Angular distributions isotropic

Evidently, correlation functions for different spherical harmonic functions of two different vectors in the same molecule are also orthogonal under equilibrium averaging for an isotropic fluid. Thus, if the excitation process photoselects particular Im components of the (solid) angular distribution of absorption dipoles, then only those same Im components of the (solid) angular distribution of emission dipoles will contribute to observed signal, regardless of the other Im components that may in principle be detected, and vice versa. The result in this case is likewise independent of the index n = N. Equation (4.7) is just the special case of Eq. (4.9) when the two dipoles coincide. 

Unpronounced polarization of regular C-H bonds such as methyl or ethyl groups does not lead us to expect the formation of dihydrogen bonds. Actually, an analysis of the Cambridge Structure Database [2] reveals numerous C-H- - -H-C contacts with H- - -H distances of 2.500 A or even more where the angular distribution is ideally isotropic. The latter is typical of nondirec-tional van der Waals interactions. The C-H and B-H bonds in the molecule l,3-bis(2,4,6-trimethylphenyl)imidazol-2-ylidene- BH3 are obviously more... 

One of the features of the derivation of the emission rate for y rays that we glossed over is that the angular distribution of the emitted radiation from a single state must be isotropic. The isotropy comes from the fact that the nuclei are oriented at random, and the process sums over all the internal magnetic substates and thus includes all... 

If we assume the angular distribution of the scattered neutrons is isotropic in the cm system, then the probability of a neutron scattering into and solid angle dfl, P(dCl), is a constant given by... 

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. 

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