Figure 1

(Color online) (a) Total, ${\sigma }_T$, and Mulholland partial elastic cross sections, in a.u., for $e^{-}\text{−}\mathrm{Hf}$ scattering versus $E$ (eV). The $n=6$ Mulholland partial cross section determines the Wigner threshold law. (b) Differential cross sections, in a.u., for elastic $e^{-}\text{−}\mathrm{Hf}$ scattering versus $E$ (eV) at $\theta =0°$, 90°, and 180° showing the differential cross section maxima at the resonance energy, corresponding to the electron affinity of the Hf atom at $0.017\mathrm{eV}$ for all the angles. (c) Mulholland contribution to the total cross section, in a.u., for $e^{-}\text{−}\mathrm{Hf}$ scattering versus $E$ (eV), corresponding to the Regge trajectory that passes near $\mathrm{Re}L=2$ at $E=0.017\mathrm{eV}$, and hence responsible for the resonance in the total cross section at that energy. This is a long-lived resonance as seen from its large angular life, proportional to ${\left(\mathrm{Im}L\right)}^{-1}$, and corresponds to the electron affinity for the Hf atom. (d) Regge trajectories, viz., $\mathrm{Im}L\left(E\right)$ versus $\mathrm{Re}L\left(E\right)$, for the ${\mathrm{Hf}}^{-}$ ion.Reuse & Permissions

Figure 2

(Color online) (a) Total, ${\sigma }_T$, and Mulholland partial elastic cross sections, in a.u., for $e^{-}\text{−}\mathrm{Lu}$ scattering versus $E$ (eV). The $n=6$ Mulholland partial cross section determines the Wigner threshold law. (b) Differential cross sections, in a.u., for elastic $e^{-}\text{−}\mathrm{Lu}$ scattering versus $E$ (eV) at $\theta =0°$, 90°, and 180° showing the maxima in the differential cross sections at the resonance energy, corresponding to the electron affinity of the Lu atom at $0.029\mathrm{eV}$ for all the angles. (c) Mulholland contribution to the total cross section, in a.u., for $e^{-}\text{−}\mathrm{Lu}$ versus $E$ (eV), corresponding to the Regge trajectory that passes near $\mathrm{Re}L=2$ at $E=0.029\mathrm{eV}$, and hence responsible for the resonance in the total cross section at that energy. This is a long-lived resonance as seen from its large angular life proportional to ${\left(\mathrm{Im}L\right)}^{-1}$ and corresponds to the electron affinity for the Lu atom. (d) Regge trajectories, viz., $\mathrm{Im}L\left(E\right)$ versus $\mathrm{Re}L\left(E\right)$, for the ${\mathrm{Lu}}^{-}$ ion.Reuse & Permissions

Figure 3

(Color online) Comparison of the electron elastic total cross sections for Hf, Lu, Yb, Ca, and Sr atoms near threshold. Note that Hf has the lowest electron affinity of the five atoms and the sharpest resonance.Reuse & Permissions