High energy approximation

The high energy approximation leads the first equation of Eq.(lOO) to... 

Here sq o are the radial adiabatic phase increments in the high energy approximation given by... 

Because of these difficulties we turn to inversion procedures which are valid in the semiclassical limit since this approximation has proved to be applicable for most of the atomic and molecular collisions. Solutions of the second step, the determination of the potential, are treated in Section IV.B.2. In general, the input information will be the phase shifts or the deflection function. Only in the high energy approximation can the potential be derived directly from the cross section. For a detailed discussion of these procedures see Buck (1974). The possibilities of determining the phase shifts or the deflection function from the cross section are treated in Section IV.B.3. The advantage of such procedures and the general requirements on the data are discussed in Section IV.B.4. The emphasis will be on procedures which have been applied to real data. Extensions to non-central or optical interaction potentials are available. Most of them, however, are still in a formal state, so that a direct application to molecular physics is not obvious. Two exceptions should be mentioned. One is a special inversion procedure for optical potentials derived by a perturbation formalism (Roberts and Ross,... 

Bernstein et al. (1966) have brought the sudden approximation (s.a.) into a very suitable form for the investigation of molecular collisions. For straight path trajectories the high energy approximation and s.a. become... 

Eq.(116) together with Eqs.(112)-(113) gives the analytical solution of the S—P resonant excitation transfer problem in the high energy approximation and can provide all the dynamics information for this problem. In particular, we can find the total cross-sections for all the related collision processes. In the semiclassical approximation the standard expression of cross-section has the form... 

Although this criterion is similar to that for Hwang s expansion, the validity of the latter also depends upon A being somewhat smaller than the mean resonance spacing. This is not necessary in the high-energy approximation in fact, it becomes better continually as A increases, and the method is therefore a useful complement to the isolated resonance approximation. 

SIMS is used to determine isotopic ratios and to date isotope-containing solid samples. SIMS uses a high-energy (approximately 10 kV) primary ion beam to sputter secondary atomic, molecular, and molecular... 

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