Impact expansions in classical and semiclassical scattering.

摘要: In the energy regime appropriate to classical and semiclassical atomic scattering theory, experimental data on differential cross sections $\ensuremath{\sigma}(\ensuremath{\theta}, E)$ interference patterns are conveniently analyzed through use of reduced variables such as $\ensuremath{\tau}=E\ensuremath{\theta}$, $\ensuremath{\rho}=\ensuremath{\theta}$ $sin\ensuremath{\theta}\ensuremath{\sigma}(\ensuremath{\theta}, E)$. forward scattering, relationship is leading term an impact expansion type $\ensuremath{\rho}(\ensuremath{\tau}, E)=\ensuremath{\Sigma}{n}^{}{E}^{\ensuremath{-}n}{\ensuremath{\rho}}_{n}(\ensuremath{\tau})$. The ${\ensuremath{\rho}}_{n}(\ensuremath{\tau})$ obtained by eliminating parameter $b$ from expansions functions $\ensuremath{\tau}(b, E)=\ensuremath{\Sigma}{n}^{}{E}^{\ensuremath{-}n}{\ensuremath{\tau}}_{n}(b)$, introduced Lehmann Leibfried. Backscattering be E)=\ensuremath{\Sigma}{n}^{}{(\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta})}^{2n}{\ensuremath{\sigma}}_{n}(E)$, derived like $\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta}=\ensuremath{\phi}(b, E)=\ensuremath{\Sigma}{n}^{}{b}^{2n+1}{\ensuremath{\phi}}_{n}(E)$. If arises a potential $V(r)$, coefficients ${\ensuremath{\tau}}_{n}(b)$, ${\ensuremath{\phi}}_{n}(E)$, etc., expressed in form integrals over potentials which lend themselves inversion procedures similar Firsov's lower bound can extracted data. addition deriving these testing them several realistic interatomic potentials, we describe how they suggest applied presentation analysis