Elastic electron scattering by a Pb atom

Differential (DCS), integral $\left(Q_{\mathrm{I}}\right)$, momentum transfer $\left(Q_{\mathrm{M}}\right)$, and viscosity $\left(Q_{\mathrm{V}}\right)$ cross sections are obtained both experimentally and theoretically for elastic electron scattering by lead atoms in the energy range from $10\text{to}100\mathrm{eV}$. The experiment is performed using an electron spectrometer with crossed electron and atom-beam arrangement. The relative DCS measurements are placed on an absolute scale using measured elastic-to-inelastic intensity ratios and the absolute DCS of the $6p7s$ ${}^{3}P_1$ state [S. Milisavljević, M. S. Rabasović, D. Šević, V. Pejčev, D. M. Filipović, L. Sharma, R. Srivastava, A. D. Stauffer, and B. P. Marinković, Phys. Rev. A 76, 022714 (2007)] at a scattering angle of 10° for incident energies of 40, 60, 80, and $100\mathrm{eV}$ and at 30° for 10 and $20\mathrm{eV}$. Corresponding theoretical results are obtained from a relativistic approach based on solving the Dirac equation using Hartree-Fock and Dirac-Fock wave functions to calculate cross sections at all the energies measured. Comparisons between the present experiment and theory, as well as comparisons with other available results, have been made.

Figure 1

(Color online) Differential cross sections for the elastic electron scattering by lead atoms at (a) $10\mathrm{eV}$, (b) $20\mathrm{eV}$, and (c) $40\mathrm{eV}$ electron-impact energies. Filled circles with error bars denote the present experimental results. The solid line shows DCSs calculated using the HF wave function and the dashed line shows the results obtained using the DF wave function. The short dashed-dotted line denotes calculated DCS values from the results of Haberland and Fritsche [7] at $11\mathrm{eV}$ derived from scattering amplitudes for direct and spin-flip scattering as presented by Kaussen et al. [6]. The open squares represent the results obtained by Williams and Trajmar [4].

Figure 2

(Color online) As for Fig. 1 except for (a) $60\mathrm{eV}$, (b) $80\mathrm{eV}$, and (c) $100\mathrm{eV}$ electron-impact energies. The dashed-dotted-dotted and dashed-dotted lines show the CP and RP results by Kumar et al. [10]. The dotted lines denote the calculations by Werner [11]. In the inset, the present experimental DCSs are normalized at 50° to the present DF calculations. The short dashed line denotes results by Fink and Yates [14].

Figure 3

(Color online) (a) Integral, (b) momentum transfer, and (c) viscosity cross sections for elastic electron scattering by lead atoms. Experiment and theories are as for Fig. 2. Open triangles denote results by Werner [11] while stars represent results obtained by Fink and Yates [14].