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In the energy regime appropriate to classical and semiclassical atomic scattering theory, experimental data on differential cross sections $\ensuremath{\sigma}(\ensuremath{\theta}, E)$ and interference patterns are conveniently analyzed through the use of reduced variables such as $\ensuremath{\tau}=E\ensuremath{\theta}$, $\ensuremath{\rho}=\ensuremath{\theta}$ $sin\ensuremath{\theta}\ensuremath{\sigma}(\ensuremath{\theta}, E)$. In forward scattering, the reduced relationship is the leading term of an impact expansion of the type $\ensuremath{\rho}(\ensuremath{\tau}, E)=\ensuremath{\Sigma}{n}^{}{E}^{\ensuremath{-}n}{\ensuremath{\rho}}_{n}(\ensuremath{\tau})$. The ${\ensuremath{\rho}}_{n}(\ensuremath{\tau})$ are obtained by eliminating the impact parameter $b$ from expansions of the classical scattering functions of the type $\ensuremath{\tau}(b, E)=\ensuremath{\Sigma}{n}^{}{E}^{\ensuremath{-}n}{\ensuremath{\tau}}_{n}(b)$, introduced by Lehmann and Leibfried. Backscattering data are to be analyzed through expansions such as $\ensuremath{\sigma}(\ensuremath{\theta}, E)=\ensuremath{\Sigma}{n}^{}{(\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta})}^{2n}{\ensuremath{\sigma}}_{n}(E)$, derived by eliminating $b$ from expansions like $\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta}=\ensuremath{\phi}(b, E)=\ensuremath{\Sigma}{n}^{}{b}^{2n+1}{\ensuremath{\phi}}_{n}(E)$. If the scattering arises from a potential $V(r)$, the coefficients ${\ensuremath{\tau}}_{n}(b)$, ${\ensuremath{\phi}}_{n}(E)$, 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.

Perturbation effects in differential elastic ion- atom scattering generated by crossing of molecular states from even potentials

The WKB method was used in the interpretation of molecular beam scattering. Particular attention was given to small angle scattering where the sensitivity to the intermolecular potential is greatest. It was found that the Lennard‐Jones potential does not fit the data and that, for the case investigated, the minimum in the potential probably needs to be broadened. Empirical relationships between the phase shifts and the intermolecular potential were found which should be of value in the inversion problem. A calculation of rainbow scattering was made.

Supported in part by the National Aeronautics and Space Administration and by the U.S. Army Research Office

Stueckelberg formulation for transition probabilities to interpret perturbation effects in elastic scattering differential cross section measurements

The validity of several approximations pertinent to molecular scattering has been investigated. The WKB method was found to be reliable and was used to demonstrate the sensitivity of molecular scattering data to the intermolecular potential.

Bei 38 weisen weiblichen Ratten wurde mittels Laparotomie eine kunstliche Tasche in der Nahe der linken Nebenniere angelegt und in diese die Hypophyse einer trachtigen oder nichttrachtigen Ratte implantiert. Die Nebennieren rechts dienten als Kontrolle. Bei weiteren 5 Ratten wurde ein Stuckchen frischen Muskels eingepflanzt. Alle Tiere wurden 15 Std nach dem Eingriff getotet.

Nuclear symmetry effect on oscillations of elastic differential scattering of helium ion-atom resonant charge exchange