Dipole polarizability small radii

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 stability will once more increase with increasing charge and decreasing radius of the ion. A large moment or a large polarizability will favour the stability, provided on the other hand the shortest distance r remains small or at any rate the dipole is situated eccentrically. 

The cavity size in the Bom/Onsager/Kirkwood models strongly influences the calculated stabilization. Unfortunately, there is no consensus on how to choose the cavity radius. In some cases, the molecular volume is calculated from the experimental density of the solvent and the cavity radius is defined by equating the cavity volume to the molecular volume. Alternatively, the cavity size may be derived from the (experimental) dielectric constant and the calculated dipole moment and polarizability. In any case, the underlying assumption of these models is that the molecule is roughly spherical or ellipsoidal, which is only generally true for small compact molecules. 

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