Coupling strong

The need for another form of approximate solution for Eq. (178) appears when ki k , where often all are small enough to overlook except f7j and U i, which may be rather large. In other words, there is strong coupling between the I and n stages. Equation (178) then reduces to the two coupled equations  

Equations (184) may be uncoupled in the case of exact resonance when = k. For such collisions it is plausible that 

With the standard simplification that both and f7, are spherically symmetric, the above equations are reduced to the methodology of Section IV-C (1), and the rest is detail. 

For the case of inexact resonance, when we must contend directly with the coupled equations (184), exact analytical solutions are not obtainable. The methods of approximation in this instance have been reviewed by Massey.  

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From tests with Level-2-inspectors [2, 3] we learn that 10 % of the errors in weld testing are caused hy too fast probe movements (indications are missed or overlooked), 34 % by too strong coupling variations (underestimation of indications) or coupling failures and 56 % by incomplete scanning (untested areas). 

The strong dependence of the PES on molecular orientation also leads to strong coupling between rotational states, and hence rotational excitation/de-excitation in the scattering. This has been observed experimentally for H2 scattering from Cu surfaces. Recent work has shown that for H2 the changes m rotational state occur almost exclusively when the molecular bond is extended, that is, longer than the gas-phase equilibrium value [ ]. 

As an illustrative example, consider the vibrational energy relaxation of the cyanide ion in water [45], The mechanisms for relaxation are particularly difficult to assess when the solute is strongly coupled to the solvent, and the solvent itself is an associating liquid. Therefore, precise experimental measurements are extremely usefiil. By using a diatomic solute molecule, this system is free from complications due to coupling... 

A nice example of this teclmique is the detennination of vibrational predissociation lifetimes of (HF)2 [55]. The HF dimer has a nonlinear hydrogen bonded structure, with nonequivalent FIF subunits. There is one free FIF stretch (v ), and one bound FIF stretch (V2), which rapidly interconvert. The vibrational predissociation lifetime was measured to be 24 ns when excitmg the free FIF stretch, but only 1 ns when exciting the bound FIF stretch. This makes sense, as one would expect the bound FIF vibration to be most strongly coupled to the weak intenuolecular bond. 

Figure B2.4.5. Simulated lineshapes for an intennolecular exchange reaction in which the bond joining two strongly coupled nuclei breaks and re-fomis at a series of rates, given beside tlie lineshape. In slow exchange, the typical spectrum of an AB spin system is shown. In the limit of fast exchange, the spectrum consists of two lines at tlie two chemical shifts and all the coupling has disappeared.

The xy magnetizations can also be complicated. Eor n weakly coupled spins, there can be n 2" lines in the spectrum and a strongly coupled spin system can have up to (2n )/((n-l) (n+l) ) transitions. Because of small couplings, and because some lines are weak combination lines, it is rare to be able to observe all possible lines. It is important to maintain the distinction between mathematical and practical relationships for the density matrix elements. 

On short length scales the coarse-grained description breaks down, because the fluctuations which build up the (smooth) intrinsic profile and the fluctuations of the local interface position are strongly coupled and camiot be distinguished. The effective interface Flamiltonian can describe the properties only on length scales large compared with the width w of the intrinsic profile. The absolute value of the cut-off is difficult... 

Savikhin S, Buck D R and Struve W S 1999 The Fenna-Mathews-Olson protein a strongly coupled photosynthetic... 

B. The Study of a Real Three-State Molecular System Strongly Coupled (2,3) and (3,4) Conical Intersections... 

We prove our statement in two steps First, we consider the special case of a Hilbert space of three states, the two lowest of which are coupled strongly to each other but the third state is only weakly coupled to them. Then, we extend it to the case of a Hilbert space of N states where M states are strongly coupled to each other, and L = N — M) states, are only loosely coupled to these M original states (but can be stiongly coupled among themselves). 

In order to demonstrate the NDCPA a model of a system of excitons strongly coupled to phonons in a crystal with one molecule per unit cell is chosen. This model is called here the molecular crystal model. The Hamiltonian of... 

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