Scattering vector description

Xab appears here as a universal parameter. However, it was found experimentally to depend on a number of factors [30-33] such as temperature, molecular weight, composition, inter-monomer distance (and therefore on the scattering vector Q), isotopic constitution, tacticity, microstructure, etc. These dependencies are shortcomings of the crude RPA description. The scattered intensity (macroscopic cross section d (Q)/d 2) is given by ... 

The molecular beam and laser teclmiques described in this section, especially in combination with theoretical treatments using accurate PESs and a quantum mechanical description of the collisional event, have revealed considerable detail about the dynamics of chemical reactions. Several aspects of reactive scattering are currently drawing special attention. The measurement of vector correlations, for example as described in section B2.3.3.5. continue to be of particular interest, especially the interplay between the product angular distribution and rotational polarization. 

In a Raman scattering experiment, the frequency, wave vector, and polarization of incident light (usually from a laser source) are known. Analysis of scattered light frequency, polarization, and relative intensity provides information on properties of elementary excitations in the material under study. General description of the Raman process as well as details of Raman instmmentation can be found elsewhere [108-110, 118]. 

The unit cell group description of the normal modes of vibration within a unit cell, many of which are degenerate, given above is adequate for the interpretation of IR or Raman spectra. The complete interpretation of vibronic spectra or neutron inelastic scattering data requires a more generalized type of analysis that can handle 30N (N=number of unit cells) normal modes of the crystal. The vibrations, resulting from interactions between different unit cells, correspond to running lattice waves, in which the motions of the elementary unit cells may not be in phase, if ky O. Vibrational wavefunctions of the crystal at vector position (r+t ) are described by Bloch wavefunctions of the form [102]... 

The potentials (94) and (95) are already quite similar to the leading effective Hamiltonians that have been used so far in one- and four-component calculations of molecular parity violating eflFects. We have assumed above that the fermions are elementary particles. The effective potentials may, however, also be applied for the description of low energy weak neutral scattering events, in which heavy non-elementary fermions like the proton and the neutron or even entire atomic nuclei are involved, provided that properly adjusted vector and axial coupling coefficients py and for non-elementary fermions are used. 

Since the atomic nucleus consists of nucleons which themselves consist of quarks, in principle the wavefunction of the quarks within the nucleons is required in order to determine appropriate equivalent potentials for the interactions between an electron and the nucleons within the nucleus. The models currently available for the calculation of the substructure of the nucleons, however, allow only for an approximate description of the wavefunctions of the quarks (see for instance [74] for a comparison of a few of these models). One may on the other hand introduce nucleon field operators, which replace the quark field operators in the scattering matrix element (equation (66)), and relate the corresponding vector and axial coupling coefficients in the resulting equivalent potential to empirical data. 

Surface ionization studies of Reaction 1 necessarily involved the detection of the much heavier product, KBr, which was constrained by the conservation of momentum to scatter close to the center of mass (c.m.). In this case, the small recoil velocity of the product KBr from the c.m. is masked by the spread of the c.m. velocity vectors arising from the distribution of parent beam velocities. Thus, it becomes diflBcult to extract any information about the motion of the KBr relative to the c.m., which would provide the desired description of the mechanism and energetics of the reaction (9). High velocity resolution experiments have since been done by Bernstein and coworkers (10,11), but the studies of Reactions 2 and 3 by Martin and Kinsey (8) were the first to provide some information on the dynamics of these reactions from a measurement of product distributions. In these experiments tritium labeling allowed radioisotope... 

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