In the energy regime appropriate to classical and semiclassical atomic scattering theory, experimental data on diGerential cross sections a(8,E) and interference patterns are conveniently analyzed through the use of reduced variables such as r =E8, p= 8 sin8o (8,E). In forward scattering, the reduced relationship is the leading term of an impact expansion of the type p(r, E) =P E "tJ"(r). The p (r) are obtained by eliminating the impact parameter b from expansions of the classical scattering functions of the type r(h, E)=P E "r"(h), introduced by Lehmann and Leibfried. Backscattering data are to be analyzed through expansions such as o(8,E)=P"(s. -8)s"o"(E), derived by eliminating b from expansions like sr -8= y(h, E) = P h'"+'e "(E).If the scattering arises from a potential V(r), the coefficients r"(b), y"(E), etc. , are expressed in the form of integrals over the potentials which lend themselves to inversion procedures similar to Firsov's by which a lower bound to the potential can be extracted from the scattering data. In addition to deriving these expansions and testing them on several realistic interatomic potentials, we describe how the reduced variables they suggest can be applied to the presentation and analysis of experimental data.' (a) C. Lehmann and G.
A gaussian beam from a CO(2) laser emitting at 10.6 mu was used to measure damage thresholds on rabbit cornea at exposure times of 55 msec, 10 msec, and 3.5 msec. A theoretical model of the radiation-tissue interaction is presented and compared with experimental data. The comparison suggests that a critical temperature exists above which lesions are caused by protein denaturation. The model is useful for establishing safe exposure levels within a limited exposure range.
One may measure the angle at which visible Cerenkov radiation appears from fast charged particles as they pass through a thin transparent plate. This angle is related to the velocity of the particle in a simple manner, and therefore offers a method of measuring the velocity. The angular width of the radiation is important in that it determines the resolution of the velocity measurement. This width contains contributions due to diffraction, energy loss of the charged particle, and multiple scattering. In this paper, the effects of multiple scattering and diffraction are considered in the following manner. The path of the particle through the transparent plate is considered to be a series of connected short straight-line segments. The radiation is calculated classically from this path, and with the aid of the results of multiple scattering theory, an ensemble average is taken over all possible paths. Two different methods are used in evaluating the radiation average. One is valid at viewing angles near the radiation maximum, and the other at viewing angles differing appreciably from the maximum. Curves are presented that give the radiation intensity as a function of the viewing angle for a variety of cases.
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