Modified Born Approximation and the Elastic Scattering of Electrons from Helium

Abstract

We discuss the elastic scattering of electrons from helium atoms in terms of an energy-dependent central-potential model having the form $V(r)=2Zlimit of\text{}\left(\frac{\ensuremath{-}{\ensuremath{\Lambda}}^{2}}{{\ensuremath{\Lambda}}^{2}\ensuremath{-}{\ensuremath{\mu}}^{2}}\frac{{e}^{\ensuremath{-}\ensuremath{\mu}r}}{r}+\frac{{\ensuremath{\mu}}^{2}}{{\ensuremath{\Lambda}}^{2}\ensuremath{-}{\ensuremath{\mu}}^{2}}\frac{{e}^{\ensuremath{-}\ensuremath{\Lambda}r}}{r}\right)\ensuremath{-}\frac{\ensuremath{\alpha}}{{({r}^{2}+{d}^{2})}^{2}}\text{as}\ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\mu},$ where $\ensuremath{\mu},\ensuremath{\alpha}$ are fixed constants (for He, $\ensuremath{\mu}=3.375$ and $\ensuremath{\alpha}=1.39$), and $d$ is an energy-dependent phenomenological parameter. The method of partial waves is adapted for a generalized Yukawa potential and a polarization potential. Phase shifts and scattering cross sections are calculated from our potential model using the first Born approximation and a modified form of it. We develop an effective-range theory for a generalized Yukawa and a polarization potential, and apply it to generate a set of energy-dependent electron-helium phase shifts in the region 0-500 eV. Recent experimental angular distribution data in the region 100-500 eV are rather satisfactorily accounted for by our potential model. Our results compare favorably with those of LaBahn and Callaway.