Differential cross sections for low-energy electron elastic scattering by lanthanide atoms: La, Ce, Pr, Nd, Eu, Gd, Dy, and Tm

Abstract

Elastic differential cross sections (DCSs) in angle of electron scattering by the representative lanthanide atoms La, Ce, Pr, Nd, Eu, Gd, Dy, and Tm have been calculated in the electron-impact energy range $0\ensuremath{\le}E\ensuremath{\le}1\text{ }\text{eV}$. Additionally, the DCSs in electron-impact energy are also presented at scattering angles $\ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{}$, $90\ifmmode^\circ\else\textdegree\fi{}$, and $180\ifmmode^\circ\else\textdegree\fi{}$ for unambiguous identification of the binding energies (BEs) of the negative ions formed during the collisions as resonances. The shape resonances and the DCSs critical minima are identified as well. A Thomas-Fermi-type potential incorporating the vital core-polarization interaction is used for the calculations. Dramatically sharp resonances are found to characterize the near-threshold electron elastic DCSs, whose energy positions are identified with the BEs of the resultant negative ions. A procedure is suggested for measuring reliably the BEs of tenuously bound $(\text{BE}<0.1\text{ }\text{eV})$, weakly bound $(\text{BE}<1\text{ }\text{eV})$, and complicated open $d$- and $f$-subshell negative ions through the elastic DCSs both in scattering angle and electron-impact energy.