Static field, classical

We present here a condensed explanation and summary of the effects. A complete discussion can be found in a paper by Hellen and Axelrod(33) which directly calculates the amount of emission light gathered by a finite-aperture objective from a surface-proximal fluorophore under steady illumination. The effects referred to here are not quantum-chemical, that is, effects upon the orbitals or states of the fluorophore in the presence of any static fields associated with the surface. Rather, the effects are "classical-optical," that is, effects upon the electromagnetic field generated by a classical oscillating dipole in the presence of an interface between any media with dissimilar refractive indices. Of course, both types of effects may be present simultaneously in a given system. However, the quantum-chemical effects vary with the detailed chemistry of each system, whereas the classical-optical effects are more universal. Occasionally, a change in the emission properties of a fluorophore at a surface may be attributed to the former when in fact the latter are responsible. 

Fig. 6.17 Tunnelling and saddle point ionization in Li. (a) Experimental map of the energy levels of Li m = 1 states in a static field. The horizontal peaks arise from ions collected after laser excitation. Energy is measured relative to the one-electron ionization limit. Disappearance of a level with increasing field indicates that the ionization rates exceed 3 x 105 s 1. The dotted line is the classical ionization limit given by Eqs. (6.35) and (6.36). One state has been emphasized by shading, (b) Energy levels for H (n = 18-20, m = 1) according to fourth order perturbation theory. Levels from nearby terms are omitted for clarity. Symbols used to denote the ionization rate are defined in the key. The tick mark indicates the field where the ionization rate equals the spontaneous radiative rate, (c) Experimental map as in (a) except that the collection method is sensitive only to states whose ionization rate exceeds 3 x 105 s-1. At high fields, the levels broaden into the continuum in agreement with tunnelling theory for H (from ref. 32).

Since, in HRS, there is no preferred orientation induced by an additional static field, there is the possibility of varying the experimental conditions in order to increase the number of independent observables. The number of theoretically possible independent observations, and hence the number of tensor components that can be obtained by HRS, is at most five. For parametric light scattering, this number is six, due to the possibility of distinguishing between the two optical fundamental fields [20]. The experimental difficulty has precluded the determination of this number of components. What is experimentally realistic in HRS is an additional depolarization measurement, apart from the classical measurement of the intensity of the second-order incoherent scattered light. The two measurements, the total intensity measurement and the depolarization ratio (or two intensity measurements, one with parallel and one with perpendicular polarization for fundamental and second harmonic), represent two independent observables and allow the experimental determination of two tensor components. For molecules of C2 symmetry, these are and P xxy resulting for the total intensity measurement in Eqn. (21),... 

The correct frame of description of interacting relativistic electrons is quantum electrodynamics (QED) where the matter field is the four-component operator-valued electron-positron field acting in the Fock space and depending on space-time = (ct, r) (x = (ct, —r)). Electron-electron interaction takes place via a photon field which is described by an operatorvalued four-potential A x ). Additionally, the system is subject to a static external classical (Bose condensed, c-number) field F , given by the four-potential (distinguished by the missing hat)... 

Dielectric properties describe the polarization, P, of a material as its response to an applied electric field E (bold symbols indicate vectors) [1—3], In the field of solution chemistry, the discussion of dielectric behavior is often reduced to the equilibrium polarization, Pq = So(s — V) Eq (eq is the electric field constant), of the isotropic and nonconducting solvent in a static field, Eq. Characteristic quantity here is the static relative permittivity (colloquially dielectric constant ), , which is a measure for the efficiency of the solvent to screen Coulomb interactions between charges (i.e., ions) embedded in the medium. As such, enters into classical electrolyte theories, like Debye-Hiickel theory or the Bom model for solvation free energy [4, 5] and is used... 

Experimentally, if all fields have parallel polarization, one can measure the parallel components of the first and second hyperpolarizabUities which take into account the classical orientational averaging. In the case of ESHG, with the optical field polarized perpendicular to the static field, one measures the perpendicular components, and in the case of a dc-Kerr experiment, the differences between the parallel and perpendicular components. 

In the semiclassical approximation the electron spin on each radical is treated quanmm mechanically, whilst the nuclear spins are treated classically. The unpaired electron processes about the static field and the resultant of the nuclear spins. 

The classical interaction energy of two magnetic dipoles oriented along the direction of the static magnetic field (Figure 1) is given by... 

We wish to stress at this point that, in the approach discussed above 161), the vibrational motion has been treated classically, as Markov processes. Typical vibrational energies are two orders of magnitude higher than the typical ZFS energies and, for the static magnetic field less than 10 T, one has also coy >> cos, where coy is the energy of vibrational transitions in angular... 

---