intensities angular dependence

Fig. 4.15. Angular dependence of the fluorescence radiation emitted from a Co-layered Si substrate. The Co-Ka intensity is plotted semi-logarithmically for layers of different thickness (mm). The maxima forthe ultra-thin Co-layers are located at the critical angle of Si (dashed vertical line). They are shifted to the critical angle of Co (dotted vertical line) ifthe layer is more than 10 mm thick ([4.21], after Ref [4.41]).

The Clebsch-Gordan coefficients and the angular dependence functions needed to calculate the relative intensities of the hyperline lines for a f -> i transition with Ml multipolarity have already been given in Table 3.2 (p. 67) and discussed in detail in Section 3.7. In this appendix are listed other useful sets of coefficients for the cases... 

The angular dependence of the intensities of a quadrupole-split spectrum from a single crystal absorber allows one to determine the line associated with the 3/2- l/2 transition from the other line, and hence the sign of the princi-... 

Fig. 3.9.3. Angular dependence of the intensity of scattering for PAA. Circles give the experimental values of Chatelain and the line represents the theoretical variation. (After de Gennes. )...

The angular dependence of scattering depends upon the correlation distance a, while the intensity depends as well upon the mean-square density fluctuation, av A plot of against leads to a straight line having a slope... 

Fig. 14. Angular dependence of the reflected light intensity in the plane of incidence from a MgO reflectance standard (thin line) and an internal reflector in a guest-host cell (heavy line). Collimated white light is incident to both samples at -45 . Arrows denote specular reflection from front surface of display cell.

To calculate the relative intensities of absorption lines in a Mossbauer spectrum, one also has to take into account that the intensity of the emitted multipole radiation is not isotropic but has a certain angular dependence Fim 0) where 6 is the polar angle that the direction of observation encloses with the z-axis of the principal axis system (defined, e.g., by the direction... 

A simple calculation yields the values of the angular-dependent factors in the forbidden line positions, given by eqs. (14) and (15), corresponding to the maximum of intensity, which occurs, respectively, for 0= 0o, i.e. when... 

In practice, the calculation is confined to the transitions belonging to the central hyperfine sextet 1/2, m -1/2, m + i (m = 5/2, 3/2, 1/2, -1/2, —3/2, —5/2), since the non-central lines are much less intense as compared to the central lines because they have a stronger angular dependence. In fact, in glasses parameter distributions totally smear out all non-central transition lines since their resonant fields contain terms linear in D and E, which is not the case for the resonant fields for the central transition lines. 

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