8 - Diffraction as tunneling

Summary

Query 1. Do not Bodies act upon Light at a distance, and by their action bend its Rays; and is not this action (cœteris paribus) strongest at the least distance?

(Newton 1704)

We now show how CAM theory deals with the first of the semiclassical critical effects, forward diffractive scattering. The impenetrable sphere model is ideal for this purpose, because the only relevant physical processes that take place in it are reflection from the surface and forward diffractive scattering.

The difficulties are connected with the transition domain between the forward diffraction peak and the wide-angle geometrical reflection region, where the WKB approximation holds (Sec. 7.5). Within the forward peak, classical diffraction is dominant, but this domain of small diffraction angles is only sensitive to the bulk blocking effect of the scatterer (Sec. 2.2). To probe the dynamics of diffraction one must go to larger diffraction angles, contained within this difficult transition domain.

Fock's theory of diffraction is not powerful enough to bridge the gap, as will be seen in several examples. For this purpose, one needs a uniform asymptotic approximation. Such an approximation was developed by Berry (1969) for forward diffractive scattering by potentials with long-range tails, but near-forward scattering in this case arises from large impact parameters, a physical mechanism completely different from diffraction by the edge of a curved surface.

The crucial physical concept is that of the effective potential. It will be seen to lead to a reinterpretation of Fock's theory, clarifying several points that remained obscure in it (Sec. 7.3).