Influence of a static electric field

Int the derivation of (8.45) we assumed that the medium was nonmagnetic. Only in this case can one consider the field H° to be independent of jj, and thus having the same value in all layers of the superlattice. In the case of an applied electric field such approximation cannot be justified. Therefore, in the presence of a static electric field instead of (8.46) we have to use the following relation 

Since for a static electric field we may take for any //, that Ej11 = l ], E = E , E = (l/e Oef El, where E° is the static field averaged over the superlattice period and -/ = f(uj 0), we find that the tensor e h can be written as 

The above relations can become useful in all situations when the influence of an external static or low-frequency electric field on the dielectric tensor has to be taken into account. 

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Several studies have been made of the behaviour of low energy positrons in gases under the influence of a static electric field e. The broad aim of this work has been to study the diffusion and drift of positrons in order to understand better the behaviour of the momentum transfer and annihilation cross sections at very low energies. The theoretical background has been given in section 6.1, and the diffusion equation with an... 

Davies, S.A., Charlton, M. and Griffith, T.C. (1989). Free positron annihilation in gases under the influence of a static electric field. J. Phys. B At. Mol. Opt. Phys. 22 327-340. 

Equations (18)-(21) were given for the case of real susceptibilities. However, they have to be treated as complex quantities if the frequency is close to or within the region of an optical transition in the medium. An example in the domain of linear optics was given in (12) where the imaginary part of the first-order susceptibility, ft) w), was related to the absorption coefficient, of the medium. An example from non-linear optics is the technique of electro-optical absorption measurements (EOAM, p. 167) where the UV-visible absorption is studied under the influence of a static electric field. In EOAM, the imaginary part of the third-order susceptibility, w,0,0), is... 

LFnder the influence of a static electric field liquid crystalline solutions of PBLG become uniaxially oriented and show both linear and circular birefringence and linear and circular dichroism. Accordingly, the measured CD shows a dependence of the microscopic angle, a, that the fast optical axis of the oriented solution makes with respect to the plane of polarization of the polarizer in the CD instrument. When the film is reasonably thin (0.01-0.1 mm thick) or/and only partially oriented (less than 5% orientation), the apparent CD of oriented film of deoxyribonucleic acid is expressed by the equation (50) ... 

In Section 1.3 the shift of the single molecule excitation line under the influence of a static electric field, the DC Stark effect, is discussed. The interaction of molecular electronic energy levels with a strong optical field is also expected to lead to level shifts and splittings and additionally to a change of relaxation rates. The shift of energy levels under optical excitation is called light shift or AC Stark effect where... 

The complex permittivity is given by s (o)= C (o) /Co, analogous to equation (1) for the static case, where Co= A.Bold is the vacuum capacitance of a parallel-plate capacitor ( =area of the plate, So the vacuum permittivity and d the plate separation (A/d) must have dimensions in cm) and C is the complex capacitance of the same capacitor filled with the material under study. Under the influence of a sinusoidal electric field, the complex permittivity relates to the impedance through ... 

Bersohn 76) has calculated the crystal field created by the molecular dipoles in the lattice of CH3C1. The static dipole moment of the molecules induces through the polarizability of the molecules an additional dipole moment which increases the dipole moment of the free molecule by a factor of about 1.05. This in turn means that the C—Cl bond has increased in ionic character under the influence of the intermolecular electric fields and therefore (see Eq. (II.9 the quadrupole coupling constant will be lower relative to the gaseous state. Besides the dipole moment induced in the direction of the static dipole, a perpendicular partial moment should be induced, too. Therefore the axial symmetry of the C—Cl bond will be disturbed and the asymmetry parameter 77 may become unequal zero. A small asymmetry parameter 17 = 0.028 has been observed for the nuclear quadrupole interaction in solid CH3I. Bersohn also calculated from the known crystal structure of 1,3,5-trichlorobenzene the induced... 

The difference between the quasi-static coupling for ammonia in the solid state — 3.47 MHz - and that measured in the gas by microwave spectroscopy — 4.08 MHz — cannot be explained by the contribution of the crystalline electric field gradient alone, but must be attributed to a redistribution of the bonding electrons in the molecule under the influence of the crystalline electric field or of the intermolecular hydrogen bonds. 

So far, we have seen that the inclusion of the angular motion critically influences the energy transfer and that LCT is not applicable in a straightforward manner to induce a fragmentation process. Therefore, we now follow another strategy and place the Nal molecule in a static electric field, i.e. an extra term of the form Eq. (50) is included. This term leads to an initial orientation in the electronic ground state [217], that is, a pendular state [218]. In this way, states with various, even and odd, rotational quantum numbers are populated in the initial state (in the sense that the radial functions in the expansion Eq. (52) are nonzero). Consequently, we now may employ a field of the form... 

When a strong static electric field is applied across a medium, its dielectric and optical properties become anisotropic. When a low frequency analyzing electric field is used to probe the anisotropy, it is called the nonlinear dielectric effect (NLDE) or dielectric saturation (17). It is the low frequency analogue of the Kerr effect. The interactions which cause the NLDE are similar to those of EFLS. For a single flexible polar molecule, the external field will influence the molecule in two ways firstly, it will interact with the total dipole moment and orient it, secondly, it will perturb the equilibrium conformation of the molecule to favor the conformations with the larger dipole moment. Thus, the orientation by the field will cause a decrease while the polarization of the molecule will cause an... 

Shielding The potential of the mobile phase in the cell may be influenced by electric field changes near the three electrode system. These changes may originate from motions of a statically charged operator or from electrically operated instruments in the vicinity of the detector. 

The terms in equation 1.166 represent total ionic polarizability, composed of electronic polarizability a plus an additional factor a , defined as a displacement term, due to the fact that the charges are not influenced by an oscillating electric field (as in the case of experimental optical measurements) but are in a static field (Lasaga, 1980) ... 

Under the influence of a uniform static electric field, the electronic energy of a chemical system can be expressed as a double power series expansion in the normal coordinates and the electric field [24] ... 

In the above discussion, we have only considered the effects due to the CTE-CTE repulsion, which contribute to the resonant nonlinear absorption (as well as to other resonant nonlinearities) by the CTE themselves. Here, however, we want to mention a more general mechanism by which the nonlinear optical properties of media containing CTEs in the excited state can be enhanced. This influence is due to the strong static electric field arising in the vicinity of an excited CTE, If, for example, the CTE (or CT complex) static electric dipole moment is 20 Debye, at a distance of 0.5 nm it creates a field Ecte of order 107 V/cm. Such strong electric fields have to be taken into account in the calculation of the nonlinear susceptibilities, because they change the hyperpolarizabilities a, / , 7, etc. of all molecules close to the CTE. For instance, in the presence of these CTE induced static fields, the microscopic molecular hyperpolarizabilities are modified as follows... 

Optimization of the molecular structure under the influence of an external homogeneous static electric field applied along the long axis of the molecule and directed in such a way as to favor charge transfer from the donor to the acceptor... 

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