Dipole scattering model

Fig. 19.9 Plot of scaled total decay rates n3r of Ba 6pmn( J = l + 1 autoionizing states in atomic units vs (. For ( = 0-4 the measured rates (O) shown are the average rates from many n values. The data for the rates for > 4 are for n = 12. The solid line is a simple theoretical calculation based on the dipole scattering of a hydrogenic Rydberg electron from the 6p core electron. Note that the core penetration of the lower states reduces the actual rate from the one calculated using the dipole scattering model. The constant total decay rate for > 8 is the spontaneous decay rate of the Ba+ 6p state (from ref. 39).

Here, a. and a L are the polarizabilities of the diatom parallel and perpendicular to the internuclear separation, R12. The electrostatic theory accounts for the distortions of the local field by the proximity of a point dipole (the polarized collisional partner) and suggests that the anisotropy is given by ft Rn) 6intermolecular interactions). This is the so-called dipole-induced dipole (DID) model, which approximates the induced anisotropy of such diatoms often fairly well. It gives rise to pressure-induced depolarization of scattered light, and to depolarized, collision-induced Raman spectra in general. 

M. Neumann. Collision induced light scattering by globular molecules Applequist s atom dipole interaction model and its implementation in computer simulation. Molec. Phys., 53 187-202 (1984). 

According to the aspherical-atom formalism proposed by Stewart [12], the one-electron density function is represented by an expansion in terms of rigid pseudoatoms, each formed by a core-invariant part and a deformable valence part. Spherical surface harmonics (multipoles) are employed to describe the directional properties of the deformable part. Our model consisted of two monopole (three for the sulfur atom), three dipole, five quadrupole, and seven octopole functions for each non-H atom. The generalised scattering factors (GSF) for the monopoles of these species were computed from the Hartree-Fockatomic functions tabulated by Clementi [14]. 

Schmitz et al (31) have proposed that the discrepancy between QLS and tracer diffusion measurements can be reconciled by considering the effects of small ions on the dynamics and scattering power of the polyelectrolyte. In this model, the slow mode arises from the formation of "temporal aggregates . These arise as the result of a balance between attractive fluctuating dipole forces coming from the sharing of small ions by several polyions, and repulsive electrostatic and Brownian diffusion forces. This concept is attractive, but needs to be formulated quantitatively before it can be adequately tested. 

However, it seems that possibilities of this model to explain some of the experimental results were not fully explored. Also, this model shows some weaknesses. First, it predicts a value of Tc in DKDP (310 K) that is higher than the experimental value (229 K). Second, the calculated rate of the proton transfer in the PE phase is too low to explain the width of the CP in the neutron scattering spectra of KDP [62]. Third, and most important, because the model assumes that dipoles of PO4 groups lie along the c-axis, it cannot to explain static and dynamic properties of the transverse polarization fluctuations, whose importance in the phase transition mechanism has been supported by several experimental results [8,20,28,31-33]. 

The characteristic ratio of atactic polylferf.-butyl vinyl ketone) is determined from light scattering and viscosimetry measurements, and at 300 K in benzene the dipole moment ratio and its temperature coefficient are measured. Calculations of Ca and Da based on a two-state RIS model, with parameters independently derived from a previously developed semiempirical potential energy surface and from epimerization equilibrium measurements for dimeric and trimeric oligomers, are in excellent agreement with the experimental results. The predicted temperature coefficient is positive but lower in magnitude than that observed. 

It is instructive to develop the solution for scattering by a small sphere of radius, a X. In such a limit the sphere is represented as a point dipole, and to determine its polarizability, the interaction of the sphere with the electric field is modeled as shown in Figure 4.5. The restriction that the sphere is much smaller that the wavelength of light suggests that to a first approximation, the electric field, at an instant in time, appears to the sphere as a uniform field. We must solve the following time-independent Maxwell s equations [1],... 

The fundamentals of the Raman effect can be understood by consideration of a classical model, in which an incident beam of radiation (i.e., laser beam, for all practical purposes, in flame diagnostics) passes through an ensemble of molecules. The resultant laser beam electric field distorts the electronic cloud distribution of each molecule, causing oscillating dipoles these induced dipoles are related to the incident laser beam electric field by the molecular polarizability. The dipoles, in turn, produce a secondary radiating field at essentially the same frequency as that for the incident beam. This radiation is termed Rayleigh scattering. 

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