Resonances in low-energy electron elastic cross sections for lanthanide atoms

Abstract

Total and Mulholland partial cross sections for the elastic scattering of electrons from the lanthanide atoms lanthanum to lutetium are calculated for the electron impact energy range $0\ensuremath{\leqslant}E\ensuremath{\leqslant}1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The recently developed Regge-pole methodology, which naturally embodies the crucial electron correlation effects together with a Thomas-Fermi-type potential incorporating the vital core-polarization interaction are used for the calculations. Dramatically sharp resonances are found to characterize the near-threshold electron elastic scattering total and Mulholland partial cross sections, whose energy positions are identified with the electron affinities (EA's) of these atoms through a close scrutiny of the imaginary part of the complex angular momentum. The unambiguous extracted EA values of the lanthanide atoms vary from a low value of $0.016\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for the Tm atom to a high value of $0.631\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for the Pr atom; none is predicted to have a lower EA value than the former. All the negative ions of the lanthanide atoms can be classified through their binding energies (BE's) as weakly bound negative ions (BE's $<1.0\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$), while only three qualify to be classified as tenuously bound (BE'$<0.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$). Ramsauer-Townsend minima, shape resonances, and the Wigner threshold behavior for these lanthanides are also determined. Comparisons of the present calculated EA's with those from various experimental measurements and other theoretical calculations are presented and discussed. In particular, our extracted EA value for the complicated open $d$- and $f$-subshell Ce atom agrees excellently with the most recently measured [Walter et al., Phys. Rev. A 76, 052702 (2007)] and calculated values, while for Nd and Eu the agreement with the latest calculated values of O'Malley and Beck [Phys. Rev. A 77, 012505 (2008); Phys. Rev. A 78, 012510 (2008)] is outstanding. These agreements give great credence to the already demonstrated predictive power of the Regge-pole methodology to extract unambiguous and reliable binding energies for tenuously bound and complicated open-shell negative ionic systems, requiring no a priori knowledge of the EA values whatsoever. This new perspective to the EA determination of atoms from low-energy electron elastic scattering resonances promises far-reaching implications for future accurate and reliable theoretical EA values, even for small molecules and clusters.