Amplitude dipole model

Another feature of the simplest model that needs modification is the assumption of a fixed dipole amplitude. Because of the efficient capture of nonpropagating near fields by a surface, a fixed-amplitude dipole emits more power, the closer it moves to a surface. However, in steady-state fluorescence, the emitted power can only be as large as the (constant) absorbed power (or less, if the intrinsic quantum yield of the isolated fluorophore is less than 100%). Therefore, the fluorophore must be modeled as a constant -power (and variable-amplitude) dipole. Many of the earlier theoretical references listed above deal only with constant-amplitude dipoles, so their results must be considered to be an approximation. 

Incorrect conclusion 1 above is sometimes said to derive from the reciprocity principle, which states that light waves in any optical system all could be reversed in direction without altering any paths or intensities and remain consistent with physical reality (because Maxwell s equations are invariant under time reversal). Applying this principle here, one notes that an evanescent wave set up by a supercritical ray undergoing total internal reflection can excite a dipole with a power that decays exponentially with z. Then (by the reciprocity principle) an excited dipole should lead to a supercritical emitted beam intensity that also decays exponentially with z. Although this prediction would be true if the fluorophore were a fixed-amplitude dipole in both cases, it cannot be modeled as such in the latter case. 

In recent molecular dynamics studies attempts were made to reproduce the shapes of the intercollisional dip from reliable pair dipole models and pair potentials [301], The shape and relative amplitude of the intercollisional dip are known to depend sensitively on the details of the intermolecular interactions, and especially on the dipole function. For a number of very dense ( 1000 amagat) rare gas mixtures spectral profiles were obtained by molecular dynamics simulation that differed significantly from the observed dips. In particular, the computed amplitudes were never of sufficient magnitude. This fact is considered compelling evidence for the presence of irreducible many-body effects, presumably mainly of the induced dipole function. 

Vibration Diagram Method. In actuality the last cases above are not described accurately by this dipole array model because actual phases of the electric fields are significantly altered from those of linear waves. (A more realistic, but complex model is to consider amplitude and phase characteristics of the oscillating vertically polarized component of electric field resulting from rotation of a line of transverse dipoles of equal magnitude but rotated relative to each other along the line such that their vertical components at some reference time are depicted by Figure 2.) For this reason and to handle details of focused laser beams one must resort to a more mathematically based description. Fortunately, numerical... 

In the 1950s, many basic nuclear properties and phenomena were qualitatively understood in terms of single-particle and/or collective degrees of freedom. A hot topic was the study of collective excitations of nuclei such as giant dipole resonance or shape vibrations, and the state-of-the-art method was the nuclear shell model plus random phase approximation (RPA). With improved experimental precision and theoretical ambitions in the 1960s, the nuclear many-body problem was born. The importance of the ground-state correlations for the transition amplitudes to excited states was recognized. 

The attenuation of die dipole of the repeat unit owing to thermal oscillations was modeled by treating the dipole moment as a simple harmonic oscillator tied to the motion of the repeat unit and characterized by the excitation of a single lattice mode, the mode, which describes the in-phase rotation of the repeat unit as a whole about the chain axis. This mode was shown to capture accurately the oscillatory dynamics of the net dipole moment itself, by comparison with short molecular dynamics simulations. The average amplitude is determined from the frequency of this single mode, which comes directly out of the CLD calculation ... 

We have shown above how the reaction field model can be used to estimate solute-solvent interactions in the absence of external fields. Now we introduce effective polarizabilities that connect the Fourier components of the induced dipole moment (33) with the macroscopic fields in the medium. In the linear case, the Fourier component / induced by an external optical field can be represented by the product of the macroscopic field amplitude " and an effective first-order polarizability a(-tu w) using (93). 

As already mentioned, one of the main weaknesses of the simple reflection method is the fact that the electronic transition dipole moment, (or the transition dipole moment surface, TDMS for polyatomic molecules in Section 4) is assumed to be constant. This weakness will remain in the Formulae (12), (27) and (29) derived below. The average value of the square of the TDM (or TDMS) is then included in amplitude A and A = A /V. In Formulae (3), (3 ) and (3") the mass (or isotopologue) dependent parameters are p and the ZPE. In contrast, W and V., which define the upper potential, are mass independent. This Formula (3) is already known even if different notations have been used by various authors. As an example, Schinke has derived the same formula in his book [6], pages 81, 102 and 111. Now, the model will be improved by including the contribution of the second derivative of the upper potential at Re- The polynomial expansion of the upper potential up to second order in R - Re) can be expressed as ... 

In the semiclassical model the molecule is treated quantum mechanically whereas the held is represented classically. The held is an externally given function of time F that is not affected by any feedback from the interaction with the molecule. We consider the simplest case of a dipole coupling. The formalism is easily extended to other types of couplings. The time dependence of the periodic Hamiltonian is introduced through the time evolution of the initial phase F = F(0 + oat) = electric held and oa is its frequency. The semiclassical Hamiltonian can be, for example, written as... 

The exciton model of linear aggregates was used to explain the evolution of the electronic state parameters with stepwise incorporation of additional monomer units [64,408,409]. In this model, the transition dipole moments have only one component directed along the main molecular axis. Thus, the amplitude of the transition dipole moment is expressed by Eq. (47) for nc< 12. 

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