Vacuum polarization tensor

In the first step of the analysis the relevant Greens functions are expressed in terms of their irreducible kernels [201], the electron self-enCTgy I>y p), the vacuum polarization tensor riv y( ) and the irreducible vertex function (p, A). 

One important use of SFG vibrational spectroscopy is the orientational analysis of ionic liquids at gas-liquid interfaces. For example, the study of the structural orientation ofionic liquids using common cation types, that is, [BMIM], combined with different anions, gives information on the effects of both cation and anion types [3, 22, 26-28]. Additional surface analytical work includes SFG studies under vacuum conditions for probing the second-order susceptibility tensor that depends on the polar orientation of the molecule and can be correlated to the measured SFG signal intensities. Supporting information is frequently obtained by complementary bulk spectroscopic techniques, such as Raman and Fourier transform infrared (FTIR) analysis, for the analysis of the pure ionic liquids. 

Erskine and Stern (1973) reported the most careful Kerr effect measurement for Gd. The samples were films deposited in vacuum and measured in situ. They are magnetized in the plane of the films. The rotation of the polarization axis and the ellipticity were measured, and from these quantities the off-diagonal conductivity tensor was deduced. The results for the real and imaginary parts of a-, at 105 K are shown in fig, 3.43. Comparing the imaginary part with the joint density of states curve for Gd in fig. 3.43, we find that the peak at 2 eV in the... 

The electric polarization from internal continuum (EPIC) model has been developed to accurately predict the polarizability tensor of molecules ". The EPIC approach uses an intramolecular effective dielectric constant, together with associated atomic radii, to represent the detailed molecular polarizability. For a single atom of radius R in vacuum under the influence of a uniform electric field (E), the polarizability is given by the electric fleld prefactor of the induced dipole moment (Sin is the inner dielectric) ... 

Macroscopically, the resulting electrical displacement, D = E = oE + P/ where s is the permittivity, P is the polarization, which is defined as the dipole moment per unit volume, and So is the permittivity of a vacuum = 8.85 x 10 farads/m (Coulomb/V-m). For an anisotropic crystal, is a tensor of rank two, but here we consider only isotropic materiab, so s will be a scalar. 

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