Alignment angle-dependent tensor

Introducing normalized parameters, namely, the Auger decay parameter ak and the angle-dependent alignment tensor s kK Jk, 0 Ox) of the photoionized intermediate hole-state J, both defined for k — even and k < 2[Pg.356]

Since the discovery of the nuclear Overhauser effect (NOE, see previous section) [4, 5] and scalar coupling constants [36, 37] decades ago, NMR-derived structure calculations of biomolecules largely depended on the measurement of these two parameters [38]. Recently it became possible to use cross-correlated relaxation (CCR) to directly measure angles between bond vectors [39] (see also Chapt 7). In addition, residual dipolar couplings of weakly aligned molecules were discovered to measure the orientation of bond vectors relative to the alignment tensor (see Sect 16.5). Measurement of cross-correlated relaxation was described experimentally earlier for homonuclear cases [40, 41] and is widely used in solid-state NMR [42 14]. 

In order to derive information on dynamical quantities from such a coincidence experiment, one has to select angles d at which other components of the alignment tensor also contribute, because then the different dependences on the dipole matrix elements, including their relative phases, are involved. As can be seen from... 

In an isotropic medium, the value of a physical property can be represented by a scalar quantity however, for an anistropic medium the value depends on the measuring angle relative to the direction of alignment designated as the director. The properties of a nematic must be represented by a tensor which in the case of a uniaxial nematic for a property X can be conventionally expressed by Xi=X2=X2 and X-i=X which are, respectively, the values of the property X perpendicular and parallel to the director ... 

Equations (14)-(17) apply to isotropic media. In an orientationally ordered material the extinction coefficient becomes dependent on the angle between the alignment axis and the polarization direction of the incident light, and has the characteristics of a second rank tensor. At a microscopic level, the optical absorption depends on the angle between the molecular transition dipole moment iJ.j for the particular absorption band, and the electric field of the light wave. Restricting attention to uniaxial systems, an effective order parameter (5op) for optical absorption can be defined as ... 

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