Elastic scattering potential, with

Fig. 28. Real optical potential strengths in infinite nuclear matter of the scalar and vector potentials for medium energy protons based on the RIA model with pseudoscalar invariant (solid curves) and the one-meson exchange model using the pseudovector invariant with explicit direct and exchange terms (dashed curves). Results of Dirac phenomenology [Ha 90] for p + °Ca elastic scattering (potentials evaluated at r = 0) are shown by the dotted curves.

Using Eqs. (29) and (30) we obtain that the coherent potential v i with elastic scattering correction is determined by the following equations... 

Consider a molecule prepared in the absolute ground state in the absence of the field and subjected to microwave field of frequency . If collided with a structureless atom in the absence of the field and at collision energies below the first excitation threshold, the molecule can undergo only elastic scattering. In the presence of the field, the ground state of the molecule becomes a field-dressed state X). And for every field-dressed state X), there is an infinite number of replica states 2 - A ), lower in energy. The states 2 - A ) and X) are coupled by the anisotropy of the atom-molecule interaction potential, so collisions can induce... 

We first follow the flow chart for the simple case of elastic scattering of structureless atoms. The number of internal states, Nc, is one, quantum scattering calculations are feasible and recommended, for even the smallest modem computer. The Numerov method has often been used for such calculations (41), but the recent method based on analytic approximations by Airy functions (2) obtains the same results with many fewer evaluations of the potential function. The WKB approximation also requires a relatively small number of function evaluations, but its accuracy is limited, whereas the piecewise analytic method (2) can obtain results to any preset, desired accuracy. 

By carrying out model calculations on the basis of the Pgl theory and comparing the resulting calculated spectrum with the observed one, quantitative information on V+(R) and V+(R) for Rpotential curves K+(7 ) are known for the systems R-H+ from elastic scattering data,53 so that rather direct information on K (R) can be obtained for the R -H systems. In a preliminary model calculation of the quantum-mechanical version101 it was found that the measured Ar -H spectrum can be well reproduced. 

For systems with larger values of aR, rainbow scattering may be completely quenched [2, 15,41,42]. This occurs, for example, in K. + Br2 and K + CBr4. The long-range potential parameters must then be calculated in a different manner [15], based on the supposition that the reaction has a zero threshold energy, so that elastic scattering occurs only from the portion... 

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